# Center Publications

The faculty home pages have a more extensive list of publications

Random Walk Initialization for Training Very Deep Feedforward Networks.

Sussillo, D. and Abbott, L.F. (2015)

arXiv1412.6558

Training very deep networks is an important open problem in machine learning.
One of many difficulties is that the norm of the back-propagated error gradient can
grow or decay exponentially. Here we show that training very deep feed-forward
networks (FFNs) is not as difficult as previously thought. Unlike when backpropagation
is applied to a recurrent network, application to an FFN amounts to
multiplying the error gradient by a different random matrix at each layer. We show
that the successive application of correctly scaled random matrices to an initial
vector results in a random walk of the log of the norm of the resulting vectors,
and we compute the scaling that makes this walk unbiased. The variance of the
random walk grows only linearly with network depth and is inversely proportional
to the size of each layer. Practically, this implies a gradient whose log-norm scales
with the square root of the network depth and shows that the vanishing gradient
problem can be mitigated by increasing the width of the layers. Mathematical
analyses and experimental results using stochastic gradient descent to optimize
tasks related to the MNIST and TIMIT datasets are provided to support these
claims. Equations for the optimal matrix scaling are provided for the linear and
ReLU cases.

Sensory Transmitter Release Determines Weighted Connectivity with Synergist Motor Neurons.

Mendelsohn, A., Simon, C.M., Abbott, L.F., Mentis, G.Z. and Jessell, T.M. (2015)

Neuron87:111-23

The construction of spinal sensory-motor circuits involves
the selection of appropriate synaptic partners
and the allocation of precise synaptic input densities.
Many aspects of spinal sensory-motor selectivity
appear to be preserved when peripheral sensory
activation is blocked, which has led to a view that
sensory-motor circuits are assembled in an activityindependent
manner. Yet it remains unclear whether
activity-dependent refinement has a role in the
establishment of connections between sensory afferents
and those motor pools that have synergistic
biomechanical functions. We show here that genetically
abolishing central sensory-motor neurotransmission
leads to a selective enhancement in the
number and density of such ‘‘heteronymous’’ connections,
whereas other aspects of sensory-motor
connectivity are preserved. Spike-timing-dependent
synaptic refinement represents one possible mechanism
for the changes in connectivity observed after
activity blockade. Our findings therefore reveal that
sensory activity does have a limited and selective
role in the establishment of patterned monosynaptic
sensory-motor connections.

Strength in More Than Numbers (News and Views).

Sawtell, N. and Abbott, L.F. (2015)

Nature Neurosci18:614-616

Theory suggests that cerebellar granule cells combine sensory and motor signals originating from different sources. An unexpected logic governing how granule cells process different input sources may enhance computational power.

Abstract Context Representations in Primate Amygdala and Prefrontal Cortex.

A. Saez, M. Rigotti, S. Ostojic, S. Fusi, and C.D. Salzman (2015)

NeuronVolume 87, Issue 4, 869-881

Neurons in prefrontal cortex (PFC) encode rules, goals, and other abstract information thought to underlie cognitive, emotional, and behavioral flexibility. Here we show that the amygdala, a brain area traditionally thought to mediate emotions, also encodes abstract information that could underlie this flexibility. Monkeys performed a task in which stimulus-reinforcement contingencies varied between two sets of associations, each defining a context. Reinforcement prediction required identifying a stimulus and knowing the current context. Behavioral evidence indicated that monkeys utilized this information to perform inference and adjust their behavior. Neural representations in both amygdala and PFC reflected the linked sets of associations implicitly defining each context, a process requiring a level of abstraction characteristic of cognitive operations. Surprisingly, when errors were made, the context signal weakened substantially in the amygdala. These data emphasize the importance of maintaining abstract cognitive information in the amygdala to support flexible behavior.

Computational principles of biological memory.

Marcus Benna and Stefano Fusi (2015)

arXiv5:1507.07580

Memories are stored, retained, and recollected through complex, coupled processes operating on multiple timescales. To understand the computational principles behind these intricate networks of interactions we construct a broad class of synaptic models that efficiently harnesses biological complexity to preserve numerous memories. The memory capacity scales almost linearly with the number of synapses, which is a substantial improvement over the square root scaling of previous models. This was achieved by combining multiple dynamical processes that initially store memories in fast variables and then progressively transfer them to slower variables. Importantly, the interactions between fast and slow variables are bidirectional. The proposed models are robust to parameter perturbations and can explain several properties of biological memory, including delayed expression of synaptic modifications, metaplasticity, and spacing effects.

Energy-efficient neuromorphic classifiers.

Daniel Marti, Mattia Rigotti, Mingoo Seok, Stefano Fusi (2015)

arXiv5:1507.0023

Neuromorphic engineering combines the architectural and computational principles of systems neuroscience with semiconductor electronics, with the aim of building efficient and compact devices that mimic the synaptic and neural machinery of the brain. Neuromorphic engineering promises extremely low energy consumptions, comparable to those of the nervous system. However, until now the neuromorphic approach has been restricted to relatively simple circuits and specialized functions, rendering elusive a direct comparison of their energy consumption to that used by conventional von Neumann digital machines solving real-world tasks. Here we show that a recent technology developed by IBM can be leveraged to realize neuromorphic circuits that operate as classifiers of complex real-world stimuli. These circuits emulate enough neurons to compete with state-of-the-art classifiers. We also show that the energy consumption of the IBM chip is typically 2 or more orders of magnitude lower than that of conventional digital machines when implementing classifiers with comparable performance. Moreover, the spike-based dynamics display a trade-off between integration time and accuracy, which naturally translates into algorithms that can be flexibly deployed for either fast and approximate classifications, or more accurate classifications at the mere expense of longer running times and higher energy costs. This work finally proves that the neuromorphic approach can be efficiently used in real-world applications and it has significant advantages over conventional digital devices when energy consumption is considered.

Hippocampal-prefrontal input supports spatial encoding in working memory.

Timothy Spellman, Mattia Rigotti, Susanne E. Ahmari, Stefano Fusi, Joseph A. Gogos & Joshua A. Gordon (2015)

Nature522, 309-314

Spatial working memory, the caching of behaviourally relevant spatial cues on a timescale of seconds, is a fundamental constituent of cognition. Although the prefrontal cortex and hippocampus are known to contribute jointly to successful spatial working memory, the anatomical pathway and temporal window for the interaction of these structures critical to spatial working memory has not yet been established. Here we find that direct hippocampal-prefrontal afferents are critical for encoding, but not for maintenance or retrieval, of spatial cues in mice. These cues are represented by the activity of individual prefrontal units in a manner that is dependent on hippocampal input only during the cue-encoding phase of a spatial working memory task. Successful encoding of these cues appears to be mediated by gamma-frequency synchrony between the two structures. These findings indicate a critical role for the direct hippocampal-prefrontal afferent pathway in the continuous updating of task-related spatial information during spatial working memory.

The stabilized supralinear network: A unifying circuit motif underlying multi-input integration in sensory cortex.

Rubin, D.B., S.D. Van Hooser and K.D. Miller (2015)

Neuron85:402-417.

Neurons in sensory cortex integrate multiple influences to parse objects and support perception. Across multiple cortical areas, integration is characterized by two neuronal response properties: (1) surround suppression-modulatory contextual stimuli suppress responses to driving stimuli; and (2) "normalization"-responses to multiple driving stimuli add sublinearly. These depend on input strength: for weak driving stimuli, contextual influences facilitate or more weakly suppress and summation becomes linear or supralinear. Understanding the circuit operations underlying integration is critical to understanding cortical function and disease. We present a simple, general theory. A wealth of integrative properties, including the above, emerge robustly from four cortical circuit properties: (1) supralinear neuronal input/output functions; (2) sufficiently strong recurrent excitation; (3) feedback inhibition; and (4) simple spatial properties of intracortical connections. Integrative properties emerge dynamically as circuit properties, with excitatory and inhibitory neurons showing similar behaviors. In new recordings in visual cortex, we confirm key model predictions.

Neurons in cat V1 show significant clustering by degree of turning.

Ziskind, A.J., A.A. Emondi, A.V. Kurgansky, S.P. Rebrik and K.D. Miller (2015)

Journal of NeurophysiologyFeb 2015, DOI: 10.1152/jn.00646.2014

Neighboring neurons in cat primary visual cortex (V1) have similar preferred orientation, direction, and spatial frequency. How diverse is their degree of tuning for these properties? To address this, we used single-tetrode recordings to simultaneously isolate multiple cells at single recording sites and record their responses to flashed and drifting gratings of multiple orientations, spatial frequencies and, for drifting gratings, directions. Orientation tuning width, spatial frequency tuning width and direction selectivity index (DSI) all showed significant clustering: pairs of neuron recorded at a single site were significantly more similar in each of these properties than pairs of neurons from different recording sites. The strength of the clustering was generally modest. The percentage decrease in the median difference between pairs from the same site, relative to pairs from different sites, was: for different measures of orientation tuning width, 29-35% (drifting gratings) or 15-25% (flashed gratings); for DSI, 24%; and for spatial frequency tuning width measured in octaves, 8% (drifting gratings). The clusterings of all of these measures were much weaker than for preferred orientation (68% decrease), but comparable to that seen for preferred spatial frequency in response to drifting gratings (26%). For the above properties, little difference in clustering was seen between simple and complex cells. In studies of spatial frequency tuning to flashed gratings, strong clustering was seen among simple-cell pairs for tuning width (70% decrease) and preferred frequency (71% decrease), whereas no clustering was seen for simple/complex or complex/complex cell pairs.

Transition to Chaos in Random Networks with Cell-Type-Specific Connectivity.

Aljadeff, J., Stern, M., Sharpee, T. (2015)

Phys. Rev. Lett. 114, 088101.

In neural circuits, statistical connectivity rules strongly depend on cell-type identity. We study dynamics of neural networks with cell-type-specific connectivity by extending the dynamic mean-field method and find that these networks exhibit a phase transition between silent and chaotic activity. By analyzing the locus of this transition, we derive a new result in random matrix theory: the spectral radius of a random connectivity matrix with block-structured variances. We apply our results to show how a small group of hyperexcitable neurons within the network can significantly increase the network's computational capacity by bringing it into the chaotic regime.

Effects of long-term representations on free recall of unrelated words.

Katkov, M., Romani, S., & Tsodyks, M. (2015)

Learning & Memory 22(2), 101-108.

Human memory stores vast amounts of information. Yet recalling this information is often challenging when specific cues are lacking. Here we consider an associative model of retrieval where each recalled item triggers the recall of the next item based on the similarity between their long-term neuronal representations. The model predicts that different items stored in memory have different probability to be recalled depending on the size of their representation. Moreover, items with high recall probability tend to be recalled earlier and suppress other items. We performed an analysis of a large data set on free recall and found a highly specific pattern of statistical dependencies predicted by the model, in particular negative correlations between the number of words recalled and their average recall probability. Taken together, experimental and modeling results presented here reveal complex interactions between memory items during recall that severely constrain recall capacity.

Eigenvalues of block structured asymmetric random matrices.

Aljadeff,J., Renfrew, D., Stern, M. (2014)

arXiv

We study the spectrum of an asymmetric random matrix with block structured variances. The rows and columns of the random square matrix are divided into D partitions with arbitrary size (linear in N). The parameters of the model are the variances of elements in each block, summarized in g in RD×D+. Using the Hermitization approach and by studying the matrix-valued Stieltjes transform we show that these matrices have a circularly symmetric spectrum, we give an explicit formula for their spectral radius and a set of implicit equations for the full density function. We discuss applications of this model to neural networks.

Dynamics of Random Neural Networks with Bistable Units.

Stern, M., Sompolinsky, H. and Abbott, L.F. (2014)

Phys. Rev. E 062710.

We construct and analyze a rate-based neural network model in which self-interacting units represent clusters
of neurons with strong local connectivity and random interunit connections reflect long-range interactions.
When sufficiently strong, the self-interactions make the individual units bistable. Simulation results, mean-field
calculations, and stability analysis reveal the different dynamic regimes of this network and identify the locations
in parameter space of its phase transitions. We identify an interesting dynamical regime exhibiting transient but
long-lived chaotic activity that combines features of chaotic and multiple fixed-point attractors.

Theta sequences are essential for internally generated hippocampal firing fields.

Wang, Y., Romani, S., Lustig, B., Leonardo, A., & Pastalkova, E. (2014)

Nature Neuroscience18,282-288.

Sensory cue inputs and memory-related internal brain activities govern the firing of hippocampal neurons, but which specific firing patterns are induced by either of the two processes remains unclear. We found that sensory cues guided the firing of neurons in rats on a timescale of seconds and supported the formation of spatial firing fields. Independently of the sensory inputs, the memory-related network activity coordinated the firing of neurons not only on a second-long timescale, but also on a millisecond-long timescale, and was dependent on medial septum inputs. We propose a network mechanism that might coordinate this internally generated firing. Overall, we suggest that two independent mechanisms support the formation of spatial firing fields in hippocampus, but only the internally organized system supports short-timescale sequential firing and episodic memory.

The Neuronal Architecture of the Mushroom Body Provides a Logic for Associative Learning.

Aso, Y., Hattori, D., Yu, Y., Johnston, R.M., Iyer, N., Ngo, T.B., Dionne, H., Abbott, L.F., Axel, R., Tanimoto, H. and Rubin, G. (2014)

eLife 3:e04577.

We identified the neurons comprising the Drosophila mushroom body (MB), an
associative center in invertebrate brains, and provide a comprehensive map describing their
potential connections. Each of the 21 MB output neuron (MBON) types elaborates segregated
dendritic arbors along the parallel axons of ~2000 Kenyon cells, forming 15 compartments that
collectively tile the MB lobes. MBON axons project to five discrete neuropils outside of the MB and
three MBON types form a feedforward network in the lobes. Each of the 20 dopaminergic neuron
(DAN) types projects axons to one, or at most two, of the MBON compartments. Convergence of
DAN axons on compartmentalized Kenyon cell-MBON synapses creates a highly ordered unit
that can support learning to impose valence on sensory representations. The elucidation of the
complement of neurons of the MB provides a comprehensive anatomical substrate from which
one can infer a functional logic of associative olfactory learning and memory

Modeling the Dynamic Interaction of Hebbian and Homeostatic Plasticity.

Toyoizumi, T., Kaneko, M., Stryker, M. P., & Miller, K. D. (2014)

Neuron 84(2):497-510.

Hebbian and homeostatic plasticity together refine neural circuitry, but their interactions are unclear. In most existing models, each form of plasticity directly modifies synaptic strength. Equilibrium is reached when the two are inducing equal and opposite changes. We show that such models cannot reproduce ocular dominance plasticity (ODP) because negative feedback from the slow homeostatic plasticity observed in ODP cannot stabilize the positive feedback of fast Hebbian plasticity. We propose a model in which synaptic strength is the product of a synapse-specific Hebbian factor and a postsynaptic-cell-specific homeostatic factor, with each factor separately arriving at a stable inactive state. This model captures ODP dynamics and has plausible biophysical substrates. We confirm model predictions experimentally that plasticity is inactive at stable states and that synaptic strength overshoots during recovery from visual deprivation. These results highlight the importance of multiple regulatory pathways for interactions of plasticity mechanisms operating over separate timescales.

Word Length Effect in Free Recall of Randomly Assembled Word Lists.

Katkov M, Romani S and Tsodyks M. (2014)

Front. Comput. Neurosci. 8:129. doi: 10.3389/fncom.2014.00129

In serial recall experiments, human subjects are requested to retrieve a list of words in the same order as they were presented. In a classical study, participants were reported to recall more words from study lists composed of short words compared to lists of long words, the word length effect. The world length effect was also observed in free recall experiments, where subjects can retrieve the words in any order. Here we analyzed a large dataset from free recall experiments of unrelated words, where short and long words were randomly mixed, and found a seemingly opposite effect: long words are recalled better than the short ones. We show that our recently proposed mechanism of associative retrieval can explain both these observations. Moreover, the direction of the effect depends solely on the way study lists are composed.

The effects of short-term synaptic depression at thalamocortical synapses on orientation tuning in cat v1.

Cimenser A, Miller KD (2014)

PLoS One.

*9(8):e106046*
We examine the effects of short-term synaptic depression on the orientation tuning of the LGN input to simple cells in cat primary visual cortex (V1). The total LGN input has an untuned component as well as a tuned component, both of which grow with stimulus contrast. The untuned component is not visible in the firing rate responses of the simple cells. The suppression of the contribution of the untuned input component to firing rate responses is key to establishing orientation selectivity and its invariance with stimulus contrast. It has been argued that synaptic depression of LGN inputs could contribute to the selective suppression of the untuned component and thus contribute to the tuning observed in simple cells. We examine this using a model fit to the depression observed at thalamocortical synapses in-vivo, and compare this to an earlier model fit based on in-vitro observations. We examine the tuning of both the conductance and the firing rate induced in simple cells by the net LGN input. We find that depression causes minimal suppression of the untuned component. The primary effect of depression is to cause the contrast response curve to saturate at lower contrasts without differentially affecting the tuned vs. untuned components. This effect is slightly weaker for in-vivo vs. in-vitro parameters. Thus, synaptic depression of LGN inputs does not appreciably contribute to the orientation tuning of V1 simple cells.

Short-term plasticity based network model of place cells dynamics

Romani, S., & Tsodyks, M. (2014)

Hippocampus. DOI: 10.1002/hipo.22355

Rodent hippocampus exhibits strikingly different regimes of population activity in different behavioral states. During locomotion, hippocampal activity oscillates at theta frequency (5 to 12 Hz) and cells fire at specific locations in the environment, the place fields. As the animal runs through a place field, spikes are emitted at progressively earlier phases of the theta cycles. During immobility, hippocampus exhibits sharp irregular bursts of activity, with occasional rapid orderly activation of place cells expressing a possible trajectory of the animal. The mechanisms underlying this rich repertoire of dynamics are still unclear. We developed a novel recurrent network model that accounts for the observed phenomena. We assume that the network stores a map of the environment in its recurrent connections, which are endowed with short-term synaptic depression. We show that the network dynamics exhibits two different regimes that are similar to the experimentally observed population activity states in the hippocampus. The operating regime can be solely controlled by external inputs. Our results suggest that short-term synaptic plasticity is a potential mechanism contributing to shape the population activity in hippocampus.

Bayesian spike inference from calcium imaging data

Pnevmatikakis, E., Merel, J., Pakman, A. & Paninski, L. (2014)

Asilomar Conf. on Signals, Systems, and Computers.

We present efficient Bayesian methods for extracting neuronal spiking information from calcium imaging data. The goal of our methods is to sample from the posterior distribution of spike trains and model parameters (baseline concentration, spike amplitude etc) given noisy calcium imaging data. We present discrete time algorithms where we sample the existence of a spike at each time bin using Gibbs methods, as well as continuous time algorithms where we sample over the number of spikes and their locations at an arbitrary resolution using Metropolis-Hastings methods for point processes. We provide Rao-Blackwellized extensions that (i) marginalize over several model parameters and (ii) provide smooth estimates of the marginal spike posterior distribution in continuous time. Our methods serve as complements to standard point estimates and allow for quantification of uncertainty in estimating the underlying spike train and model parameters.

On quadrature methods for refractory point process likelihoods

Mena, G. & Paninski, L. (2014)

Neural Comp.

*in press*
Parametric models of the conditional intensity of a point process (e.g., generalized linear models) are popular in statistical neuroscience, as they allow us to characterize the variability in neural responses in terms of sjosh server timuli and spiking history. Parameter estimation in these models relies heavily on accurate evaluations of the log-likelihood and its derivatives. Classical approaches use
a discretized time version of the spiking process, and recent work has exploited the existence of a refractory period (during which the conditional intensity is zero following a spike) to obtain more accurate estimates of the likelihood. In this brief note we demonstrate that this method can be improved significantly by applying classical quadrature methods directly to the resulting continuous-time integral.

Analyzing neural data at huge scale

Cunningham JP (2014)

Nature Methods

*In press*
A new distributed computing framework for data analysis enables neuroscientists to meet the computational demands of modern experimental technologies.

Dimensionality reduction for large-scale neural recordings

Cunningham JP and Yu BM (2014)

Nature Neuroscience

*In press*
Most sensory, cognitive and motor functions depend on the interactions of many neurons. In recent years, there has been rapid development and increasing use of technologies for recording from large numbers of neurons, either sequentially or simultaneously. A key question is what scientific insight can be gained by studying a population of recorded neurons beyond studying each neuron individually. Here, we examine three important motivations for population studies: single-trial hypotheses requiring statistical power, hypotheses of population response structure and exploratory analyses of large data sets. Many recent studies have adopted dimensionality reduction to analyze these populations and to find features that are not apparent at the level of individual neurons. We describe the dimensionality reduction methods commonly applied to population activity and offer practical advice about selecting methods and interpreting their outputs. This review is intended for experimental and computational researchers who seek to understand the role dimensionality reduction has had and can have in systems neuroscience, and who seek to apply these methods to their own data.

Image interpolation and denoising for division of focal plane sensors using Gaussian Processes.

Gilboa E, Cunningham JP, Nehorai A, and Gruev V (2014)

Optics Express.

*22:15277-15291*
Image interpolation and denoising are important techniques in image processing. These methods are inherent to digital image acquisition as most digital cameras are composed of a 2D grid of heterogeneous imaging sensors. Current polarization imaging employ four different pixelated polarization filters, commonly referred to as division of focal plane polarization sensors. The sensors capture only partial information of the true scene, leading to a loss of spatial resolution as well as inaccuracy of the captured polarization information. Interpolation is a standard technique to recover the missing information and increase the accuracy of the captured polarization information. Here we focus specifically on Gaussian process regression as a way to perform a statistical image interpolation, where estimate
s of sensor noise are used to improve the accuracy of the estimated pixel information

Bayesian optimization with inequality constraints.

Gardner JR, Kusner MJ, Xu Z, Weinberger KQ, and Cunningham JP (2014)

ICML 2014: JMLR W+CP.

Bayesian optimization is a powerful frame-
work for minimizing expensive objective
functions while using very few function eval-
uations. It has been successfully applied to a
variety of problems, including hyperparam-
eter tuning and experimental design. How-
ever, this framework has not been extended
to the inequality-constrained optimization
setting, particularly the setting in which eval-
uating feasibility is just as expensive as eval-
uating the objective. Here we present con-
strained Bayesian optimization, which places
a prior distribution on both the objective and
the constraint functions. We evaluate our
method on simulated and real data, demon-
strating that constrained Bayesian optimiza-
tion can quickly find optimal and feasible
points, even when small feasible regions cause
standard methods to fail.

The spatiotemporal receptive fields of barrel cortex neurons revealed by reverse correlation of synaptic input

Ramirez, A., Pnevmatikakis, E., Merel, J., Miller, K., Paninski, L. & Bruno, R. (2014)

Nat. Neurosci.

*17(6)*: 866-75.
Of all of the sensory areas, barrel cortex is among the best understood in terms of circuitry, yet least understood in terms of sensory function. We combined intracellular recording in rats with a multi-directional, multi-whisker stimulator system to estimate receptive fields by reverse correlation of stimuli to synaptic inputs. Spatiotemporal receptive fields were identified orders of magnitude faster than by conventional spike-based approaches, even for neurons with little spiking activity. Given a suitable stimulus representation, a linear model captured the stimulus-response relationship for all neurons with high accuracy. In contrast with conventional single-whisker stimuli, complex stimuli revealed markedly sharpened receptive fields, largely as a result of adaptation. This phenomenon allowed the surround to facilitate rather than to suppress responses to the principal whisker. Optimized stimuli enhanced firing in layers 4-6, but not in layers 2/3, which remained sparsely active. Surround facilitation through adaptation may be required for discriminating complex shapes and textures during natural sensing.

Hierarchical Control Using Networks Trained with Higher-Level Forward Models

Wayne, G. and Abbott, L.F. (2014)

Neural Comp.

*26*: 2163-2193.
We propose and develop a hierarchical approach to network control of
complex tasks. In this approach, a low-level controller directs the activity of a plant, the system that performs the task. However, the low-level controller may be able to solve only fairly simple problems involving the plant. To accomplish more complex tasks, we introduce a higher-level controller that controls the lower-level controller. We use this system to direct an articulated truck to a specified location through an environment filled with static or moving obstacles. The final system consists of networks that have memorized associations between the sensory data they receive and the commands they issue. These networks are trained on a set of optimal associations generated by minimizing cost functions.Cost function minimization requires predicting the consequences of sequences of commands, which is achieved by constructing forward models, including a model of the lower-level controller. The forward models and cost minimization are used only during training, allowing the trained networks to respond rapidly. In general, the hierarchical approach can be extended to larger numbers of levels, dividing complex tasks into more manageable subtasks. The optimization procedure and the construction of the forward models and controllers can be performed in similar ways at each level of the hierarchy, which allows the system to be modified to perform other tasks or to be extended for more complex tasks without retraining lower-levels

A Computational Model of Motor Neuron Degeneration

Le Masson, G., Przedborski, S. and Abbott, L.F. (2014)

Neuron

*83*: 975-988.
To explore the link between bioenergetics and mo-
tor neuron degeneration, we used a computational
model in which detailed morphology and ion
conductance are paired with intracellular ATP pro-
duction and consumption. We found that reduced
ATP availability increases the metabolic cost of a
single action potential and disrupts K/Na
homeo-stasis, resulting in a chronic depolarization. The
magnitude of the ATP shortage at which this ionic
instability occurs depends on the morphology and
intrinsic conductance characteristic of the neuron.
If ATP shortage is confined to the distal part of the
axon, the ensuing local ionic instability eventually
spreads to the whole neuron and involves fascicula-
tion-like spiking events. A shortage of ATP also
causes a rise in intracellular calcium. Our modeling
work supports the notion that mitochondrial
dysfunction can account for salient features of the
paralytic disorder amyotrophic lateral sclerosis,
including motor neuron hyperexcitability, fascicula-
tion, and differential vulnerability of motor neuron
subpopulations.

Presynaptic inhibition of spinal sensory feedback ensures smooth movement.

Fink, A.J.P., Croce, K.R., Huang, Z.J., Abbott, L.F., Jessel, T.M., and Azim, E. (2014)

Nature

*509*: 43-48.
The precision of skilled movement depends on sensory feedback and its refinement by local inhibitory microcircuits. One specialized set of spinal GABAergic interneurons forms axoâ€“axonic contacts with the central terminals of sensory afferents, exerting presynaptic inhibitory control over sensoryâ€“motor transmission. The inability to achieve selective access to the GABAergic neurons responsible for this unorthodox inhibitory mechanism has left unresolved the contribution of presynaptic inhibition to motor behaviour. We used Gad2 as a genetic entry point to manipulate the interneurons that contact sensory terminals, and show that activation of these interneurons in mice elicits the defining physiological characteristics of presynaptic inhibition. Selective genetic ablation of Gad2-expressing interneurons severely perturbs goal-directed reaching movements, uncovering a pronounced and stereotypic forelimb motor oscillation, the core features of which are captured by modelling the consequences of sensory feedback at high gain. Our findings define the neural substrate of a genetically hardwired gain control system crucial for the smooth execution of movement.

Continuous attractor network model for conjunctive position-by-velocity tuning of grid cells.

Si, B., Romani S., and Tsodyks M. (2014)

PLoS Comput. Bio.

*10(4): e1003558*.
The spatial responses of many of the cells recorded in layer II of rodent medial
entorhinal cortex (MEC) show a triangular grid pattern, which appears to provide an
accurate population code for animal spatial position. In layer III, V and VI of the rat MEC,
grid cells are also selective to head-direction and are modulated by the speed of the
animal. Several putative mechanisms of grid-like maps were proposed, including
attractor network dynamics, interactions with theta oscillations or single-unit
mechanisms such as firing rate adaptation. In this paper, we present a new attractor
network model that accounts for the conjunctive position-by-velocity selectivity of grid
cells. Our network model is able to perform robust path integration even when the
recurrent connections are subject to random perturbations.

A temporal basis for predicting the sensory consequences of motor commands in an electric fish.

Kennedy, A., Wayne, G., Kaifosh, P., Alvina, K., Abbott, L.F., and Sawtell, N.B. (2014)

Nature Neurosci.

**17**: 415-424.
Mormyrid electric fish are a model system for understanding how neural circuits predict the sensory consequences of motor acts. Medium ganglion cells in the electrosensory lobe create negative images that predict sensory input resulting from the
fish's electric organ discharge (EOD). Previous studies have shown that negative images can be created through plasticity a
t granule cell-medium ganglion cell synapses, provided that granule cell responses to the brief EOD command are sufficientl
y varied and prolonged. Here we show that granule cells indeed provide such a temporal basis and that it is well-matched to
the temporal structure of self-generated sensory inputs, allowing rapid and accurate sensory cancellation and explaining p
aradoxical features of negative images. We also demonstrate an unexpected and critical role of unipolar brush cells (UBCs)
in generating the required delayed responses. These results provide a mechanistic account of how copies of motor commands
are transformed into sensory predictions.

Temporal responses of C. elegans chemosensory neurons are matched to behavior.

Kato, S., Xu, Y., Cho, C., Abbot, L.F., and Bargmann, C. (2014)

Neuron

**81**: 616-628.
Animals track fluctuating stimuli over multiple timescales during natural olfactory behaviors. Here, we define mechanisms underlying these computations in

*Caenorhabditis elegans*. By characterizing neuronal calcium responses to rapidly fluctuating odor sequences, we show that sensory neurons reliably track stimulus fluctuations relevant to behavior. AWC olfactory neurons respond to multiple odors with subsecond precision required for chemotaxis, whereas ASH nociceptive neurons integrate noxious cues over several seconds to reach a threshold for avoidance behavior. Each neuron's response to fluctuating stimuli is largely linear and can be described by a biphasic temporal filter and dynamical model. A calcium channel mutation alters temporal filtering and avoidance behaviors initiated by ASH on similar timescales. A sensory G-alpha protein mutation affects temporal filtering in AWC and alters steering behavior in a way that supports an active sensing model for chemotaxis. Thus, temporal features of sensory neurons can be propagated across circuits to specify behavioral dynamics.Properties of networks with partially structured and partially random connectivity

Ahmadian, Y., F. Fumarola and K.D. Miller (2013)

Physical Review E 91:012820

We provide a general formula for the eigenvalue density of large random N×N matrices of the form A=M+LJR, where M, L and R are arbitrary deterministic matrices and J is a random matrix of zero-mean independent and identically distributed elements. For A nonnormal, the eigenvalues do not suffice to specify the dynamics induced by A, so we also provide general formulae for the transient evolution of the magnitude of activity and frequency power spectrum in an N-dimensional linear dynamical system with a coupling matrix given by A. These quantities can also be thought of as characterizing the stability and the magnitude of the linear response of a nonlinear network to small perturbations about a fixed point. We derive these formulae and work them out analytically for some examples of M, L and R motivated by neurobiological models. We also argue that the persistence as N goes to infinity of a finite number of randomly distributed outlying eigenvalues outside the support of the eigenvalue density of A, as previously observed, arises in regions of the complex plane where there are nonzero singular values of L-1(z1-M)R-1 that vanish as N goes to infinity. When such singular values do not exist and L and R are equal to the identity, there is a correspondence in the normalized Frobenius norm (but not in the operator norm) between the support of the spectrum of A for J of norm sigma and the sigma-pseudospectrum of M.

Scaling multidimensional inference for structured Gaussian processes.

Gilboa, E., Saatci, Y., and Cunningham, J.P. (2013)

IEEE Trans Pattern Analysis and Machine Intelligence,

*in press*
Exact Gaussian process (GP) regression has O(N^3) runtime for data size N, making it intractable for large N. Many algorithms for improving GP scaling approximate the covariance with lower rank matrices. Other work has exploited structure inherent in particular covariance functions, including GPs with implied Markov structure, and inputs on a lattice (both enable O(N) or O(N log N) runtime). However, these GP advances have not been well extended to the multidimensional input setting, despite the preponderance of multidimensional applications. This paper introduces and tests three novel extensions of structured GPs to multidimensional inputs, for models with additive and multiplicative kernels. First we present a new method for inference in additive GPs, showing a novel connection between the classic backfitting method and the Bayesian framework. We extend this model using two advances: a variant of projection pursuit regression, and a Laplace approximation for non-Gaussian observations. Lastly, for multiplicative kernel structure, we present a novel method for GPs with inputs on a multidimensional grid. We illustrate the power of these three advances on several datasets, achieving performance equal to or very close to the naive GP at orders of magnitude less cost.

Bayesian inference and online experimental design for mapping neural microcircuits.

Shababo, B., Paige, B., Pakman, A., and Paninski, L. (2013)

NIPS,

*to appear*
With the advent of modern stimulation techniques in neuroscience, the opportunity
arises to map neuron to neuron connectivity. In this work, we develop
a method for efficiently inferring posterior distributions over synaptic strengths
in neural microcircuits. The input to our algorithm is data from experiments in
which action potentials from putative presynaptic neurons can be evoked while
a subthreshold recording is made from a single postsynaptic neuron. We present
a realistic statistical model which accounts for the main sources of variability in
this experiment and allows for significant prior information about the connectivity
and neuronal cell types to be incorporated if available. Due to the technical challenges
and sparsity of these systems, it is important to focus experimental time
stimulating the neurons whose synaptic strength is most ambiguous, therefore we
also develop an online optimal design algorithm for choosing which neurons to
stimulate at each trial.

Sparse nonnegative deconvolution for compressive calcium imaging: algorithms and phase transitions.

Pnevmatikakis, E., and Paninski, L. (2013)

NIPS,

*to appear*
We propose a compressed sensing (CS) calcium imaging framework for monitoring
large neuronal populations, where we image randomized projections of the spatial
calcium concentration at each timestep, instead of measuring the concentration at
individual locations. We develop scalable nonnegative deconvolution methods for
extracting the neuronal spike time series from such observations. We also address
the problem of demixing the spatial locations of the neurons using rank-penalized
matrix factorization methods. By exploiting the sparsity of neural spiking we
demonstrate that the number of measurements needed per timestep is significantly
smaller than the total number of neurons, a result that can potentially enable
imaging of larger populations at considerably faster rates compared to traditional
raster-scanning techniques. Unlike traditional CS setups, our problem involves a
block-diagonal sensing matrix and a non-orthogonal sparse basis that spans multiple
timesteps. We provide tight approximations to the number of measurements needed
for perfect deconvolution for certain classes of spiking processes, and show that
this number undergoes a "phase transition," which we characterize using modern
tools relating conic geometry to compressed sensing.

Robust learning of low-dimensional dynamics from large neural ensembles.

Pfau, D., Pnevmatikakis, E., and Paninski, L. (2013)

NIPS,

*to appear*
Recordings from large populations of neurons make it possible to search for hypothesized
low-dimensional dynamics. Finding these dynamics requires models
that take into account biophysical constraints and can be fit efficiently and robustly.
Here, we present an approach to dimensionality reduction for neural data
that is convex, does not make strong assumptions about dynamics, does not require
averaging over many trials and is extensible to more complex statistical models
that combine local and global influences. The results can be combined with spectral
methods to learn dynamical systems models. The basic method extends PCA
to the exponential family using nuclear norm minimization. We evaluate the effectiveness
of this method using an exact decomposition of the Bregman divergence
that is analogous to variance explained for PCA. We show on model data that
the parameters of latent linear dynamical systems can be recovered, and that even
if the dynamics are not stationary we can still recover the true latent subspace.
We also demonstrate an extension of nuclear norm minimization that can separate
sparse local connections from global latent dynamics. Finally, we demonstrate
improved prediction on real neural data from monkey motor cortex compared to
fitting linear dynamical models without nuclear norm smoothing.

Auxiliary-variable exact Hamiltonian Monte Carlo samplers for binary distributions.

Pakman, A., and Paninski, L. (2013)

NIPS,

*to appear*
We present a new approach to sample from generic binary distributions, based
on an exact Hamiltonian Monte Carlo algorithm applied to a piecewise continuous
augmentation of the binary distribution of interest. An extension of this idea to
distributions over mixtures of binary and possibly-truncated Gaussian or exponential
variables allows us to sample from posteriors of linear and probit regression
models with spike-and-slab priors and truncated parameters. We illustrate the advantages
of these algorithms in several examples in which they outperform the
Metropolis or Gibbs samplers.

A multi-agent control framework for co-adaptation in brain-computer interfaces.

Merel, J., Fox, R., Jebara, T., and Paninski, L. (2013)

NIPS,

*to appear*
In a closed-loop brain-computer interface (BCI), adaptive decoders are used to
learn parameters suited to decoding the user.s neural response. Feedback to the
user provides information which permits the neural tuning to also adapt. We
present an approach to model this process of co-adaptation between the encoding
model of the neural signal and the decoding algorithm as a multi-agent formulation
of the linear quadratic Gaussian (LQG) control problem. In simulation
we characterize how decoding performance improves as the neural encoding and
adaptive decoder optimize, qualitatively resembling experimentally demonstrated
closed-loop improvement. We then propose a novel, modified decoder update rule
which is aware of the fact that the encoder is also changing and show it can improve
simulated co-adaptation dynamics. Our modeling approach offers promise
for gaining insights into co-adaptation as well as improving user learning of BCI
control in practical settings.

Adult neurogenesis in the mammalian hippocampus: Why the dentate gyrus?

Drew, L.J., Fusi, S., and Hen, R. (2013)

Learn. Mem.

**20**: 710-729.
In the adult mammalian brain, newly generated neurons are continuously incorporated into two networks: interneurons born in the subventricular zone migrate to the olfactory bulb, whereas the dentate gyrus (DG) of the hippocampus integrates locally born principal neurons. That the rest of the mammalian brain loses significant neurogenic capacity after the perinatal period suggests that unique aspects of the structure and function of DG and olfactory bulb circuits allow them to benefit from the adult generation of neurons. In this review, we consider the distinctive features of the DG that may account for it being able to profit from this singular form of neural plasticity. Approaches to the problem of neurogenesis are grouped as "bottom-up," where the phenotype of adult-born granule cells is contrasted to that of mature developmentally born granule cells, and "top-down," where the impact of altering the amount of neurogenesis on behavior is examined. We end by considering the primary implications of these two approaches and future directions.

A complex-valued firing-rate model that approximates the dynamics of spiking networks.

Schaffer, E.S., Ostojic, S., and Abbott, L.F. (2013)

PLoS Comput. Biol.

**9**:e1003301.
Firing-rate models provide an attractive approach for studying large neural networks because they can be simulated rapidly
and are amenable to mathematical analysis. Traditional firing-rate models assume a simple form in which the dynamics are
governed by a single time constant. These models fail to replicate certain dynamic features of populations of spiking
neurons, especially those involving synchronization. We present a complex-valued firing-rate model derived from an
eigenfunction expansion of the Fokker-Planck equation and apply it to the linear, quadratic and exponential integrate-and-fire models. Despite being almost as simple as a traditional firing-rate description, this model can reproduce firing-rate
dynamics due to partial synchronization of the action potentials in a spiking model, and it successfully predicts the
transition to spike synchronization in networks of coupled excitatory and inhibitory neurons.

Random convergence of afferent olfactory inputs in the

*drosophila*mushroom body.Caron, S.J.C., Ruta, V., Abbott, L.F., and Axel, R. (2013)

Nature

**497**: 113-117.
The mushroom body in the fruitfly

*Drosophila melanogaster*is an associative brain centre that translates odour representationsinto learned behavioural responses. Kenyon cells, the intrinsic neurons of the mushroom body, integrate input from olfactory glomeruli to encode odours as sparse distributed patterns of neural activity. We have developed anatomic tracing techniques to identify the glomerular origin of the inputs that converge onto 200 individual Kenyon cells. Here we show that each Kenyon cell integrates input from a different and apparently random combination of glomeruli. The glomerular inputs to individual Kenyon cells show no discernible organization with respect to their odour tuning, anatomic features or developmental origins. Moreover, different classes of Kenyon cells do not seem to preferentially integrate inputs from specific combinations of glomeruli. This organization of glomerular connections to the mushroom body could allow the fly to contextualize novel sensory experiences, a feature consistent with the role of this brain centre in mediating learned olfactory associations and behaviours.A theory of the transition to critical period plasticity: Inhibition selectively suppresses spontaneous activity.

Toyoizumi, T., Miyamoto, H., Yazaki-Sugiyama, T., Atapour, N., Hensch, T.K., and Miller, K.D. (2013)

Neuron

**80**: 51-63.
What causes critical periods (CPs) to open? For the best-studied case, ocular dominance plasticity in primary visual cortex in response to monocular deprivation (MD), the maturation of inhibition is necessary and sufficient. How does inhibition open the CP? We present a theory: the transition from pre-CP to CP plasticity arises because inhibition preferentially suppresses responses to spontaneous relative to visually driven input activity, switching learning cues from internal to external sources. This differs from previous proposals in (1) arguing that the CP can open without changes in plasticity mechanisms when activity patterns become more sensitive to sensory experience through circuit development, and (2) explaining not simply a transition from no plasticity to plasticity, but a change in outcome of MD-induced plasticity from pre-CP to CP. More broadly, hierarchical organization of sensory-motor pathways may develop through a cascade of CPs induced as circuit maturation progresses from "lower" to "higher" cortical areas.

Analysis of the stabilized supralinear network.

Ahmadian, Y., Rubin, D.B., and Miller, K.D. (2013)

Neural Comput.

**25**: 1994-2037.
We study a rate-model neural network composed of excitatory and inhibitory neurons
in which neuronal input-output functions are power laws with a power greater than 1,
as observed in primary visual cortex. This supralinear input-output function leads to
supralinear summation of network responses to multiple inputs for weak inputs. We
show that for stronger inputs, which would drive the excitatory subnetwork to insta-
bility, the network will dynamically stabilize provided feedback inhibition is su^Nciently
strong. This dynamic stabilization yields a transition from supralinear to sublinear
summation of network responses to multiple inputs. We compare this to the dynamic
stabilization in the “balanced network”, which yields only linear behavior. We more
exhaustively analyze the 2-dimensional case of 1 excitatory and 1 inhibitory population.
We show that in this case dynamic stabilization will occur whenever the determinant of
the weight matrix is positive and the inhibitory time constant is su^Nciently small, and
analyze the conditions for “supersaturation”, or decrease of ^Lring rates with increasing
stimulus contrast (which represents increasing input ^Lring rates). In work to be pre-
sented elsewhere, we show that this transition from supralinear to sublinear summation
can explain a wide variety of nonlinearities in cerebral cortical processing

Dynamical regimes in neural network models of matching behavior.

Iigaya, K. and Fusi, S. (2013)

Neural Comput.

**25**: 1-20.
The matching law constitutes a quantitative description of choice behavior that is often observed in foraging tasks. According to the matching law, organisms distribute their behavior across available response alternatives in the same proportion that reinforcers are distributed across those alternatives. Recently a few biophysically plausible neural network models have been proposed to explain the matching behavior observed in the experiments. Here we study systematically the learning dynamics of these networks while performing a matching task on the concurrent variable interval (VI) schedule. We found that the model neural network can operate in one of three qualitatively different regimes depending on the parameters that characterize the synaptic dynamics and the reward schedule: (1) a matching behavior regime, in which the probability of choosing an option is roughly proportional to the baiting fractional probability of that option; (2) a perseverative regime, in which the network tends to make always the same decision; and (3) a tristable regime, in which the network can either perseverate or choose the two targets randomly approximately with the same probability. Different parameters of the synaptic dynamics lead to different types of deviations from the matching law, some of which have been observed experimentally. We show that the performance of the network depends on the number of stable states of each synapse and that bistable synapses perform close to optimal when the proper learning rate is chosen. Because our model provides a link between synaptic dynamics and qualitatively different behaviors, this work provides us with insight into the effects of neuromodulators on adaptive behaviors and psychiatric disorders.

Efficient Partitioning of Memory Systems and Its Importance for Memory Consolidation.

Roxin, A. and Fusi, S. (2013)

PLoS Comput. Biol.

**9(6)**: e1003146.
Long-term memories are likely stored in the synaptic weights of neuronal networks in the brain. The storage capacity of such networks depends on the degree of plasticity of their synapses. Highly plastic synapses allow for strong memories, but these are quickly overwritten. On the other hand, less labile synapses result in long-lasting but weak memories. Here we show that the trade-off between memory strength and memory lifetime can be overcome by partitioning the memory system into multiple regions characterized by different levels of synaptic plasticity and transferring memory information from the more to less plastic region. The improvement in memory lifetime is proportional to the number of memory regions, and the initial memory strength can be orders of magnitude larger than in a non-partitioned memory system. This model provides a fundamental computational reason for memory consolidation processes at the systems level.

The Importance of Mixed Selectivity in Complex Cognitive Tasks.

Rigotti, M. et al. (2013)

Nature, doi: 10.1038/nature12160

Single-neuron activity in the prefrontal cortex (PFC) is tuned to mixtures of multiple task-related aspects. Such mixed selectivity is highly heterogeneous, seemingly disordered and therefore difficult to interpret. We analysed the neural activity recorded in monkeys during an object sequence memory task to identify a role of mixed selectivity in subserving the cognitive functions ascribed to the PFC. We show that mixed selectivity neurons encode distributed information about all task-relevant aspects. Each aspect can be decoded from the population of neurons even when single-cell selectivity to that aspect is eliminated. Moreover, mixed selectivity offers a significant computational advantage over specialized responses in terms of the repertoire of input-output functions implementable by readout neurons. This advantage originates from the highly diverse nonlinear selectivity to mixtures of task-relevant variables, a signature of high-dimensional neural representations. Crucially, this dimensionality is predictive of animal behaviour as it collapses in error trials. Our findings recommend a shift of focus for future studies from neurons that have easily interpretable response tuning to the widely observed, but rarely analysed, mixed selectivity neurons.

Limber Neurons for a Nimble Mind.

Miller E.K., and Fusi, S. (2013)

Neuron Previews,

**78(2)**: 211-213.In this issue of Neuron, Stokes et al. (2013) demonstrate that cortical neurons that adapt their properties with task demands form patterns reflecting the shifting mental states needed to solve the task. Adaptive neurons may be critical to hallmarks of cognition: behavioral complexity and flexibility.

Scaling Laws of Associative Memory Retrieval.

Romani, S., Pinkoviezky, I., Rubin, A., and Tsodyks, M. (2013)

Neural Comput.,

**10**: 2523-2544.
Most people have great difficulty in recalling unrelated items. For example, in "free recall" experiments, lists of more than a few randomly selected words cannot be accurately repeated. Here we introduce a phenomenological model of memory retrieval inspired by theories of neuronal population coding of information. The model predicts nontrivial scaling behaviors for the mean and standard deviation of the number of recalled words for lists of increasing length. Our results suggest that associative information retrieval is a dominating factor that limits the number of recalled items.

Synaptic Encoding of Temporal Contiguity.

Ostojic, S., and Fusi, S. (2013)

Front. Comput. Neurosci., doi: 10.3389/fncom.2013.00032.

Often we need to perform tasks in an environment that changes stochastically. In these situations it is important to learn the statistics of sequences of events in order to predict the future and the outcome of our actions. The statistical description of many of these sequences can be reduced to the set of probabilities that a particular event follows another event (temporal contiguity). Under these conditions, it is important to encode and store in our memory these transition probabilities. Here we show that for a large class of synaptic plasticity models, the distribution of synaptic strengths encodes transitions probabilities. Specifically, when the synaptic dynamics depend on pairs of contiguous events and the synapses can remember multiple instances of the transitions, then the average synaptic weights are a monotonic function of the transition probabilities. The synaptic weights converge to the distribution encoding the probabilities also when the correlations between consecutive synaptic modifications are considered. We studied how this distribution depends on the number of synaptic states for a specific model of a multi-state synapse with hard bounds. In the case of bistable synapses, the average synaptic weights are a smooth function of the transition probabilities and the accuracy of the encoding depends on the learning rate. As the number of synaptic states increases, the average synaptic weights become a step function of the transition probabilities. We finally show that the information stored in the synaptic weights can be read out by a simple rate-based neural network. Our study shows that synapses encode transition probabilities under general assumptions and this indicates that temporal contiguity is likely to be encoded and harnessed in almost every neural circuit in the brain.

From Fixed Points to Chaos: Three Models of Delayed Discrimination.

Barak, O., Sussillo, D., Romo, R., Tsodyks, M., and Abbott, L.F. (2013)

Prog. in Neurobio.,

**103:**214-222.
Working memory is a crucial component of most cognitive tasks. Its neuronal mechanisms are still unclear despite intensive experimental and theoretical explorations. Most theoretical models of working memory assume both time-invariant neural representations and precise connectivity schemes based on the tuning properties of network neurons. A different, more recent class of models assumes randomly connected neurons that have no tuning to any particular task, and bases task performance purely on adjustment of network readout. Intermediate between these schemes are networks that start out random but are trained by a learning scheme. Experimental studies of a delayed vibrotactile discrimination task indicate that some of the neurons in prefrontal cortex are persistently tuned to the frequency of a remembered stimulus, but the majority exhibit more complex relationships to the stimulus that vary considerably across time.We compare three models, ranging from a highly organized line attractor model to a randomly connected network with chaotic activity, with data recorded during this task. The random network does a surprisingly good job of both performing the task and matchin certain aspects of the data. The intermediate model, in which an initially random network is partially trained to perform the working memory task by tuning its recurrent and readout connections, provides a better description, although none of the models matches all features of the data. Our results suggest that prefrontal networks may begin in a random state relative to the task and initially rely on modified readout for task performance. With further training, however, more tuned neurons with less time-varying responses should emerge as the networks become more structured.

The Sparseness of Mixed Selectivity Neurons Controls the Generalization-Discrimination Trade-Off.

Barak, O., Rigotti, M., and Fusi, S. (2013)

J. Neurosci.,

**33(9):**3844-3856.
Intelligent behavior requires integrating several sources of information in a meaningful fashion.be it context with stimulus or shape with color and size. This requires the underlying neural mechanism to respond in a different manner to similar inputs (discrimination), while maintaining a consistent response for noisy variations of the same input (generalization). We show that neurons that mix information sources via random connectivity can form an easy to read representation of input combinations. Using analytical and numerical tools, we show that the coding level or sparseness of these neurons. activity controls a trade-off between generalization and discrimination, with the optimal level depending on the task at hand. In all realistic situations that we analyzed, the optimal fraction of inputs to which a neuron responds is closeto 0.1. Finally, we predict a relation between a measurable property of the neural representation and task performance.

Optimal Properties of Analog Perceptrons with Excitatory Weights.

Clopath, C., and Brunel, N. (2013)

PLOS Comp. Biol.,

**9(2):**e1002919.
The cerebellum is a brain structure which has been traditionally devoted to supervised learning. According to this theory, plasticity at the Parallel Fiber (PF) to Purkinje Cell (PC) synapses is guided by the Climbing fibers (CF), which encode an error signal. Purkinje cells have thus been modeled as perceptrons, learning input/output binary associations. At maximal capacity, a perceptron with excitatory weights expresses a large fraction of zero-weight synapses, in agreement with experimental findings. However, numerous experiments indicate that the firing rate of Purkinje cells varies in an analog, not binary, manner. In this paper, we study the perceptron with analog inputs and outputs. We show that the optimal input has a sparse binary distribution, in good agreement with the burst firing of the Granule cells. In addition, we show that the weight distribution consists of a large fraction of silent synapses, as in previously studied binary perceptron models, and as seen experimentally.

Fast penalized state-space methods for inferring dendritiy synaptic connectivity.

Pakman, A., Huggins, J., Smith, C., and Paninski, L. (2013)

J. Comput. Neurosci.,

*in press*
We present fast methods for ltering voltage measurements and performing optimal inference
of the location and strength of synaptic connections in large dendritic trees. Given noisy, subsampled
voltage observations we develop fast l1-penalized regression methods for Kalman state-space
models of the neuron voltage dynamics. The value of the l1-penalty parameter is chosen using crossvalidation
or, for low signal-to-noise ratio, a Mallows' Cp-like criterion. Using low-rank approximations,
we reduce the inference runtime from cubic to linear in the number of dendritic compartments.
We also present an alternative, fully Bayesian approach to the inference problem using a spike-andslab
prior. We illustrate our results with simulations on toy and real neuronal geometries. We
consider observation schemes that either scan the dendritic geometry uniformly or measure linear
combinations of voltages across several locations with random coefficients. For the latter, we show
how to choose the coefficients to offset the correlation between successive measurements imposed by
the neuron dynamics. This results in a "compressed sensing" observation scheme, with an important
reduction in the number of measurements required to infer the synaptic weights.

Fast generalized linear model estimation via expected log-likelihoods.

Ramirez, A., and Paninski, L. (2013)

J. Comput. Neurosci.,

*in press*
Generalized linear models play an essential role in a wide variety of statistical applications. This
paper discusses an approximation of the likelihood in these models that can greatly facilitate computation.
The basic idea is to replace a sum that appears in the exact log-likelihood by an expectation
over the model covariates; the resulting "expected log-likelihood" can in many cases be computed signi
cantly faster than the exact log-likelihood. In many neuroscience experiments the distribution over
model covariates is controlled by the experimenter and the expected log-likelihood approximation becomes
particularly useful; for example, estimators based on maximizing this expected log-likelihood (or
a penalized version thereof) can often be obtained with orders of magnitude computational savings compared
to the exact maximum likelihood estimators. A risk analysis establishes that these maximum EL
estimators often come with little cost in accuracy (and in some cases even improved accuracy) compared
to standard maximum likelihood estimates. Finally, we nd that these methods can signicantly decrease
the computation time of marginal likelihood calculations for model selection and of Markov chain
Monte Carlo methods for sampling from the posterior parameter distribution. We illustrate our results
by applying these methods to a computationally-challenging dataset of neural spike trains obtained via
large-scale multi-electrode recordings in the primate retina.

Computing loss of efficiency in optimal Bayesian decoders given noisy or incomplete spike trains.

Smith, C., and Paninski, L. (2013)

Network: Comput. in Neural Systems,

*in press*
We investigate Bayesian methods for optimal decoding of noisy or incompletely-observed spike trains. Information about neural identity or temporal resolution may be lost during spike detection and sorting, or spike times measured near the soma may be corrupted with noise due to stochastic membrane channel effects in the axon. We focus on neural encoding models in which the (discrete) neural state evolves according to stimulus-dependent Markovian dynamics. Such models are sufficiently flexible that we may incorporate realistic stimulus encoding and spiking dynamics, but nonetheless permit exact computation via efficient hidden Markov model forward-backward methods. We analyze two types of signal degradation. First, we quantify the information lost due to jitter or downsampling in the spike-times. Second, we quantify the informaiton lost when knowledge of the identities of different spiking neurons is corrupted. In each case the methods introduced here make it possible to quantify the dependence of the information loss on biophysical parameters such as firing rate, spike jitter amplitude, spike observation noise, etc. In particular, decoders that model the probability distribution of spike-neuron assignments significantly outperform decoders that use only the most likely spike assignments, and are ignorant of the posterior spike assignment uncertainty.

The emergence of functional microcircuits in visual cortex.

Ko, H., Cossell, L., Baragli, C., Antolik, J., Clopath, C., Hofer, S.B., and Mrsic-Flogel, TD. (2013)

Nature,

**496**: 96-100.
Sensory processing occurs in neocortical microcircuits in which synaptic connectivity is highly structured and excitatory neurons form subnetworks that process related sensory information. However, the developmental mechanisms underlying the formation of functionally precise connectivity in cortical microcircuits remain unknown. Here we directly related patterns of excitatory synaptic connectivity to visual response properties of neighbouring layer 2/3 pyramidal neurons in mouse visual cortex at different postnatal ages, using two-photon calcium imaging in vivo and multiple patch-clamp recordings in vitro. Although neural responses were highly selective for visual stimuli already at eye opening, neurons responding to similar visual features were not yet preferentially connected, indicating that the emergence of feature selectivity does not depend on the precise arrangement of local synaptic connections. After eye opening, local connectivity reorganised extensively, as more connections formed selectively between neurons with similar visual responses, and connections were eliminated between visually unresponsive neurons, while the average number of connections did not change. We propose a unified model of cortical microcircuit development based on activity-dependent mechanisms of plasticity: neurons first acquire feature preference by selecting feedforward inputs before the onset of sensory experience . a process that may be facilitated by early electrical coupling between neuronal subsets . after which patterned input drives the formation of precise functional subnetworks through a balanced redistribution of recurrent synaptic connections.

Fast Kalman filtering and forward-backward smoothing via a low-rank perturbative approach.

Pnevmatikakis, E.A., Rahnama Rad, K., Huggins, J. and Paninski, L. (2013)

J. Comput. and Graph. Stats., doi: 10.1080/10618600.2012.760461

Kalman filtering-smoothing is a fundamental tool in statistical time series analysis.
However, standard implementations of the Kalman filter-smoother require O(d^3) time
and O(d^2) space per timestep, where d is the dimension of the state variable, and
are therefore impractical in high-dimensional problems. In this paper we note that
if a relatively small number of observations are available per time step, the Kalman
equations may be approximated in terms of a low-rank perturbation of the prior state
covariance matrix in the absence of any observations. In many cases this approximation
may be computed and updated very eciently (often in just O(k^2 d) or O(k^2 d+kdlogd)
time and space per timestep, where k is the rank of the perturbation and in general
k much less than d), using fast methods from numerical linear algebra. We justify our approach
and give bounds on the rank of the perturbation as a function of the desired accuracy.
For the case of smoothing we also quantify the error of our algorithm due to the
low rank approximation and show that it can be made arbitrarily low at the expense
of a moderate computational cost. We describe applications involving smoothing of
spatiotemporal neuroscience data.

Exact Hamiltonian Monte Carlo for Truncated Multivariate Gaussians.

Pakman, A. and Paninski, L. (2013)

J. Comput. and Graph. Stats., in press.

We present a Hamiltonian Monte Carlo algorithm to sample from
multivariate Gaussian distributions in which the target space is
constrained by linear and quadratic inequalities or products thereof.
The Hamiltonian equations of motion can be integrated exactly and
there are no parameters to tune. The algorithm mixes faster and is
more efficient than Gibbs sampling. The runtime depends on the number
and shape of the constraints but the algorithm is highly
parallelizable. In many cases, we can exploit special structure in the
covariance matrices of the untruncated Gaussian to further speed up
the runtime. A simple extension of the algorithm permits sampling from
distributions whose log-density is piecewise quadratic, as in the
"Bayesian Lasso" model.

Opening the black box: low-dimensional dynamics in high-dimensional recurrent neural networks.

Sussillo, D. and Barak, O. (2013)

Neural Comput.

**3:**626-49.
Recurrent neural networks (RNNs) are useful tools for learning nonlinear relationships between time-varying inputs and outputs with complex temporal dependencies. Recently developed algorithms have been successful at training RNNs to perform a wide variety of tasks, but the resulting networks have been treated as black boxes: their mechanism of operation remains unknown. Here we explore the hypothesis that fixed points, both stable and unstable, and the linearized dynamics around them, can reveal crucial aspects of how RNNs implement their computations. Further, we explore the utility of linearization in areas of phase space that are not true fixed points but merely points of very slow movement. We present a simple optimization technique that is applied to trained RNNs to find the fixed and slow points of their dynamics. Linearization around these slow regions can be used to explore, or reverse-engineer, the behavior of the RNN. We describe the technique, illustrate it using simple examples, and finally showcase it on three high-dimensional RNN examples: a 3-bit flip-flop device, an input-dependent sine wave generator, and a two-point moving average. In all cases, the mechanisms of trained networks could be inferred from the sets of fixed and slow points and the linearized dynamics around them.

Pairwise Analysis Can Account for Network Structures Arising from Spike-Timing Dependent Plasticity.

Babadi, B. and Abbott, L.F. (2013)

PLoS Comput. Biol.

**9:**e1002906.
Spike timing-dependent plasticity (STDP) modifies synaptic strengths based on timing information available locally at each synapse. Despite this, it induces global structures within a recurrently connected network. We study such structures both through simulations and by analyzing the effects of STDP on pair-wise interactions of neurons. We show how conventional STDP acts as a loop-eliminating mechanism and organizes neurons into in- and out-hubs. Loop-elimination increases when depression dominates and turns into loop-generation when potentiation dominates. STDP with a shifted temporal window such that coincident spikes cause depression enhances recurrent connections and functions as a strict buffering mechanism
that maintains a roughly constant average firing rate. STDP with the opposite temporal shift functions as a loop eliminator at low rates and as a potent loop generator at higher rates. In general, studying pairwise interactions of neurons provides important insights about the structures that STDP can produce in large networks.

Monte Carlo methods for localization of cones given multielectrode retinal ganglion cell recordings.

Sadeghi, K., Gauthier, J., Field, G., Greschner, M., Agne, M., Chichilnisky, E.J., and Paninski, L. (2013)

Network: Comput. in Neural Systems

**24:**27-51.
It has recently become possible to identify cone photoreceptors in primate retina from multi-electrode recordings of ganglion cell spiking driven by visual stimuli of sufficiently high spatial resolution. In this paper we present a statistical approach to the problem of identifying the number, locations, and color types of the cones observed in this type of experiment. We develop an adaptive Markov Chain Monte Carlo (MCMC) method that explores the space of cone configurations, using a Linear-Nonlinear-Poisson (LNP) encoding model of ganglion cell spiking output, while analytically integrating out the functional weights between cones and ganglion cells. This method provides information about our posterior certainty about the inferred cone properties, and additionally leads to improvements in both the speed and quality of the inferred cone maps, compared to earlier "greedy" computational approaches.

Efficient coding of spatial information in the primate retina.

Doi, E., Gauthier, J.L., Field, G.D., Shlens, J., She, A., Greschner, M., Machado, T.A., Jepson, L.H., Mathieson, K., Gunning, D.E., Litke, A.M., Paninski, L., Chichilnisky, E.J., and Simoncelli, E.P. (2012)

J. Neurosci.

**32**: 16256-16264.
Sensory neurons have been hypothesized to efficiently encode signals from the natural environment subject to resource constraints. The predictions of this efficient coding hypothesis regarding the spatial filtering properties of the visual system have been found consistent with human perception, but they have not been compared directly with neural responses. Here, we analyze the information that retinal ganglion cells transmit to the brain about the spatial information in natural images subject to three resource constraints: the number of retinal ganglion cells, their total response variances, and their total synaptic strengths. We derive a model that optimizes the transmitted information and compare it directly with measurements of complete functional connectivity between cone photoreceptors and the four major types of ganglion cells in the primate retina, obtained at single-cell resolution. We find that the ganglion cell population exhibited 80% efficiency in transmitting spatial information relative to the model. Both the retina and the model exhibited high redundancy (.30%) among ganglion cells of the same cell type. A novel and unique prediction of efficient coding, the relationships between projection patterns of individual cones to all ganglion cells, was consistent with the observed projection patterns in the retina. These results indicate a high level of efficiency with near-optimal redundancy in visual signaling by the retina.

Suppression of cortical neural variability is stimulus- and state-dependent.

White, B., Abbott, L. F., and Fiser, J. (2012)

J. Neurophysiol.

**108:**2383-2392.
Internally generated, spontaneous activity is ubiquitous in the cortex,
yet it does not appear to have a signi?cant negative impact on sensory
processing. Various studies have found that stimulus onset reduces the
variability of cortical responses, but the characteristics of this suppression
remained unexplored. By recording multiunit activity from
awake and anesthetized rats, we investigated whether and how this
noise suppression depends on properties of the stimulus and on the
state of the cortex. In agreement with theoretical predictions, we
found that the degree of noise suppression in awake rats has a
nonmonotonic dependence on the temporal frequency of a flickering
visual stimulus with an optimal frequency for noise suppression ~2
Hz. This effect cannot be explained by features of the power spectrum
of the spontaneous neural activity. The nonmonotonic frequency
dependence of the suppression of variability gradually disappears
under increasing levels of anesthesia and shifts to a monotonic pattern
of increasing suppression with decreasing frequency. Signal-to-noise
ratios show a similar, although inverted, dependence on cortical state
and frequency. These results suggest the existence of an active noise
suppression mechanism in the awake cortical system that is tuned to support
signal propagation and coding.

Two layers of neural variability (news and views).

Churchland, M. M. and Abbott, L. F. (2012)

Nature Neurosci.

**15:**1472-1474.
Variability in neuronal firing rates and spike timing can be modeled as doubly stochastic. A study now suggests that
these phenomena could arise from a network built of deterministic neurons with balanced excitation and inhibition.

Fast nonnegative spatiotemporal calcium smoothing in dendritic trees.

Pnevmatikakis, E., Kelleher, K., Chen, R., Josic, K., Saggau, P. & Paninski, L. (2012)

PLoS Comp. Bio.,

**8(6):**e1002569
We discuss methods for fast spatiotemporal smoothing of calcium signals in dendritic trees, given
spatially localized imaging data obtained via multi-photon microscopy. By analyzing the dynamics of
calcium binding to probe molecules and the e
ects of the imaging procedure, we show that calcium con-
centration can be estimated up to an ane transformation, i.e., an additive and multiplicative constant.
To obtain a full spatiotemporal estimate, we model calcium dynamics within the cell using a functional
approach. The evolution of calcium concentration is represented through a smaller set of hidden vari-
ables that incorporate fast transients due to backpropagating action potentials (bAPs), or other forms
of stimulation. Because of the resulting state space structure, inference can be done in linear time using
forward-backward maximum-a-posteriori methods. Non-negativity constraints on the calcium concentra-
tion can also be incorporated using a log-barrier method that does not a
ect the computational scaling.
Moreover, by exploiting the neuronal tree structure we show that the cost of the algorithm is also linear
in the size of the dendritic tree, making the approach applicable to arbitrarily large trees. We apply this
algorithm to data obtained from hippocampal CA1 pyramidal cells with experimentally evoked bAPs,
some of which were paired with excitatory postsynaptic potentials (EPSPs). The algorithm recovers
the timing of the bAPs and provides an estimate of the induced calcium transient throughout the tree.
The proposed methods could be used to further understand the interplay between bAPs and EPSPs in
synaptic strength modication. More generally, this approach allows us to infer the concentration on
intracellular calcium across the dendritic tree from noisy observations at a discrete set of points in space.

Robust particle filters via sequential pairwise reparameterized Gibbs sampling.

Paninski, L., Rahnama Rad, K. & Vidne, M. (2012)

CISS '12.

Sequential Monte Carlo (“particle filtering”) methods provide a powerful set of tools for recursive optimal Bayesian filtering in state-space models. However, these methods are based on importance sampling, which is known to be nonrobust in several key scenarios, and therefore standard particle fitering methods can fail in these settings. We present a filtering method which solves the key forward recursion using a reparameterized Gibbs sampling method, thus sidestepping the need for importance sampling. In many cases the resulting filter is much more robust and efficient than standard importance sampling particle filter implementations. We illustrate the method with an application to a nonlinear, non-Gaussian model from neuroscience.

Bayesian compressed sensing approach to reconstructing neural connectivity from subsampled anatomical data.

Mishchenko, Y. & Paninski, L. (2012)

J. Comput. Neuro.,

**33**: 371-388.
In recent years, the problem of reconstructing the connectivity in large neural circuits
("connectomics") has re-emerged as one of the main objectives of neuroscience. Classically, reconstructions of neural connectivity have been approached anatomically, using
electron or light microscopy and histological tracing methods. This paper describes a
statistical approach for connectivity reconstruction that relies on measurements of relatively easy-to-obtain ï¬‚uorescent probes such as synaptic markers, cytoplasmic dyes,
transsynaptic tracers, or activity-dependent dyes. We describe the possible design of these experiments and develop a Bayesian framework for extracting neural connectivity
from compilations of such data. We show that the statistical reconstruction problem can
be formulated naturally as a tractable L1-regularized quadratic optimization. As a concrete example, we consider a realistic hypothetical connectivity reconstruction experiment
in C. elegans, a popular neuroscience model where a complete wiring diagram has been
previously obtained based on long-term electron microscopy work. We show that the new
statistical approach could lead to an orders of magnitude reduction in experimental eï¬€ort
in reconstructing the connectivity in this circuit. We further demonstrate that the spatial heterogeneity and biological variability in the connectivity matrixâ€”not just the "average"
connectivityâ€”can also be estimated using the same method.

Mathematical Equivalence of Two Common Forms of Firing Rate Models of Neural Networks.

Fumarola, F. and Miller K.D. (2012)

Neural Computation

**24:**25-31
We demonstrate the mathematical equivalence of two commonly used
forms of ring rate model equations for neural networks. In addition, we
show that what is commonly interpreted as the ring rate in one form of
model may be better interpreted as a low-pass-ltered ring rate, and we
point out a conductance-based ring rate model.

Transferring Learning from External to Internal Weights in Echo-State Networks with Sparse Connectivity.

Sussillo, D. and Abbott, L.F. (2012)

PLoS One

**7:**e37372
Modifying weights within a recurrent network
to improve performance on a task has proven to be difficult. Echo-state networks in which
modification is restricted to the weights of connections onto network outputs provide an
easier alternative, but at the expense of modifying the typically sparse architecture of the
network by including feedback from the output back into the network. We derive methods for
using the values of the output weights from a trained echo-state network to set recurrent
weights within the network. The result of this “transfer of learning” is
a recurrent network that performs the task without requiring the output feedback present in
the original network. We also discuss a hybrid version in which online learning is applied
to both output and recurrent weights. Both approaches provide efficient ways of training
recurrent networks to perform complex tasks. Through an analysis of the conditions required
to make transfer of learning work, we define the concept of a “self-sensing”
network state, and we compare and contrast this with compressed sensing.

Fast interior-point inference in high-dimensional sparse, penalized state-space models.

Pnevmatikakis & Paninski, L. (2012)

AISTATS '12.

Low rank continuous-space graphical models.

Smith, C., Wood, F. & Paninski, L. (2012)

AISTATS '12.

A Computational Approach Enhances Learning in Aplysia (news and views)

Abbott, L.F. and Kandel, E.R. (2012)

Nature Neurosci.

**15:**178-179
A mathematical model based on the dynamics of molecular signaling pathways predicts an optimal training regimen that enhances learning and memory.

The impact of common noise on the activity of a large network of retinal ganglion cells.

Vidne, M. et al (2012)

J. Comput. Neuro., in press.

Inferring synaptic inputs given a noisy voltage trace.

Paninski, L., Vidne, M., DePasquale, B., & Ferreira, D. (2012)

J. Comput. Neuro., in press.

We discuss methods for optimally inferring the synaptic inputs to an electrotonically
compact neuron, given intracellular voltage-clamp or current-clamp recordings from the
postsynaptic cell. These methods are based on sequential Monte Carlo techniques (“par-
ticle ltering”). We demonstrate, on model data, that these methods can recover the
time course of excitatory and inhibitory synaptic inputs accurately on a single trial. De-
pending on the observation noise level, no averaging over multiple trials may be required.
However, excitatory inputs are consistently inferred more accurately than inhibitory in-
puts at physiological resting potentials, due to the stronger driving force associated with
excitatory conductances. Once these synaptic input time courses are recovered, it be-
comes possible to t (via tractable convex optimization techniques) models describing the
relationship between the sensory stimulus and the observed synaptic input. We develop
both parametric and nonparametric expectation-maximization (EM) algorithms that con-
sist of alternating iterations between these synaptic recovery and model estimation steps.
We employ a fast, robust convex optimization-based method to e
ectively initialize the
lter; these fast methods may be of independent interest. The proposed methods could
be applied to better understand the balance between excitation and inhibition in sensory
processing in vivo.

Optimal experimental design for sampling voltage on dendritic trees.

Huggins, J. & Paninski, L. (2012)

J Comput. Neuro., in press.

Due to the limitations of current voltage sensing techniques, optimal ltering of noisy, undersampled voltage signals on dendritic trees is a key problem in computational cellular neuroscience. These
limitations lead to voltage data that is incomplete (in the sense of only capturing a small portion of the
full spatiotemporal signal) and often highly noisy. In this paper we use a Kalman ltering framework
to develop optimal experimental design methods for voltage sampling. Our approach is to use a simple
greedy algorithm with lazy evaluation to minimize the expected square error of the estimated spatiotemporal voltage signal. We take advantage of some particular features of the dendritic ltering problem to
eciently calculate the Kalman estimators covariance. We test our framework with simulations of real
dendritic branching structures and compare the quality of both time-invariant and time-varying sampling
schemes. While the benet of using the experimental design methods was modest in the time-invariant
case, improvements of 25-100% over more na¨ve methods were found when the observation locations were
allowed to change with time. We also present a heuristic approximation to the greedy algorithm that is
an order of magnitude faster while still providing comparable results.

A simple derivation of a bound on the Perceptron margin using Singular Value Decomposition.

Barak, O, Rigotti, M. (2011)

Neural Computation.

**23(10):**1935-1943.The perceptron is a simple supervised algorithm to train a linear classier
that has been analyzed and used extensively. The classier separates the
data into two groups using a decision hyperplane, with the margin between the data and the hyperplane determining the classiers ability to
generalize and its robustness to input noise. Exact results for the maximal
size of the separating margin are known for specic input distributions,
and bounds exist for arbitrary distributions, but both rely on lengthy
statistical mechanics calculations carried out in the limit of innite input
size. Here we present a short analysis of perceptron classication using
singular value decomposition. We provide a simple derivation of a lower
bound on the margin and an explicit formula for the perceptron weights
that converges to the optimal result for large separating margins.

EMG prediction from motor cortical recordings via a non-negative point process filter.

Nazarpour, K., Ethier, C., Paninski, L., Rebesco, J., Miall, C., & Miller, L. (2011)

IEEE Transactions on Biomedical Engineering, in press.

A constrained point process ltering mechanism
for prediction of electromyogram (EMG) signals from multichannel neural spike recordings is proposed here. Filters from the
Kalman family are inherently sub-optimal in dealing with nonGaussian observations, or a state evolution that deviates from the
Gaussianity assumption. To address these limitations, we modeled
the non-Gaussian neural spike train observations by using a
generalized linear model (GLM) that encapsulates covariates of
neural activity, including the neurons own spiking history, concurrent ensemble activity, and extrinsic covariates (EMG signals).
In order to predict the envelopes of EMGs, we reformulated the
Kalman lter (KF) in an optimization framework and utilized a
non-negativity constraint. This structure characterizes the nonlinear correspondence between neural activity and EMG signals
reasonably. The EMGs were recorded from twelve forearm and
hand muscles of a behaving monkey during a grip-force task.
For the case of limited training data, the constrained point
process lter improved the prediction accuracy when compared
to a conventional Wiener cascade lter (a linear causal lter
followed by a static non-linearity) for dierent bin sizes and
delays between input spikes and EMG output. For longer training
data sets, results of the proposed lter and that of the Wiener
cascade lter were comparable.

Information rates and optimal decoding in large neural populations.

Rahnama Rad, K. & Paninski, L. (2011)

NIPS

Many fundamental questions in theoretical neuroscience involve optimal decoding and the computation of Shannon information rates in populations of spiking
neurons. In this paper, we apply methods from the asymptotic theory of statistical
inference to obtain a clearer analytical understanding of these quantities. We nd
that for large neural populations carrying a nite total amount of information, the
full spiking population response is asymptotically as informative as a single observation from a Gaussian process whose mean and covariance can be characterized
explicitly in terms of network and single neuron properties. The Gaussian form
of this asymptotic sufcient statistic allows us in certain cases to perform optimal
Bayesian decoding by simple linear transformations, and to obtain closed-form
expressions of the Shannon information carried by the network. One technical
advantage of the theory is that it may be applied easily even to non-Poisson point
process network models; for example, we nd that under some conditions, neural
populations with strong history-dependent (non-Poisson) effects carry exactly the
same information as do simpler equivalent populations of non-interacting Poisson
neurons with matched ring rates. We argue that our ndings help to clarify some
results from the recent literature on neural decoding and neuroprosthetic design.

Learning unbelievable marginal probabilities.

Pitkow, X., Ahmadian Y. and Miller K.D. (2011)

Advances in Neural Information Processing Systems

**24**
Loopy belief propagation performs approximate inference on graphical models
with loops. One might hope to compensate for the approximation by adjusting
model parameters. Learning algorithms for this purpose have been explored previously,
and the claim has been made that every set of locally consistent marginals
can arise from belief propagation run on a graphical model. On the contrary, here
we show that many probability distributions have marginals that cannot be reached
by belief propagation using any set of model parameters or any learning algorithm.
We call such marginals unbelievable. This problem occurs whenever the Hessian
of the Bethe free energy is not positive-denite at the target marginals. All learning
algorithms for belief propagation necessarily fail in these cases, producing
beliefs or sets of beliefs that may even be worse than the pre-learning approximation.
We then show that averaging inaccurate beliefs, each obtained from belief
propagation using model parameters perturbed about some learned mean values,
can achieve the unbelievable marginals

Efficient methods for sampling spike trains in networks of coupled neurons.

Mishchenko, Y. & Paninski, L. (2011)

Annals of Applied Statistics

**5:**1893-1919.Monte Carlo approaches have recently been proposed to quantify connectivity in neuronal networks. The key problem is to sample from the conditional distribution of a single
neuronal spike train, given the activity of the other neurons in the network. Dependencies between neurons are usually relatively weak; however, temporal dependencies within
the spike train of a single neuron are typically strong. In this paper we develop several
specialized Metropolis-Hastings samplers which take advantage of this dependency structure. These samplers are based on two ideas: 1) an adaptation of fast forward-backward
algorithms from the theory of hidden Markov models to take advantage of the local dependencies inherent in spike trains, and 2) a rst-order expansion of the conditional likelihood
which allows for ecient exact sampling in the limit of weak coupling between neurons.
We also demonstrate that these samplers can eectively incorporate side information,
in particular noisy uorescence observations in the context of calcium-sensitive imaging
experiments. We quantify the eciency of these samplers in a variety of simulated experiments in which the network parameters are closely matched to data measured in real
cortical networks, and also demonstrate the sampler applied to real calcium imaging data

Designing optimal stimuli to control neuronal spike timing.

Ahmadian, Y., Packer, A., Yuste, R. & Paninski, L. (2011)

J. Neurophys.

**106:**1038-1053.
Recent advances in experimental stimulation methods have raised the following important
computational question: how can we choose a stimulus that will drive a neuron to output
a target spike train with optimal precision, given physiological constraints? Here we adopt
an approach based on models which describe how a stimulating agent (such as an injected
electrical current, or a laser light interacting with caged neurotransmitters or photosensitive
ion channels) a
ect the spiking activity of neurons. Based on these models, we solve the
reverse problem of nding the best time-dependent modulation of the input, subject to
hardware limitations as well as physiologically inspired safety measures, that causes the
neuron to emit a spike train which with highest probability will be close to a target spike
train. We adopt fast convex constrained optimization methods to solve this problem. Our
methods can potentially be implemented in real time and may also be generalized to the
case of many cells, suitable for neural prosthesis applications. Using biologically sensible
parameters and constraints, our method nds stimulation patterns that generate very precise
spike trains in simulated experiments. We also tested the intracellular current injection
method on pyramidal cells in mouse cortical slices, quantifying the dependence of spiking
reliability and timing precision on constraints imposed on the applied currents.

Beyond the Edge of Chaos: Amplification and Temporal Integration by Recurrent Networks in the Chaotic Regime.

Toyoizumi, T. and Abbott, L.F. (2011)

Phys. Rev E

**84:**051908.
Randomly connected networks of neurons exhibit a transition from fixed-point to chaotic activity as the variance of their synaptic connection strengths is increased. In this study, we analytically evaluate how well a small external input can be reconstructed from a sparse linear readout of network activity. At the transition point, known as the edge of chaos, networks display a number of desirable features, including large gains and integration times. Away from this edge, in the nonchaotic regime that has been the focus of most models and studies, gains and integration times fall off dramatically, which implies that parameters must be fine tuned with considerable precision if high performance is required. Here we show that, near the edge, decoding performance is characterized by a critical exponent that takes a different value on the two sides. As a result, when the network units have an odd saturating nonlinear response function, the falloff in gains and integration times is much slower
on the chaotic side of the transition. This means that, under appropriate conditions, good performance can be achieved with less fine tuning beyond the edge, within the chaotic regime.

Temporal precision in the visual pathway through the interplay of excitation and stimulus-driven suppression.

Butts, D., Weng, C., Jin, J. Alonso, J.-M. & Paninski, L. (2011)

J. Neurosci.

**31:**11313-11327.Hidden Markov models for the inference of neural states and improved estimation of linear receptive fields.

Escola, S., Fontanini, A., Katz, D. & Paninski, L. (2011)

Neural Computation

**23:**1071:1132.
Given recent experimental results suggesting that neural circuits may evolve through
multiple ring states, we develop a framework for estimating state-dependent neural re-
sponse properties from spike-train data. We modify the traditional hidden Markov model
(HMM) framework to incorporate stimulus-driven, non-Poisson point process observa-
tions. For maximal
exibility, we allow external, time-varying stimuli and the neurons'
own spike histories to drive both the spiking behavior in each state and the transitioning
behavior between states. We employ an appropriately modied expectation-maximization
algorithm to estimate the model parameters. The expectation step is solved by the stan-
dard forward-backward algorithm for HMMs. The maximization step reduces to a set of
separable concave optimization problems if the model is restricted slightly. We rst test
our algorithm on simulated data and are able both to fully recover the parameters used
to generate the data and to accurately recapitulate the sequence of hidden states. We
then apply our algorithm to a recently published data set in which the observed neuronal
ensembles displayed multi-state behavior and show that inclusion of spike-history infor-
mation signicantly improves the t of the model. Additionally, we show that a simple
reformulation of the state-space of the underlying Markov chain allows us to implement a
hybrid half-multistate/half-histogram model which may be more appropriate for captur-
ing the complexity of certain data sets than either a simple HMM or a simple peri-stimulus
time histogram (PSTH) model alone.

Kalman filter mixture model for spike sorting of non-stationary data.

Calabrese, A. & Paninski, L. (2011)

J. Neurosci. Methods

**196:**159-169.
Nonstationarity in extracellular recordings can present a major problem during in vivo
experiments. In this paper we present automatic methods for tracking time-varying spike
shapes. Our algorithm is based on a computationally ecient Kalman lter model; the
recursive nature of this model allows for on-line implementation of the method. The model
parameters can be estimated using a standard expectation-maximization approach. In
addition, refractory e
ects may be incorporated via closely-related hidden Markov model
techniques. We present an analysis of the algorithm's performance on both simulated and
real data.

A penalized GLM approach for estimating spectrotemporal receptive fields from responses to natural sounds.

Calabrese, A., Schumacher, J., Schneider, D., Woolley, S. & Paninski, L. (2011)

PLoS One

**6(1):**e16104.In the auditory system, the stimulus-response properties of single neurons are often described in
terms of the spectrotemporal receptive field (STRF), a linear kernel relating the spectrogram of
the sound stimulus to the instantaneous firing rate of the neuron. Several algorithms have been
used to estimate STRFs from responses to natural stimuli; these algorithms differ in their
functional models, cost functions, and regularization methods. Here, we characterize the
stimulus-response function of auditory neurons using a generalized linear model (GLM). In this
model, each cells input is described by: 1) a stimulus filter (STRF); and 2) a post-spike filter,
which captures dependencies on the neurons spiking history. The output of the model is given by
a series of spike trains rather than instantaneous firing rate, allowing the prediction of spike train
responses to novel stimuli. We fit the model by maximum penalized likelihood to the spiking
activity of zebra finch auditory midbrain neurons in response to conspecific vocalizations (songs)
and modulation limited (ml) noise. We compare this model to normalized reverse correlation
(NRC), the traditional method for STRF estimation, in terms of predictive power and the basic
tuning properties of the estimated STRFs. We find that a GLM with a sparse prior predicts novel
responses to both stimulus classes significantly better than NRC. Importantly, we find that STRFs
from the two models derived from the same responses can differ substantially and that GLM
STRFs are more consistent between stimulus classes than NRC STRFs. These results suggest
that a GLM with a sparse prior provides a more accurate characterization of spectrotemporal
tuning than does the NRC method when responses to complex sounds are studied in these
neurons.

Canny Minds and Uncanny Questions.

Wayne, G. and Pasternack, A. (2011)

Science

**333(6047):**1223-1224.Incorporating naturalistic correlation structure improves spectrogram reconstruction from neuronal activity in the songbird auditory midbrain.

Ramirez, A.D., Ahmadian, Y., Schumacher, J., Schneider, D., Woolley, S.M., and Paninski, L. (2011)

J. Neurosci.

**31(10):**3828-3842.
Birdsong is comprised of rich spectral and temporal organization, which might be used for vocal perception. To quantify how this structure could be used, we have reconstructed birdsong spectrograms by combining the spike trains of zebra finch auditory midbrain neurons with information about the correlations present in song. We calculated maximum a posteriori estimates of song spectrograms using a generalized linear model of neuronal responses and a series of prior distributions, each carrying different amounts of statistical information about zebra finch song. We found that spike trains from a population of mesencephalicus lateral dorsalis (MLd) neurons combined with an uncorrelated Gaussian prior can estimate the amplitude envelope of song spectrograms. The same set of responses can be combined with Gaussian priors that have correlations matched to those found across multiple zebra finch songs to yield song spectrograms similar to those presented to the animal. The fidelity of spectrogram reconstructions from MLd responses relies more heavily on prior knowledge of spectral correlations than temporal correlations. However, the best reconstructions combine MLd responses with both spectral and temporal correlations.

Interspike interval distributions of spiking neurons driven by fluctuating inputs.

Ostojic, S. (2011)

J. Neurophysiol.

**106:**361-373.
Interspike interval (ISI) distributions of cortical neurons exhibit a range of different shapes. Wide ISI distributions are believed to stem from a balance of excitatory and inhibitory inputs that leads to a strongly fluctuating total drive. An important question is whether the full range of experimentally observed ISI distributions can be reproduced by modulating this balance. To address this issue, we investigate the shape of the ISI distributions of spiking neuron models receiving fluctuating inputs. Using analytical tools to describe the ISI distribu- tion of a leaky integrate-and-fire (LIF) neuron, we identify three key features: 1) the ISI distribution displays an exponential decay at long ISIs independently of the strength of the fluctuating input; 2) as the amplitude of the input fluctuations is increased, the ISI distribution evolves progressively between three types, a narrow distribution (suprathreshold input), an exponential with an effective refractory period (subthreshold but suprareset input), and a bursting exponential (subreset input); 3) the shape of the ISI distribution is approximately independent of the mean ISI and determined only by the coefficient of variation. Numerical simulations show that these features are not specific to the LIF model but are also present in the ISI distributions of the exponential integrate-and-fire model and a Hodgkin-Huxley- like model. Moreover, we observe that for a fixed mean and coeffi- cient of variation of ISIs, the full ISI distributions of the three models are nearly identical. We conclude that the ISI distributions of spiking neurons in the presence of fluctuating inputs are well described by gamma distributions.

Modular Realignment of Entorhinal Grid Cell Activity as a Basis for Hippocampal Remapping.

Monaco, J.D. and Abbott, L.F. (2011)

J. Neurosci.

**31:**9414-9425.
Hippocampal place fields, the local regions of activity recorded from place cells in exploring rodents, can undergo large changes in relative location during remapping. This process would appear to require some form of modulated global input. Grid-cell responses recorded
from layer II of medial entorhinal cortex in rats have been observed to realign concurrently with hippocampal remapping, making them a candidate input source. However, this realignment occurs coherently across colocalized ensembles of grid cells (Fyhn et al., 2007). The
hypothesized entorhinal contribution to remapping depends on whether this coherence extends to all grid cells, which is currently unknown. We study whether dividing grid cells into small numbers of independently realigning modules can both account for this
localized coherence and allow for hippocampal remapping. To do this, we construct a model in which place-cell responses arise from network competition mediated by global inhibition. We show that these simulated responses approximate the sparsity and spatial
specificity of hippocampal activity while fully representing a virtual environment without learning. Place-field locations and the set of active place cells in one environment can be independently rearranged by changes to the underlying grid-cell inputs. We introduce new
measures of remapping to assess the effectiveness of grid-cell modularity and to compare shift realignments with other geometric transformations of grid-cell responses. Complete hippocampal remapping is possible with a small number of shifting grid modules,
indicating that entorhinal realignment may be able to generate place-field randomization despite substantial coherence.

From Spiking Neuron Models to Linear-Nonlinear Models.

Ostojic, S. and Brunel, N. (2011)

PLoS Comput. Biol.

**7(1):**e1001056.
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping
from current input to output firing rate is often represented with the help of phenomenological models such as the linearnonlinear
(LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal
filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential
generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron
models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-andfire
(LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsaki models in presence of background
synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static
non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static nonlinearity
determined using standard reverse correlation analysis. We then quantitatively compare the output of the
corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the
parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing
rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsaki models, we show that the LN cascade
can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive
timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to
highly accurate estimates of instantaneous firing rates.

Interactions Between Intrinsic and Stimulus-Dependent Activity in Recurrent Neural Networks.

Abbott, L.F., Rajan, K. and Sompolinksy, H. (2011)

In M. Ding and D. Glanzman, eds.

**The Dynamic Brain: An Exploration of Neuronal Variability and Its Functional Significance.**(Oxford University Press, New York, NY) pp. 65-82.Functional connectivity in the retina at the resolution of photoreceptors.

Field, G., Gauthier, J., Sher, A. et al. (2010)

Nature,

**467:**673-677.
To understand a neural circuit requires knowledge of its connectivity. Here we report measurements of functional connectivity between the input and ouput layers of the macaque retina at single-cell resolution and the implications of these for colour vision. Multi-electrode technology was used to record simultaneously from complete populations of the retinal ganglion cell types (midget, parasol and small bistratified) that transmit high-resolution visual signals to the brain. Fine-grained visual stimulation was used to identify the location, type and strength of the functional input of each cone photoreceptor to each ganglion cell. The populations of ON and OFF midget and parasol cells each sampled the complete population of long- and middle-wavelength-sensitive cones. However, only OFF midget cells frequently received strong input from short-wavelength-sensitive cones. ON and OFF midget cells showed a small non-random tendency to selectively sample from either long- or middle-wavelength-sensitive cones to a degree not explained by clumping in the cone mosaic. These measurements reveal computations in a neural circuit at the elementary resolution of individual neurons.

Efficient estimation of two-dimensional firing rate surfaces via Gaussian process methods

Rahnama Rad, K. & Paninski, L. (2010)

Network: Computation in Neural Systems

**21:**142-68.
Estimating two-dimensional ring rate maps is a common problem, arising in a number of contexts: the estimation of place elds in hippocampus, the analysis of temporally
nonstationary tuning curves in sensory and motor areas, the estimation of ring rates
following spike-triggered covariance analyses, etc. Here we introduce methods based on
Gaussian process nonparametric Bayesian techniques for estimating these two-dimensional
rate maps. These techniques oer a number of advantages: the estimates may be computed eciently,
come equipped with natural errorbars, adapt their smoothness automatically to the local density and informativeness of the observed data, and permit direct
tting of the model hyperparameters (e.g., the prior smoothness of the rate map) via
maximum marginal likelihood. We illustrate the exibility and performance of the new
techniques on a variety of simulated and real data.

Inferring Stimulus Selectivity from the Spatial Structure of Neural Network Dynamics.

Rajan, K., Abbott, L.F., and Sompolinsky, H. (2010)

Lafferty, J., Williams, C.K.I., Shawe-Taylor, J., Zemel, R.S. and Culotta, A. eds.

**Advances in Neural Information Processing Systems**23.
How are the spatial patterns of spontaneous and evoked population responses re-lated? We study the impact of connectivity on the spatial pattern of fluctuations in the input-generated response, by comparing the distribution of evoked and intrinsically generated activity across the different units of a neural network. We develop a complementary approach to principal component analysis in which separate high-variance directions are derived for each input condition. We analyze subspace angles to compute the difference between the shapes of trajectories corresponding to different network states, and the orientation of the low-dimensional subspaces that driven trajectories occupy within the full space of neuronal activity. In addition to revealing how the spatiotemporal structure of spontaneous activity affects input-evoked responses, these methods can be used to infer input selectivity induced by network dynamics from experimentally accessible measures of spontaneous activity (e.g. from voltage- or calcium-sensitive optical imaging experiments). We conclude that the absence of a detailed spatial map of afferent inputs and cortical connectivity does not limit our ability to design spatially extended stimuli that evoke strong responses.

π = Visual Cortex.

Miller, K.D. (2010)

Science,

**330(6007)**:1059-60.
Three distantly-related mammals share a brain architecture characterized by a density of π.

Intrinsic Stability of Temporally Shifted Spike-Timing Dependent Plasticity.

Babadi, B. and Abbott, L.F. (2010)

PLoS Comput. Biol.

**11:**e1000961
Spike-timing dependent plasticity (STDP), a widespread synaptic modification mechanism, is sensitive to correlations between presynaptic spike trains and it generates competition among synapses. However, STDP has an inherent instability because strong synapses are more likely to be strengthened than weak ones, causing them to grow in strength until some biophysical limit is reached. Through simulations and analytic calculations, we show that a small temporal shift in the STDP window that causes synchronous, or nearly synchronous, pre- and postsynaptic action potentials to induce long-term depression can stabilize synaptic strengths. Shifted STDP also stabilizes the postsynaptic firing rate and can implement both Hebbian and anti-Hebbian forms of competitive synaptic plasticity. Interestingly, the overall level of inhibition determines whether plasticity is Hebbian or anti-Hebbian. Even a random symmetric jitter of a few milliseconds in the STDP window can stabilize synaptic strengths while retaining these features. The same results hold for a shifted version of the more recent "triplet" model of STDP. Our results indicate that the detailed shape of the STDPwindow function near the transition fromdepression to potentiation is of the utmost importance in determining the consequences of STDP, suggesting that this region warrants further experimental study.

Stimulus-dependent suppression of chaos in recurrent neural networks.

Rajan, K., Abbott, L.F., and Sompolinsky, H. (2010)

Phys. Rev. E

**82:**011903
Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a “resonant” frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

Emotion, cognition, and mental state representation in amygdala and prefrontal cortex.

Salzman, C.D. and Fusi, S. (2010)

Annu Rev Neurosci.

**33:**173-202
Neuroscientists have often described cognition and emotion as separable processes implemented by different regions of the brain, such as the amygdala for emotion and the prefrontal cortex for cognition. In this framework, functional interactions between the amygdala and prefrontal cortex mediate emotional influences on cognitive processes such as decision-making, as well as the cognitive regulation of emotion. However, neurons in these structures often have entangled representations, whereby single neurons encode multiple cognitive and emotional variables. Here we review studies using anatomical, lesion, and neurophysiological approaches to investigate the representation and utilization of cognitive and emotional parameters. We propose that these mental state parameters are inextricably linked and represented in dynamic neural networks composed of interconnected prefrontal and limbic brain structures. Future theoretical and experimental work is required to understand how these mental state representations form and how shifts between mental states occur, a critical feature of adaptive cognitive and emotional behavior.

Attractor concretion as a mechanism for the formation of context representations.

Rigotti, M., Ben Dayan Rubin, D., Morrison, S.E., Salzman, C.D., and Fusi, S. (2010)

Neuroimage.

**52**:833-847
Complex tasks often require the memory of recent events, the knowledge about the context in which they occur, and the goals we intend to reach. All this information is stored in our mental states. Given a set of mental states, reinforcement learning (RL) algorithms predict the optimal policy that maximizes future reward. RL algorithms assign a value to each already-known state so that discovering the optimal policy reduces to selecting the action leading to the state with the highest value. But how does the brain create representations of these mental states in the first place? We propose a mechanism for the creation of mental states that contain information about the temporal statistics of the events in a particular context. We suggest that the mental states are represented by stable patterns of reverberating activity, which are attractors of the neural dynamics. These representations are built from neurons that are selective to specific combinations of external events (e.g. sensory stimuli) and pre-existent mental states. Consistent with this notion, we find that neurons in the amygdala and in orbitofrontal cortex (OFC) often exhibit this form of mixed selectivity. We propose that activating different mixed selectivity neurons in a fixed temporal order modifies synaptic connections so that conjunctions of events and mental states merge into a single pattern of reverberating activity. This process corresponds to the birth of a new, different mental state that encodes a different temporal context. The concretion process depends on temporal contiguity, i.e. on the probability that a combination of an event and mental states follows or precedes the events and states that define a certain context. The information contained in the context thereby allows an animal to assign unambiguously a value to the events that initially appeared in different situations with different meanings.

Internal representation of task rules by recurrent dynamics: the importance of the diversity of neural response.

Rigotti, M., Ben Dayan Rubin, D., Wang, X-J., and Fusi, S. (2010)

Front. Comput. Neurosci., doi:10.3389/fncom.2010.00024

Neural activity of behaving animals, especially in the prefrontal cortex, is highly heterogeneous, with selective responses to diverse aspects of the executed task. We propose a general model of recurrent neural networks that perform complex rule-based tasks, and we show that the diversity of neuronal responses plays a fundamental role when the behavioral responses are context dependent. Specifically, we found that when the inner mental states encoding the task rules are represented by stable patterns of neural activity (attractors of the neural dynamics), the neurons must be selective for combinations of sensory stimuli and inner mental states. Such mixed selectivity is easily obtained by neurons that connect with random synaptic strengths both to the recurrent network and to neurons encoding sensory inputs. The number of randomly connected neurons needed to solve a task is on average only three times as large as the number of neurons needed in a network designed ad hoc. Moreover, the number of needed neurons grows only linearly with the number of task-relevant events and mental states, provided that each neuron responds to a large proportion of events (dense/distributed coding). A biologically realistic implementation of the model captures several aspects of the activity recorded from monkeys performing context dependent tasks. Our findings explain the importance of the diversity of neural responses and provide us with simple and general principles for designing attractor neural networks that perform complex computation.

Fast Kalman filtering on quasilinear dendritic trees.

Paninski, L. (2010)

J. Comp. Neurosci.

**28:**211-228
Optimal filtering of noisy voltage signals on dendritic trees is a key problem in computational cellular neuroscience. However, the state variable in this problem --- the vector of voltages at every compartment --- is very high-dimensional: typical realistic multicompartmental models have on the order of $N=10^4$ compartments. Standard implementations of the Kalman filter require $O(N^3)$ time and $O(N^2)$ space, and are therefore impractical. Here we take advantage of three special features of the dendritic filtering problem to construct an efficient filter: (1) dendritic dynamics are governed by a cable equation on a tree, which may be solved using sparse matrix methods in $O(N)$ time; and current methods for observing dendritic voltage (2) provide low SNR observations and (3) only image a relatively small number of compartments at a time. The idea is to approximate the Kalman equations in terms of a low-rank perturbation of the steady-state (zero-SNR) solution, which may be obtained in $O(N)$ time using methods that exploit the sparse tree structure of dendritic dynamics. The resulting methods give a very good approximation to the exact Kalman solution, but only require $O(N)$ time and space. We illustrate the method with applications to real and simulated dendritic branching structures, and describe how to extend the techniques to incorporate spatially subsampled, temporally filtered, and nonlinearly transformed observations.

Fast non-negative deconvolution for spike train inference from population calcium imaging.

Vogelstein, J., Packer, A., Machado, T., Sippy, T. Babadi, B., Yuste, R. and Paninski, L. (2010)

J. Neurophys.

*In press*
Fluorescent calcium indicators are becoming increasingly popular as a means for observing the spiking activity of large neuronal populations. Unfortunately, extracting the spike train of each neuron from a raw fluorescence movie is a nontrivial problem. This work presents a fast non-negative deconvolution filter to infer the approximately most likely spike train of each neuron, given the fluorescence observations. This algorithm outperforms optimal linear deconvolution (Wiener filtering) on both simulated and biological data. The performance gains come from restricting the inferred spike trains to be positive (using an interior-point method), unlike the Wiener filter. The algorithm runs in linear time, like the Wiener filter, and is fast enough that even when imaging over 100 neurons simultaneously, inference can be performed on the set of all observed traces faster than real-time. Performing optimal spatial filtering on the images further refines the inferred spike train estimates. Importantly, all the parameters required to perform the inference can be estimated using only the fluorescence data, obviating the need to perform joint electrophysiological and imaging calibration experiments.

Efficient Markov chain Monte Carlo methods for decoding neural spike trains.

Ahmadian, Y., Pillow, J., and Paninski, L. (2010)

Neural Computation

*In press*
Stimulus reconstruction or decoding methods provide an important tool for understanding how sensory and motor information is represented in neural activity. We discuss Bayesian decoding methods based on an encoding generalized linear model (GLM) that accurately describes how stimuli are transformed into the spike trains of a group of neurons. The form of the GLM likelihood ensures that the posterior distribution over the stimuli that caused an observed set of spike trains is log-concave so long as the prior is. This allows the maximum a posteriori (MAP) stimulus estimate to be obtained using efficient optimization algorithms. Unfortunately, the MAP estimate can have a relatively large average error when the posterior is highly non-Gaussian. Here we compare several Markov chain Monte Carlo (MCMC) algorithms that allow for the calculation of general Bayesian estimators involving posterior expectations (conditional on model parameters). An efficient version of the hybrid Monte Carlo (HMC) algorithm was significantly superior to other MCMC methods for Gaussian priors. When the prior distribution has sharp edges and corners, on the other hand, the "hit-and-run" algorithm performed better than other MCMC methods. Using these algorithms we show that for this latter class of priors the posterior mean estimate can have a considerably lower average error than MAP, whereas for Gaussian priors the two estimators have roughly equal efficiency. We also address the application of MCMC methods for extracting non-marginal properties of the posterior distribution. For example, by using MCMC to calculate the mutual information between the stimulus and response, we verify the validity of a computationally efficient Laplace approximation to this quantity for Gaussian priors in a wide range of model parameters; this makes direct model-based computation of the mutual information tractable even in the case of large observed neural populations, where methods based on binning the spike train fail. Finally, we consider the effect of uncertainty in the GLM parameters on the posterior estimators.

Model-based decoding, information estimation, and change-point detection techniques for multi-neuron spike trains.

Pillow, J., Ahmadian, Y., and Paninski, L. (2010)

Neural Computation

*In press*
One of the central problems in systems neuroscience is to understand how neural spike trains convey sensory information. Decoding methods, which provide an explicit means for reading out the information contained in neural spike responses, offer a powerful set of tools for studying the neural coding problem. Here we develop several decoding methods based on point-process neural encoding models, or "forward" models that predict spike responses to stimuli. These models have concave log-likelihood functions, which allow for efficient maximum-likelihood model fitting and stimulus decoding. We present several applications of the encoding-model framework to the problem of decoding stimulus information from population spike responses: (1) a tractable algorithm for computing the maximum a posteriori (MAP) estimate of the stimulus, the most probable stimulus to have generated an observed single- or multiple-neuron spike train response, given some prior distribution over the stimulus; (2) a Gaussian approximation to the posterior stimulus distribution that can be used to quantify the fidelity with which various stimulus features are encoded; (3) an efficient method for estimating the mutual information between the stimulus and the spike trains emitted by a neural population; and (4) a framework for the detection of change-point times (e.g. the time at which the stimulus undergoes a change in mean or variance), by marginalizing over the posterior stimulus distribution. We provide several examples illustrating the performance of these estimators with simulated and real neural data.

Automating the design of informative sequences of sensory stimuli.

Lewi, J., Schneider, D., Woolley, S., and Paninski, L. (2010)

J. Comput. Neuro.

*In press*
Adaptive stimulus design methods can potentially improve the efficiency of sensory neurophysiology experiments significantly; however, designing optimal stimulus sequences in real time remains a serious technical challenge. Here we describe two approximate methods for generating informative stimulus sequences: the first approach provides a fast method for scoring the informativeness of a batch of specific potential stimulus sequences, while the second method attempts to compute an optimal stimulus distribution from which the experimenter may easily sample. We apply these methods to single-neuron spike train data recorded from the auditory midbrain of zebra finches, and demonstrate that the resulting stimulus sequences do in fact provide more information about neuronal tuning in a shorter amount of time than do more standard experimental designs.

Population decoding of motor cortical activity using a generalized linear model with hidden states.

Lawhern, V., Wu, W., Hatsopoulos, N.G., and Paninski, L. (2010)

J. Neurosci. Meth.

*In press*
Generalized linear models (GLMs) have been developed for modeling and decod- ing population neuronal spiking activity in the motor cortex. These models provide reasonable characterizations between neural activity and motor behavior. However, they lack a description of movement-related terms which are not observed directly in these experiments, such as muscular activation, the subject's level of attention, and other internal or external states. Here we propose to include a multi-dimensional hidden state to address these states in a GLM framework where the spike count at each time is described as a function of the hand state (position, velocity, and acceleration), truncated spike history, and the hidden state. The model can be identified by an Expectation-Maximization algorithm. We tested this new method in two datasets where spikes were simultaneously recorded using a multi-electrode array in the primary motor cortex of two monkeys. It was found that this method significantly improves the model-fitting over the classical GLM, for hidden dimensions varying from 1 to 4. This method also provides more accurate decoding of hand state (lowering the Mean Square Error by up to 29% in some cases), while retaining real-time computational efficiency. These improvements on representation and decoding over the classical GLM model suggest that this new approach could contribute as a useful tool to motor cortical decoding and prosthetic applications.

A Bayesian approach for inferring neuronal connectivity from calcium fluorescent imaging data.

Mishchencko, Y., Vogelstein, J., and Paninski, L. (2010)

Annals of applied statistics

*In press*
Deducing the structure of neural circuits is one of the central problems of modern neuroscience. Recently-introduced calcium fluorescent imaging methods permit experimentalists to observe network activity in large populations of neurons, but these techniques provide only indirect observations of neural spike trains, with limited time resolution and signal quality. In this work, we present a Bayesian approach for inferring neural circuitry given this type of imaging data. We model the network activity in terms of a collection of coupled hidden Markov chains, with each chain corresponding to a single neuron in the network and the coupling between the chains reflecting the network's connectivity matrix. We derive a Monte Carlo Expectation- Maximization algorithm for fitting the model parameters; to obtain the sufficient statistics in a computationally-efficient manner, we introduce a specialized blockwise-Gibbs algorithm for sampling from the joint activity of all observed neurons given the observed fluorescence data. We perform large-scale simulations of randomly connected neuronal networks with biophysically realistic parameters and find that the proposed methods can accurately infer the connectivity in these networks given reasonable experimental and computational constraints. In addition, the estimation accuracy may be improved significantly by incorporating prior knowledge about the sparseness of connectivity in the network, via standard L1 penalization methods.

A new look at state-space models for neural data.

Paninski, L., Ahmadian, Y., Ferreira, D.G., Koyama, S, Rahnama Rad, K., Vidne, M., Vogelstein, J., and Wu, W. (2010)

J. Comput. Neuro. (special issue on statistical analysis of neural data)

*In press*
State space methods have proven indispensable in neural data analysis. However, common methods for performing inference in state-space models with non-Gaussian observations rely on certain approximations which are not always accurate. Here we review direct optimization methods that avoid these approximations, but that nonetheless retain the computational efficiency of the approximate methods. We discuss a variety of examples, applying these direct optimization techniques to problems in spike train smoothing, stimulus decoding, parameter estimation, and inference of synaptic properties. Along the way, we point out connections to some related standard statistical methods, including spline smoothing and isotonic regression. Finally, we note that the computational methods reviewed here do not in fact depend on the state-space setting at all; instead, the key property we are exploiting involves the bandedness of certain matrices. We close by discussing some applications of this more general point of view, including Markov chain Monte Carlo methods for neural decoding and efficient estimation of spatially-varying firing rates.

Neuropeptide feedback modifies odor-evoked dynamics in C. elegans olfactory neurons.

Chalasani, S., Kato, S., Albrecht, D., Nakagawa, T., Abbott, L.F. and Bargmann, C. (2010)

Nature Neurosci.

**13:**615-621
Many neurons release classical transmitters together with neuropeptide co-transmitters whose functions are incompletely understood. Here we define the relationship between two transmitters in the olfactory system of C. elegans, showing that a neuropeptide-to-neuropeptide feedback loop alters sensory dynamics in primary olfactory neurons. The AWC olfactory neuron is glutamatergic and also expresses the peptide NLP-1. Worms with nlp-1 mutations show increased AWC-dependent behaviors, suggesting that NLP-1 limits the normal response. The receptor for NLP-1 is the G protein-coupled receptor NPR-11, which acts in postsynaptic AIA interneurons. Feedback from AIA interneurons modulates odor-evoked calcium dynamics in AWC olfactory neurons and requires INS-1, a neuropeptide released from AIA. The neuropeptide feedback loop dampens behavioral responses to odors on short and long timescales. Our results point to neuronal dynamics as a site of behavioral regulation and reveal the ability of neuropeptide feedback to remodel sensory networks on multiple timescales.

Generating sparse and selective third-order responses in the olfactory system of the fly.

Luo, S., Axel, R. and Abbott, L.F. (2010)

Proc. Natl. Acad. Sci. USA

**107:**10713–10718
In the antennal lobe of Drosophila, information about odors is transferred from olfactory receptor neurons (ORNs) to projection neurons (PNs), which then send axons to neurons in the lateral horn of the protocerebrum (LHNs) and to Kenyon cells (KCs) in the mushroom body. The transformation from ORN to PN responses can be described by a normalization model similar to what has been used in modeling visually responsive neurons. We study the implications of this transformation for the generation of LHN and KC responses under the hypothesis that LHN responses are highly selective and therefore suitable for driving innate behaviors, whereas KCs provide a more general sparse representation of odors suitable for forming learned behavioral associations. Our results indicate that the transformation from ORN to PN !ring rates in the antennal lobe equalizes the magnitudes of and decorrelates responses to different odors through feedforward nonlinearities and lateral suppression within the circuitry of the antennal lobe, and we study how these two components affect LHN and KC responses.

The relationship between optimal and biologically plausible decoding of stimulus velocity in the retina.

Lalor, E., Ahmadian, Y. and Paninski, L. (2009)

Journal of the Optical Society of America A (special issue on ideal observers and efficiency)

**26**:B25-42
A major open problem in systems neuroscience is to understand the relationship between behavior and the detailed spiking properties of neural populations. We assess how faithfully velocity information can be decoded from a population of spiking model retinal neurons whose spatiotemporal receptive fields and ensemble spike train dynamics are closely matched to real data. We describe how to compute the optimal Bayesian estimate of image velocity given the population spike train response and show that, in the case of global translation of an image with known intensity profile, on average the spike train ensemble signals speed with a fractional standard deviation of about 2% across a specific set of stimulus conditions. We further show how to compute the Bayesian velocity estimate in the case where we only have some a priori information about the (naturalistic) spatial correlation structure of the image but do not know the image explicitly. As expected, the performance of the Bayesian decoder is shown to be less accurate with decreasing prior image information. There turns out to be a close mathematical connection between a biologically plausible "motion energy" method for decoding the velocity and the Bayesian decoder in the case that the image is not known. Simulations using the motion energy method and the Bayesian decoder with unknown image reveal that they result in fractional standard deviations of 10% and 6%, respectively, across the same set of stimulus conditions. Estimation performance is rather insensitive to the details of the precise receptive field location, correlated activity between cells, and spike timing.

Neural decoding of hand motion using a linear state-space model with hidden states.

Wu, W., Kulkarni, J.E., Hatsopoulos, N.G., and Paninski, L. (2009)

IEEE Trans. Neural Systems and Rehabilitation Engineering

**17**:370-378
The Kalman filter has been proposed as a model to decode neural activity measured from the motor cortex in order to obtain real-time estimates of hand motion in behavioral neurophysiological experiments. However, currently used linear state-space models underlying the Kalman filter do not take into account other behavioral states such as muscular activity or the subject's level of attention, which are often unobservable during experiments but may play important roles in characterizing neural controlled hand movement. To address this issue, we depict these unknown states as one multi-dimensional hidden state in the linear state-space framework. This new model assumes that the observed neural firing rate is directly related to this hidden state. The dynamics of the hand state are also allowed to impact the dynamics of the hidden state, and vice versa. The parameters in the model can be identified by a conventional Expectation- Maximization algorithm. Since this model still uses the linear Gaussian framework, hand-state decoding can be performed by the efficient Kalman filter algorithm. Experimental results show that this new model provides a more appropriate representation of the neural data and generates more accurate decoding. Furthermore, we have used recently developed computationally efficient methods by incorporating a priori information of the targets of the reaching movement. Our results show that the hidden-state model with target-conditioning further improves decoding accuracy.

Generating Coherent Patterns of Activity from Chaotic Neural Networks.

Sussillo, D. and Abbott, L.F. (2009)

Neuron

**63:**544-557
Neural circuits display complex activity patterns both spontaneously and when responding to a stimulus or generating a motor output. How are these two forms of activity related? We develop a procedure called FORCE learning for modifying synaptic strengths either external to or within a model neural network to change chaotic spontaneous activity into a wide variety of desired activity patterns. FORCE learning works even though the networks we train are spontaneously chaotic and we leave feedback loops intact and unclamped during learning. Using this approach, we construct networks that produce a wide variety of complex output patterns, input-output transformations that require memory, multiple outputs that can be switched by control inputs, and motor patterns matching human motion capture data. Our results reproduce data on premovement activity in motor and premotor cortex, and suggest that synaptic plasticity may be a more rapid and powerful modulator of network activity than generally appreciated.

Stability of Hippocampal Representations and Neuronal Synchrony are Differentially Modulated by Attention to Spatial and Non-Spatial Contingencies.

Muzzio, I.A., Levita, L., Kulkarni, J., Monaco, J., Kentros, C., Stead, M., Abbott, L.F. and Kandel, E.R. (2009)

PLoS Biol. 7:e1000140

A key question in the analysis of hippocampal memory relates to how attention modulates the encoding and long-term
retrieval of spatial and nonspatial representations in this region. To address this question, we recorded from single cells over
a period of 5 days in the CA1 region of the dorsal hippocampus while mice acquired one of two goal-oriented tasks. These
tasks required the animals to find a hidden food reward by attending to either the visuospatial environment or a particular
odor presented in shifting spatial locations. Attention to the visuospatial environment increased the stability of visuospatial
representations and phase locking to gamma oscillations - a form of neuronal synchronization thought to underlie the
attentional mechanism necessary for processing task-relevant information. Attention to a spatially shifting olfactory cue
compromised the stability of place fields and increased the stability of reward-associated odor representations, which were
most consistently retrieved during periods of sniffing and digging when animals were restricted to the cup locations.
Together, these results suggest that attention selectively modulates the encoding and retrieval of hippocampal
representations by enhancing physiological responses to task-relevant information.

Equalization of ocular dominance columns induced by an activity-dependent learning rule and the maturation of inhibition.

Toyoizumi T. and Miller K.D. (2009)

J Neurosci

**29(20):**6514-25
Early in development, the cat primary visual cortex (V1) is dominated by inputs driven by the contralateral eye. The pattern then reorganizes into ocular dominance columns that are roughly equally distributed between inputs serving the two eyes. This reorganization does not occur if the eyes are kept closed. The mechanism of this equalization is unknown. It has been argued that it is unlikely to involve Hebbian activity-dependent learning rules, on the assumption that these would favor an initially dominant eye. The reorganization occurs at the onset of the critical period (CP) for monocular deprivation (MD), the period when MD can cause a shift of cortical innervation in favor of the nondeprived eye. In mice, the CP is opened by the maturation of cortical inhibition, which does not occur if the eyes are kept closed. Here we show how these observations can be united: under Hebbian rules of activity-dependent synaptic modification, strengthening of intracortical inhibition can lead to equalization of the two eyes' inputs. Furthermore, when the effects of homeostatic synaptic plasticity or certain other mechanisms are incorporated, activity-dependent learning can also explain how MD causes a shift toward the open eye during the CP despite the drive by inhibition toward equalization of the two eyes' inputs. Thus, assuming similar mechanisms underlie the onset of the CP in cats as in mice, this and activity-dependent learning rules can explain the interocular equalization observed in cat V1 and its failure to occur without visual experience.

Inhibitory Stabilization of the Cortical Network Underlies Visual Surround Suppression

Ozeki H., Finn I.M., Schaffer E.S., Miller K.D., and Ferster D. (2009)

Neuron

**62(4):**578-592
In what regime does the cortical circuit operate? Our intracellular studies of surround suppression in cat primary visual cortex (V1) provide strong evidence on this question. Although suppression has been thought to arise from an increase in lateral inhibition, we find that the inhibition that cells receive is reduced, not increased, by a surround stimulus. Instead, suppression is mediated by a withdrawal of excitation. Thalamic recordings and previous work show that these effects cannot be explained by a withdrawal of thalamic input. We find in theoretical work that this behavior can only arise if V1 operates as an inhibition-stabilized network (ISN), in which excitatory recurrence alone is strong enough to destabilize visual responses but feedback inhibition maintains stability. We confirm two strong tests of this scenario experimentally and show through simulation that observed cell-to-cell variability in surround effects, from facilitation to suppression, can arise naturally from variability in the ISN.

HCN hyperpolarization-activated cation channels
inhibit EPSPs by interactions with M-type K+ channels

George M.S., Abbott L.F., and Siegelbaum S. A. (2009)

Nature Neuroscience

**12(5):**577-584
The processing of synaptic potentials by neuronal dendrites depends on both their passive cable properties and active voltage-gated channels, which can generate complex effects as a result of their nonlinear properties. We characterized the actions of HCN (hyperpolarization-activated cyclic nucleotide-gated cation) channels on dendritic processing of subthreshold excitatory postsynaptic potentials (EPSPs) in mouse CA1 hippocampal neurons. The HCN channels generated an excitatory inward current (Ih) that exerted a direct depolarizing effect on the peak voltage of weak EPSPs, but produced a paradoxical hyperpolarizing effect on the peak voltage of stronger, but still subthreshold, EPSPs. Using a combined modeling and experimental approach, we found that the inhibitory action of Ih was caused by its interaction with the delayed-rectifier M-type K1 current. In this manner, Ih can enhance spike firing in response to an EPSP when spike threshold is low and can inhibit firing when spike threshold is high.

Gating multiple signals through detailed balance of excitation and inhibition in spiking networks

Vogels, T. P. and Abbott, L.F. (2009)

Nature Neuroscience

**12(4):**483-491
Recent theoretical work has provided a basic understanding of signal propagation in networks of spiking neurons, but mechanisms for gating and controlling these signals have not been investigated previously. Here we introduce an idea for the gating of multiple signals in cortical networks that combines principles of signal propagation with aspects of balanced networks. Specifically, we studied networks in which incoming excitatory signals are normally cancelled by locally evoked inhibition, leaving the targeted layer unresponsive. Transmission can be gated 'on' by modulating excitatory and inhibitory gains to upset this detailed balance. We illustrate gating through detailed balance in large networks of integrate-and-fire neurons. We show successful gating of multiple signals and study failure modes that produce effects reminiscent of clinically observed pathologies. Provided that the individual signals are detectable, detailed balance has a large capacity for gating multiple signals.

Efficient computation of the maximum a posteriori path and parameter estimation in integrate-and-fire and more general state-space models

Shinsuke Koyama and Liam Paninski (2009)

Journal of Computational Neuroscience, 2009 Apr 28 [Epub ahead of print]

A number of important data analysis problems in neuroscience can be solved using state-space models. In this article,
we describe fast methods for computing the exact maximum a posteriori (MAP) path of the hidden state variable in these
models, given spike train observations. If the state transition density is log-concave and the observation model
satisfies certain standard assumptions, then the optimization problem is strictly concave and can be solved rapidly
with Newton-Raphson methods, because the Hessian of the loglikelihood is block tridiagonal. We can further exploit
this block-tridiagonal structure to develop efficient parameter estimation methods for these models. We describe
applications of this approach to neural decoding problems, with a focus on the classic integrate-and-fire model
as a key example.

Maximally reliable Markov chains under energy constraints

Sean Escola, Michael Eisele, Kenneth D. Miller, and Liam Paninski (2009)

Neural Computation,

**21(7)**:1863-1912
Signal to noise ratios in physical systems can be signi cantly degraded if the output of a system is
highly variable. Biological processes for which highly stereotyped signal generation is a necessary
feature appear to have reduced their signal variabilities by employing multiple processing steps.
To better understand why this multi-step cascade structure might be desirable, we prove that the
reliability of a signal generated by a multi-state system with no memory (i.e. a Markov chain) is
maximal if and only if the system topology is such that the process steps irreversibly through
each state, with transition rates chosen such that an equal fraction of the total signal is generated
in each state. Furthermore, our result indicates that by increasing the number of states, it is
possible to arbitrarily increase the reliability of the system. In a physical system, however,
there is an energy cost associated with maintaining irreversible transitions, and this cost
increases with the number of such transitions (i.e. the number of states). Thus an infinite length
chain, which would be perfectly reliable, is infeasible. To model the e ects of energy demands on
the maximally reliable solution, we numerically optimize the topology under two distinct energy
functions that penalize either irreversible transitions or incommunicability between states respectively.
In both cases, the solutions are essentially irreversible linear chains, but with upper bounds
on the number of states set by the amount of available energy. We therefore conclude that a
physical system for which signal reliability is important should employ a linear architecture
with the number of states (and thus the reliability) determined by the intrinsic energy constraints
of the system.

Balanced amplification: A new mechanism of selective amplification of neural activity patterns

Murphy, B.K. and K.D. Miller (2009)

Neuron

**61:**635-648
In cerebral cortex, ongoing activity absent a stimulus
can resemble stimulus-driven activity in size and
structure. In particular, spontaneous activity in cat
primary visual cortex (V1) has structure significantly
correlated with evoked responses to oriented stimuli.
This suggests that, from unstructured input, cortical
circuits selectively amplify specific activity patterns.
Current understanding of selective amplification
involves elongation of a neural assembly's lifetime
by mutual excitation among its neurons. We introduce
a new mechanism for selective amplification
without elongation of lifretime:'balanced amplification'.
Strong balanced amplification arises when
feedback inhibition stabilizes strong recurrent excitation,
a pattern likely to be typical of cortex. Thus,
balanced amplification should ubiquitously contribute
to cortical activity. Balanced amplification
depends on the fact that individual neurons project
only excitatory or only inhibitory synapses. This
leads to a hidden feedforward connectivity between
activity patterns. We show in a detailed biophysical
model that this can explain the cat V1 observations.

Sequential optimal design of neurophysiology experiments

Lewi, J., Butera, R., and Paninski, L. (2009)

Neural Computation,

**21(3)**:619-687
Adaptively optimizing experiments has the potential to significantly reduce the number of trials needed to build parametric statistical
models of neural systems. However, application of adaptive methods to neurophysiology has been limited by severe computational challenges.
Since most neurons are high-dimensional systems, optimizing neurophysiology experiments requires computing high-dimensional integrations
and optimizations in real time. Here we present a fast algorithm for choosing the most informative stimulus by maximizing the mutual
information between the data and the unknown parameters of a generalized linear model (GLM) that we want to fit to the neuron's activity.
We rely on important log concavity and asymptotic normality properties of the posterior to facilitate the required computations. Our
algorithm requires only low-rank matrix manipulations and a two-dimensional search to choose the optimal stimulus. The average running
time of these operations scales quadratically with the dimensionality of the GLM, making real-time adaptive experimental design feasible
even for high-dimensional stimulus and parameter spaces. For example, we require roughly 10 milliseconds on a desktop computer to optimize
a 100-dimensional stimulus. Despite using some approximations to make the algorithm efficient, our algorithm asymptotically decreases the
uncertainty about the model parameters at a rate equal to the maximum rate predicted by an asymptotic analysis. Simulation results show
that picking stimuli by maximizing the mutual information can speed up convergence to the optimal values of the parameters by an order
of magnitude compared to using random (nonadaptive) stimuli. Finally, applying our design procedure to real neurophysiology experiments
requires addressing the nonstationarities that we would expect to see in neural responses; our algorithm can efficiently handle both fast
adaptation due to spike history effects and slow, nonsystematic drifts in a neuron's activity.

Bayesian image recovery for dendritic structures under low signal-to-noise conditions

Geoff Fudenberg and Liam Paninski (2009)

IEEE Transactions on Image Processing,

**18:**471-482
Experimental research seeking to quantify neuronal structure constantly contends with restrictions on image resolution and variability.
In particular, experimentalists often need to analyze images with very low signal-to-noise ratio (SNR). In many experiments dye
toxicity scales with the light intensity; this leads experimentalists to reduce image SNR in order to preserve the viability of the
specimen. In this work we present a Bayesian approach for estimating the neuronal shape given low-SNR observations. This Bayesian
framework has two major advantages. First, the method effectively incorporates known facts about 1) the image formation process,
including blur and the Poisson nature of image noise at low intensities, and 2) dendritic shape, including the fact that dendrites
are simply-connected geometric structures with smooth boundaries. Second, we may employ standard Markov chain Monte Carlo (MCMC)
techniques for quantifying the posterior uncertainty in our estimate of the dendritic shape. We describe an efficient computational
implementation of these methods and demonstrate the algorithm's performance on simulated noisy two-photon laser-scanning microscopy images.

Smoothing of, and parameter estimation from, noisy biophysical recordings

Quentin Huys and Liam Paninski (2009)

PLOS Comp. Bio., May;5(5):e1000379

Background: Biophysically detailed models of single cells are difficult to fit to real data. Recent advances in imaging
techniques allow simultaneous access to various intracellular variables, and these data can be used to significantly
facilitate the modelling task. These data, however, are noisy, and current approaches to building biophysically
detailed models are not designed to deal with this.

Methodology: We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo methods in combination with a detailed biophysical description of a cell are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a nonparametric manner.

Conclusions / Significance: Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances and observation noise) are inferred automatically from noisy data via expectation-maximisation. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise.

Methodology: We extend previous techniques to take the noisy nature of the measurements into account. Sequential Monte Carlo methods in combination with a detailed biophysical description of a cell are used for principled, model-based smoothing of noisy recording data. We also provide an alternative formulation of smoothing where the neural nonlinearities are estimated in a nonparametric manner.

Conclusions / Significance: Biophysically important parameters of detailed models (such as channel densities, intercompartmental conductances, input resistances and observation noise) are inferred automatically from noisy data via expectation-maximisation. Overall, we find that model-based smoothing is a powerful, robust technique for smoothing of noisy biophysical data and for inference of biophysical parameters in the face of recording noise.

Theoretical Neuroscience Rising

Abbott, L.F. (2008)

Neuron,

**60:**489-495
Theoretical neuroscience has experienced explosive growth over the past 20 years. In addition to bringing
new researchers into the field with backgrounds in physics, mathematics, computer science, and engineering,
theoretical approaches have helped to introduce new ideas and shape directions of neuroscience research.
This review presents some of the developments that have occurred and the lessons they have taught us.

Simulating In Vivo Background Activity in a Slice with the Dynamic Clamp.

Chance, F.C. and Abbott, L.F. (2008)

In T. Bal and A. Destexhe, eds.

**Dynamic-Clamp: From Principles To Applications**(Springer Science, New York) pp. 73-87
Neurons in vivo receive a large amount of internally generated "background" activity in addition to synaptic input directly driven by an external stimulus. Stimulus-driven and background synaptic inputs interact, through the nonlinearities of neuronal integration, in interesting ways. The dynamic clamp can be used in vitro to duplicate background input, allowing the experimenter to take advantage of the accessibility of neurons in vitro while still studying them under in vivo conditions. In this chapter we discuss some results from experiments in which a neuron is driven by current injection that simulates a stimulusdriven
input as well as dynamic-clamp-generated background activity. One of the effects uncovered in this way is multiplicative gain modulation, achieved by varying the level of background synaptic input. We discuss how the dynamic clamp was used to discover this effect and also how to choose parameters to simulate in vivo background synaptic input in slice neurons.

Designing neurophysiology experiments to optimally constrain receptive field models along parametric submanifolds

Jeremy Lewi, Robert Butera, David Schneider, Sarah Woolley, and Liam Paninski (2008)

NIPS

**2008**
Sequential optimal design methods hold great promise for improving the efficiency of neurophysiology experiments.
However, previous methods for optimal experimental design have incorporated only weak prior information about the
underlying neural system (e.g., the sparseness or smoothness of the receptive field). Here we describe how to
use stronger prior information, in the form of parametric models of the receptive field, in order to construct
optimal stimuli and further improve the efficiency of our experiments. For example, if we believe that the
receptive field is well-approximated by a Gabor function, then our method constructs stimuli that optimally
constrain the Gabor parameters (orientation, spatial frequency, etc.) using as few experimental trials as possible.
More generally, we may believe a priori that the receptive field lies near a known sub-manifold of the full
parameter space; in this case, our method chooses stimuli in order to reduce the uncertainty along the tangent
space of this sub-manifold as rapidly as possible. Applications to simulated and real data indicate that these
methods may in many cases improve the experimental efficiency by an order of magnitude.

Memory traces in dynamical systems

Surya Ganguli, Dongsung Huh, and Haim Sompolinsky (2008)

PNAS

**105:**18970-18975
To perform nontrivial, real-time computations on a sensory input
stream, biological systems must retain a short-term memory trace
of their recent inputs. It has been proposed that generic
highdimensional dynamical systems could retain a memory trace for
past inputs in their current state. This raises important questions
about the fundamental limits of such memory traces and the
properties required of dynamical systems to achieve these limits.
We address these issues by applying Fisher information theory to
dynamical systems driven by time-dependent signals corrupted by
noise. We introduce the Fisher Memory Curve (FMC) as a measure
of the signal-to-noise ratio (SNR) embedded in the dynamical state
relative to the input SNR. The integrated FMC indicates the total
memory capacity. We apply this theory to linear neuronal networks
and show that the capacity of networks with normal
connectivity matrices is exactly 1 and that of any network of N
neurons is, at most, N. A nonnormal network achieving this bound
is subject to stringent design constraints: It must have a hidden
feedforward architecture that superlinearly amplifies its input for
a time of order N, and the input connectivity must optimally match
this architecture. The memory capacity of networks subject to
saturating nonlinearities is further limited, and cannot exceed N.
This limit can be realized by feedforward structures with divergent
fan out that distributes the signal across neurons, thereby avoiding
saturation. We illustrate the generality of the theory by showing
that memory in fluid systems can be sustained by transient nonnormal
amplification due to convective instability or the onset of
turbulence.

Cell groups reveal structure of stimulus space

C. Curto and V. Itskov (2008)

PLoS Computational Biology

**4(10)**
An important task of the brain is to represent the outside world. It
is unclear how the brain may do this, however, as it can only rely on
neural responses and has no independent access to external stimuli in
order to ?decode? what those responses mean. We investigate what can
be learned about a space of stimuli using only the action potentials
(spikes) of cells with stereotyped?but unknown?receptive fields. Using
hippocampal place cells as a model system, we show that one can (1)
extract global features of the environment and (2) construct an
accurate representation of space, up to an overall scale factor, that
can be used to track the animal's position. Unlike previous approaches
to reconstructing position from place cell activity, this information
is derived without knowing place fields or any other functions
relating neural responses to position. We find that simply knowing
which groups of cells fire together reveals a surprising amount of
structure in the underlying stimulus space; this may enable the brain
to construct its own internal representations.

Internally Generated Cell Assembly Sequences in the Rat Hippocampus

E. Pastalkova, V. Itskov, A. Amarasingham, G. Buzsaki (2008)

Science

**321(5894)**:1322-1327
A long-standing conjecture in neuroscience is that aspects of
cognition depend on the brain's ability to self-generate sequential
neuronal activity. We found that reliably and continually changing
cell assemblies in the rat hippocampus appeared not only during
spatial navigation but also in the absence of changing environmental
or body-derived inputs. During the delay period of a memory task, each
moment in time was characterized by the activity of a particular
assembly of neurons. Identical initial conditions triggered a similar
assembly sequence, whereas different conditions gave rise to different
sequences, thereby predicting behavioral choices, including
errors. Such sequences were not formed in control (nonmemory)
tasks. We hypothesize that neuronal representations, evolved for
encoding distance in spatial navigation, also support episodic recall
and the planning of action sequences.

Theta-mediated dynamics of spatial information in hippocampus

V. Itskov, E. Pastalkova, K. Mizuseki, G. Buzsaki, K.D. Harris (2008)

Journal of Neuroscience

**28(23)**
In rodent hippocampus, neuronal activity is organized by a 6-10 Hz
theta oscillation. The spike timing of hippocampal pyramidal cells
with respect to the theta rhythm correlates with an animal's position
in space. This correlation has been suggested to indicate an explicit
temporal code for position. Alternatively, it may be interpreted as a
byproduct of theta-dependent dynamics of spatial information flow in
hippocampus. Here we show that place cell activity on different phases
of theta reflects positions shifted into the future or past along the
animal's trajectory in a two-dimensional environment. The phases
encoding future and past positions are consistent across recorded CA1
place cells, indicating a coherent representation at the network
level. Consistent theta-dependent time offsets are not simply a
consequence of phase-position correlation (phase precession), because
they are no longer seen after data randomization that preserves the
phase-position relationship. The scale of these time offsets, 100?300
ms, is similar to the latencies of hippocampal activity after sensory
input and before motor output, suggesting that offset activity may
maintain coherent brain activity in the face of information processing delays.

Gating Deficits in Model Networks:A Path to Schizophrenia?

Vogels,T.P and Abbott, L.F. (2008)

Pharmacopsychiatry

**40**:S73-S77
Gating deficits and hallucinatory sensations are
prominent symptoms of schizophrenia. Comparing
these abnormalities with the failure modes of
network models is an interesting way to explore
how they arise. We present a network model
that can both propagate and gate signals. The
model exhibits effects reminiscent of clinically
observed pathologies when the balance between
excitation and inhibition that it requires is not
properly maintained.

Perceptron for Sparse Discrimination

Itskov, V. and Abbott, L.F. (2008)

Phys. Rev. Lett

**101**018101
We evaluate the capacity and performance of a perceptron discriminator
operating in a highly sparse regime where classic perceptron results do not apply. The perceptron
is constructed to respond to a specified set of q stimuli, with only statistical information provided
about other stimuli to which it is not supposed to respond. We compute the probability of both false-positive
and false-negative errors and determine the capacity of the system for not responding to nonselected
stimuli and for responding to selected stimuli in the presence of noise. If q is a sublinear
function of N, the number of inputs to the perceptron, these capacities are exponential in N=q.

Mean-field approximations for coupled populations of generalized linear model spiking neurons with Markov refractoriness

Taro Toyoizumi, Kamiar Rahnama Rad, and Liam Paninski (2008)

Neural Computation,

**21(5)**:1203-1243
There has recently been a great deal of interest in inferring network
connectivity from the spike trains in populations of neurons. One
class of useful models which can be fit easily to spiking data is
based on generalized linear point process models from statistics. Once
the parameters for these models are fit, the analyst is left with a
nonlinear spiking network model with delays, which in general may be
very difficult to understand analytically. Here we develop mean-field
methods for approximating the stimulus-driven firing rates (both in
the time-varying and steady-state case), auto- and cross-correlations,
and stimulus-dependent filtering properties of these networks. These
approximations are valid when the contributions of individual network
coupling terms are small and, hence, the total input to a neuron is
approximately Gaussian. These approximations lead to deterministic
ordinary differential equations that are much easier to solve and
analyze than direct Monte Carlo simulation of the network
activity. These approximations also provide analytical way to evaluate
the linear input-output filter of neurons and how the filters are
modulated by network interactions and some stimulus feature. Finally,
in the case of strong refractory effects, the mean-field
approximations in the generalized linear model become inaccurate;
therefore we introduce a model that captures strong refractoriness,
retains all of the easy fitting properties of the standard generalized
linear model, and leads to much more accurate approximations of mean
firing rates and cross-correlations that retain fine temporal behaviors.

Statistical models of spike trains

Liam Paninski, Emery Brown, Satish Iyengar, and Rob Kass (2008)

Book chapter in Stochastic Methods in Neuroscience, Oxford University Press, ed. Laing, C. and Lord, G.

Spiking neurons make inviting targets for analytical methods based on
stochastic processes: spike trains carry information in their temporal
patterning, yet they are often highly irregular across time and across
experimental replications. The bulk of this volume is devoted to
mathematical and biophysical models useful in understanding
neurophysiological processes. In this chapter we consider statistical
models for analyzing spike train data.
Strictly speaking, what we would call a statistical model for spike
trains is simply a probabilistic description of the sequence of
spikes. But it is somewhat misleading to ignore the data-analytical
context of these models. In particular, we want to make use of these
probabilistic tools for the purpose of scientific inference.
The leap from simple descriptive uses of probability to inferential
applications is worth emphasizing for two reasons. First, this leap
was one of the great conceptual advances in science, taking roughly
two hundred years. It was not until the late 1700s that there emerged
any clear notion of inductive (or what we would now call statistical)
reasoning; it was not until the first half of the twentieth century
that modern methods began to be developed systematically; and it was
only in the second half of the twentieth century that these methods
became well understood in terms of both theory and practice. Second,
the focus on inference changes the way one goes about the modeling
process. It is this change in perspective we want to highlight here,
and we will do so by discussing one of the most important models in
neuroscience, the stochastic integrate-and-fire (IF) model for spike
trains.
The stochastic IF model has a long history (Gerstein and Mandelbrot,
1964; Stein, 1965; Knight, 1972; Burkitt, 2006): it is the simplest
dynamical model that captures the basic properties of neurons,
including the temporal integration of noisy subthreshold inputs, all-
or-none spiking, and refractoriness. Of course, the IF model is a
caricature of true neural dynamics (see, e.g., (Ermentrout and Kopell,
1986; Brunel and Latham, 2003; Izhikevich, 2007) for more elaborate
models) but, as demonstrated in this book and others (Ricciardi, 1977;
Tuckwell, 1989; Gerstner and Kistler, 2002), it has provided much
insight into the behavior of single neurons and neural populations. In
this chapter we explore some of the key statistical questions that
arise when we use this model to perform inference with real neuronal
spike train data. How can we efficiently fit the model to spike train
data? Once we have estimated the model parameters, what can the model
tell us about the encoding properties of the observed neuron? We also
briefly consider some more general approaches to statistical modeling
of spike train data.
We begin, in section 1, by discussing three distinct useful ways of
approaching the IF model, via the language of stochastic (diffusion)
processes, hidden Markov models, and point processes,
respectively. Each of these viewpoints comes equipped with its own
specialized analytical tools, and the power of the IF model is most
evident when all of these tools may be brought to bear
simultaneously. We discuss three applications of these methods in
section 2, and then close in 3 by indicating the scope of the general
point process framework of which the IF model is a part, and the
possibilities for solving some key outstanding data-analytic problems
in systems neuroscience.

A coincidence-based test for uniformity given very sparsely-sampled discrete data

Paninski, L. (2008)

IEEE Transactions on Information Theory,

**54(10)**:4750-4755
How many independent samples N do we need from a distribution p to decide that p is epsilon-distant from uniform in
an L1 sense, Sigma(i=1 to m) |p(i) - 1/m| > epsilon? (Here m is the number of bins on which the distribution is supported,
and is assumed known a priori.) Somewhat surprisingly, we only need N*epsilon^2 >> m^1/2 to make this decision
reliably (this condition is both sufficient and necessary). The test for uniformity introduced here is based
on the number of observed "coincidences" (samples that fall into the same bin), the mean and variance of
which may be computed explicitly for the uniform distribution and bounded nonparametrically for any distribution
that is known to be epsilon-distant from uniform. Some connections to the classical birthday problem are noted.

Spatio-temporal correlations and visual signaling in a complete neuronal population

Pillow, J., Shlens, J., Paninski, L.,Sher, A., Litke, A., Chichilnisky, E., Simoncelli, E. (2008)

Nature,

**454(7206)**:995-999
Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which
downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies, their origin and
importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete
population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses. The model, with parameters fit
directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in
population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population
level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be
predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional
sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information
about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal
linear decoding. This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and
provides a general framework for understanding the importance of correlated activity in populations of neurons.

Undersmoothed kernel entropy estimators

Paninski, L. and Yajima, M. (2008)

IEEE Transactions on Information Theory, (in press)

We develop a "plug-in" kernel estimator for the differential entropy that is consistent even if the kernel width tends to zero
as quickly as 1/N, where N is the number of independent and identically distributed (i.i.d.) samples. Thus, accurate density estimates
are not required for accurate kernel entropy estimates; in fact, it is a good idea when estimating entropy to sacrifice some accuracy
in the quality of the corresponding density estimate.

State-space decoding of goal-directed movements

Kulkarni, J. and Paninski, L. (2008)

IEEE Signal Processing Magazine (special issue on brain-computer interfaces),

**25:**78-86This article reviews an earlier recursive approach for computing such reach trajectories and presents a new nonrecursive approach,
with computations that may be performed analytically for the most part, leading to a significant gain in the accuracy of the inferred trajectory while
imposing a very small computational burden. Extensions of the approach are discussed including the incorporation of multiple target observations at
different times, and multiple possible target locations.

Inferring input nonlinearities in neural encoding models

Ahrens, M., Paninski, L. and Sahani, M. (2008)

Network: Computation in Neural Systems

**19:**35-67We describe a class of models that predict how the instantaneous firing rate of a neuron depends on a dynamic stimulus.
The models utilize a learnt pointwise nonlinear transform of the stimulus, followed by a linear filter that acts on the sequence of transformed inputs.
In one case, the nonlinear transform is the same at all filter lag-times. Thus, this "input nonlinearity" converts the initial numerical representation
of stimulus value to a new representation that provides optimal input to the subsequent linear model. We describe algorithms that estimate both the
input nonlinearity and the linear weights simultaneously; and present techniques to regularise and quantify uncertainty in the estimates. In a second
approach, the model is generalized to allow a different nonlinear transform of the stimulus value at each lag-time. Although more general, this model
is algorithmically more straightforward to fit. However, it has many more degrees of freedom than the first approach, thus requiring more data for
accurate estimation. We test the feasibility of these methods on synthetic data, and on responses from a neuron in rodent barrel cortex. The models
are shown to predict responses to novel data accurately, and to recover several important neuronal response properties.

Spike inference from calcium imaging using sequential Monte Carlo methods

Joshua Vogelstein, Brendon Watson, Adam Packer, Bruno Jedynak, Rafael Yuste, and Liam Paninski (2008)

Biophysical Journal,

**97(2)**:636-655
As recent advances in calcium sensing technologies enable us to simultaneously image many neurons, complementary analytical tools must also
be developed to maximize the utility of this experimental paradigm. While the observations here are fluorescence images, the signals of
interest - spike trains and/or time varying intracellular calcium concentrations - are hidden. Inferring these hidden signals is often
problematic due to noise, nonlinearities, slow imaging rate, and unknown biophysical parameters. We overcome these difficulties by
developing a family of particle filters based on biophysical models of spiking, calcium dynamics, and fluorescence. We show that even in
simple cases, the particle filters outperform the optimal linear (i.e., Wiener) filter, both by obtaining better estimates and by providing
errorbars. We then relax a number of our model assumptions to incorporate nonlinear saturation of the fluorescence signal, as well external
stimulus and spike history dependence of the spike trains. Using both simulations and in vitro fluorescence observations, we demonstrate
superresolution by inferring when within a frame each spike occurs. Furthermore, the model parameters may be estimated using
expectation-maximization with only a very limited amount of data, without the requirement of any simultaneous electrophysiology
and imaging experiments.

One-dimensional dynamics of attention and decision making in LIP

Ganguli, S., Bisley, J.W., Roitman, J.D., Shadlen, M.N., Goldberg, M.E., Miller, K.D. (2008)

Neuron

**58**:15-25Where we allocate our visual spatial attention depends
upon a continual competition between internally gen-
erated goals and external distractions. Recently it
was shown that single neurons in the macaque lateral
intraparietal area (LIP) can predict the amount of time
a distractor can shift the locus of spatial attention
away from a goal. We propose that this remarkable dy-
namical correspondence between single neurons and
attention can be explained by a network model in
which generically high-dimensional firing-rate vectors
rapidly decay to a single mode. We find direct experi-
mental evidence for this model, not only in the original
attentional task, but also in a very different task involv-
ing perceptual decision making. These results confirm
a theoretical prediction that slowly varying activity pat-
terns are proportional to spontaneous activity, pose
constraints on models of persistent activity, and sug-
gest a network mechanism for the emergence of ro-
bust behavioral timing from heterogeneous neuronal
populations.

On the importance of the static nonlinearity in estimating spatiotemporal neural filters with natural stimuli

Sharpee, T.O,. Miller, K.D., Stryker, M.P. (2008)

J Neurophysiol.

**99(5)**:2496-2509Understanding neural responses with natural stimuli has increasingly become an
essential part of characterizing neural coding. Neural responses are commonly
characterized by a linear-nonlinear (LN) model, in which the output of a linear filter
applied to the stimulus is transformed by a static nonlinearity to determine neural
response. To estimate the linear filter in the LN model, studies of responses to natural
stimuli commonly use methods that are unbiased only for a linear model (in which there
is no static nonlinearity): spike-triggered averages with correction for stimulus power
spectrum, with or without regularization. While these methods work well for artificial
stimuli, such as Gaussian white noise, we show here that they estimate neural filters of
LN models from responses to natural stimuli much more poorly. We studied simple cells
in cat primary visual cortex. We demonstrate that the filters computed by directly taking
the nonlinearity into account have better predictive power and depend less on the
stimulus than those computed under the linear model. With noise stimuli, filters
computed using the linear and LN models were similar, as predicted theoretically. With
natural stimuli, filters of the two models can differ profoundly. Noise and natural
stimulus filters differed significantly in spatial properties, but these differences were
exaggerated when filters were computed using the linear rather that the LN model. While
regularization of filters computed under the linear model improved their predictive
power, it also led to systematic distortions of their spatial frequency profiles, especially at
low spatial and temporal frequencies.

Statistical models for neural encoding, decoding, and optimal stimulus design

Liam Paninski, Jonathan Pillow, Jeremy Lewi (2008)

Book chapter in Computational Neuroscience:
Progress in Brain Research, eds. Cisek, P., Drew, T. and Kalaska, J.

**pp 493-507**There are two basic problems in the statistical analysis of neural data. The ``encoding'' problem concerns how information is encoded in neural spike trains: can we predict the spike trains of a neuron (or population of neurons), given an arbitrary stimulus or observed motor response? Conversely, the ``decoding'' problem concerns how much information is in a spike train: in particular, how well can we estimate the stimulus that gave rise to the spike train?
This chapter describes statistical model-based techniques that in some cases provide a unified solution to these two coding problems.
These models can capture stimulus dependencies as well as spike history and interneuronal interaction effects in population spike trains, and are
intimately related to biophysically-based models of integrate-and-fire type. We describe flexible, powerful likelihood-based methods for fitting
these encoding models and then for using the models to perform optimal decoding. Each of these (apparently quite difficult) tasks turn out to be
highly computationally tractable, due to a key concavity property of the model likelihood. Finally, we return to the encoding problem to describe
how to use these models to adaptively optimize the stimuli presented to the cell on a trial-by-trial basis, in order that we may infer the optimal
model parameters as efficiently as possible.

Long memory lifetimes require complex synapses and limited sparseness

Ben Dayan Rubin, D. and Fusi, S. (2007)

Front. Comput. Neurosci.

**1**:7Theoretical studies have shown that memories last longer if the neural representations are sparse, that is, when each neuron is selective for a small fraction of the events creating the memories. Sparseness reduces both the interference between stored memories and the number of synaptic modifications which are necessary for memory storage. Paradoxically, in cortical areas like the inferotemporal cortex, where presumably memory lifetimes are longer than in the medial temporal lobe, neural representations are less sparse. We resolve this paradox by analyzing the effects of sparseness on complex models of synaptic dynamics in which there are metaplastic states with different degrees of plasticity. For these models, memory retention in a large number of synapses across multiple neurons is significantly more efficient in case of many metaplastic states, that is, for an elevated degree of complexity. In other words, larger brain regions allow to retain memories for significantly longer times only if the synaptic complexity increases with the total number of synapses. However, the initial memory trace, the one experienced immediately after memory storage, becomes weaker both when the number of metaplastic states increases and when the neural representations become sparser. Such a memory trace must be above a given threshold in order to permit every single neuron to retrieve the information stored in its synapses. As a consequence, if the initial memory trace is reduced because of the increased synaptic complexity, then the neural representations must be less sparse. We conclude that long memory lifetimes allowed by a larger number of synapses require more complex synapses, and hence, less sparse representations, which is what is observed in the brain.

Mechanisms of Gain Modulation at Single Neuron and Network Levels

Brozovic, M., Abbott, L.F. and Andersen, R.A. (2007)

J. Computational Neuroscience

**25**:158-168Gain modulation, in which the sensitivity of a neural response to one input is modified by
a second input, is studied at single-neuron and network levels. At the single neuron level,
gain modulation can arise if the two inputs are subject to a direct multiplicative
interaction. Alternatively, these inputs can be summed in a linear manner by the neuron
and gain modulation can arise, instead, from a nonlinear input-output relationship. We
derive a mathematical constraint that can distinguish these two mechanisms even though
they can look very similar, provided sufficient data of the appropriate type are available.
Previously, it has been shown in coordinate transformation studies that artificial neurons
with sigmoid transfer functions can acquire a nonlinear additive form of gain modulation
through learning-driven adjustment of synaptic weights. We use the constraint derived
for single-neuron studies to compare responses in this network with those of another
network model based on a biologically inspired transfer function that can support
approximately multiplicative interactions.

A Step Toward Optimal Coding in Olfaction (news and views)

Abbott, L.F. and Luo, S.X. (2007)

Nature Neurosci

**10**:1342-1343Receptor neurons may not encode sensory information in an efficient manner.
A new paper supports the idea that the brain achieves optimal encoding downstream of sensory
transduction through additional processing.

Effects of Inhibitory Gain and Conductance Fluctuations in a Simple Model for Contrast-Invariant Orientation Tuning in Cat V1

Palmer, S.E. and Miller K.D. (2007)

Journal of Neurophysiology

**98**:63-78The origin of orientation selectivity in primary visual cortex (V1) is a model problem for understanding cerebral cortical
circuitry. A key constraint is that orientation tuning width is invariant under changes in stimulus contrast. We have previously shown that this
can arise from the combination of feedforward lateral geniculate nucleus (LGN) input and an orientation-untuned component of feedforward inhibition
that dominates excitation. However, these models did not include the large background voltage noise observed in vivo. Here, we include this noise
and examine a simple model of cat V1 response. Constraining our simulations to fit physiological data, our single model parameter is the strength of
feedforward inhibition relative to LGN excitation. With physiological noise, the contrast invariance of orientation tuning depends little on
inhibition level, although very weak or very strong inhibition leads to weak broadening or sharpening, respectively, of tuning with contrast.
For any inhibition level, an alternative measure of orientation tuning -- the circular variance -- decreases with contrast as
observed experimentally. These results arise primarily because the voltage noise causes large inputs to be much more strongly amplified than
small ones in evoking spiking responses, relatively suppressing responses to nonpreferred stimuli. However, inhibition comparable to or
stronger than excitation appears necessary to suppress spiking responses to nonpreferred orientations to the extent seen in vivo and to allow the
emergence of a tuned mean voltage response. These two response properties provide the strongest constraints on model details. Antiphase inhibition
from inhibitory simple cells, and not just untuned inhibition from inhibitory complex cells, appears necessary to fully explain these aspects of
cortical orientation tuning.

A Neural Circuit Model of Flexible Sensorimotor mapping: Learning and Forgetting on Multiple Timescales

Stefano Fusi, Wael Asaad, Earl Miller, Xiao-Jing Wang (2007)

Neuron

**54**:319-333Volitional behavior relies on the brain's ability to
remap sensory flow to motor programs whenever
demanded by a changed behavioral context.
To investigate the circuit basis of such
flexible behavior, we have developed a biophysically
based decision-making network
model of spiking neurons for arbitrary sensorimotor
mapping. The model quantitatively reproduces
behavioral and prefrontal single-cell
data from an experiment in which monkeys
learn visuomotor associations that are reversed
unpredictably from time to time. We show that
when synaptic modifications occur on multiple
timescales, the model behavior becomes flexible
only when needed: slow components of
learning usually dominate the decision process.
However, if behavioral contexts change frequently
enough, fast components of plasticity
take over, and the behavior exhibits a quick
forget-and-learn pattern. This model prediction
is confirmed by monkey data. Therefore, our
work reveals a scenario for conditional associative
learning that is distinct from instant switching
between sets of well-established sensorimotor
associations.

Differentiable integral equation methods for computing likelihoods in the stochastic integrate-and-fire model

Paninski, L., Haith, A., Szirtes, G. (2007)

Journal of Computational Neuroscience

**24**:69-72We recently introduced likelihood-based methods for fitting stochastic integrate-and-fire models
to spike train data. The key component of this method involves the likelihood that the model will emit a spike at a given time t.
Computing this likelihood is equivalent to computing a Markov first passage time density (the probability that the model voltage crosses threshold
for the first time at time t). Here we detail an improved method for computing this likelihood, based on solving a certain integral equation.
This integral equation method has several advantages over the techniques discussed in our previous work: in particular, the new method has
fewer free parameters and is easily differentiable (for gradient computations). The new method is also easily adaptable for the case in
which the model conductance, not just the input current, is time-varying. Finally, we describe how to incorporate large deviations
approximations to very small likelihoods.

Network model of spontaneous activity exhibiting synchronous transitions between up and down states

Parga, N., Abbott, L.F. (2007)

Frontiers in Neuroscience,

**1**:57-66Both in vivo and in vitro recordings indicate that neuronal mem-
brane potentials can make spontaneous transitions between distinct up
and down states. At the network level, populations of neurons have been
observed to make these transitions synchronously. Although synap-
tic activity and intrinsic neuron properties play an important role, the
precise nature of the processes responsible for these phenomena is not
known. Using a computational model we explore the interplay between
intrinsic neuronal properties and synaptic fluctuations. Model neurons
of the integrate-and-fire type were extended by adding a nonlinear mem-
brane current. Networks of these neurons exhibit large amplitude syn-
chronous spontaneous fluctuations that make the neurons jump between
up and down states, thereby producing bimodal membrane potential
distributions. The effect of sensory stimulation on network responses
depends on whether the stimulus is applied during an up state or deeply
inside a down state. External noise can be varied to modulate the net-
work continuously between two extreme regimes in which it remains
permanently in either the up or the down state.

Common-input models for multiple neural spike-train data

by Kulkarni J. and Paninski L. (2007)

Network: Computation in Neural Systems,

**18**:375-407Recent developments in multi-electrode recordings enable the
simultaneous measurement of the spiking activity of many neurons.
Analysis of such multineuronal data is one of the key challenges in
computational neuroscience today. In this work, we develop a
multivariate point-process model in which the observed activity of a
network of neurons depends on three terms: 1) the
experimentally-controlled stimulus; 2) the spiking history of the
observed neurons; and 3) a latent noise source that corresponds, for
example, to ``common input'' from an unobserved population of neurons
that is presynaptic to two or more cells in the observed population.
We develop an expectation-maximization algorithm for fitting the model
parameters; here the expectation step is based on a continuous-time
implementation of the extended Kalman smoother, and the maximization
step involves two concave maximization problems which may be solved in
parallel. The techniques developed allow us to solve a variety of
inference problems in a straightforward, computationally efficient
fashion; for example, we may use the model to predict network activity
given an arbitrary stimulus, infer a neuron's firing rate given the
stimulus and the activity of the other observed neurons, and perform
optimal stimulus decoding and prediction. We present several detailed
simulation studies which explore the strengths and limitations of our
approach.

Limits on the memory-storage capacity of bounded synapses

by Fusi, S. and Abbott, L.F. (2007)

Nature Neurosci.

**10**:485-493Memories maintained in patterns of synaptic connectivity are rapidly over-written
and destroyed by ongoing plasticity due to the storage of new memories. Short
memory lifetimes arise from the bound that must be imposed on synaptic efficacy in
any realistic model. We explore whether memory performance can be improved by
allowing synapses to traverse a large number of states before reaching their bounds,
or by changing the way these bounds are imposed. In the case of hard bounds
memory lifetimes grow proportional to the square of the number synaptic states,
but only if potentiation and depression are precisely balanced. Improved
performance can be obtained without fine tuning by imposing soft bounds, but this
improvement is only linear in the number of synaptic states. We explore a number
of other possibilities and conclude that improving memory performance requires a
more radical modification of the standard model of memory storage.

Temperature Compensation of Chemical Reactions

by Rajan, K. and Abbott, L.F. (2007)

Phys. Rev. E

**75**:022902Circadian rhythms are daily oscillations in behaviors that persist in constant light/dark conditions
with periods close to 24 hours. A striking feature of these rhythms is that their periods remain fairly
constant over a wide range of physiological temperatures, a feature called temperature compensa-
tion. Although circadian rhythms have been associated with periodic oscillations in mRNA and
protein levels, the question of how to construct a network of chemical reactions that is temperature
compensated remains unanswered. We discuss a general framework for building such a network.

Lexico-Semantic Structure and the Word-Frequency Effect in Recognition Memory

by J.D. Monaco, L.F. Abbott, and M.J. Kahana (2007)

Learn. Mem.

**14(3)**:204-213The word-frequency effect (WFE) in recognition memory refers to the finding that more rare words are better recognized than more common words.
We demonstrate that a familiarity-discrimination model operating on data from a semantic word-association space yields a robust WFE in data on both hit rates and
false-alarm rates. Our modeling results suggest that word frequency is encoded in the semantic structure of language, and that this encoding contributes to the
WFE observed in item-recognition experiments.

Eigenvalue Spectra of Random Matrices for Neural Networks

by K. Rajan and L.F. Abbott (2006)

Phys. Rev. Lett.

**97**:188104The dynamics of neural networks is influenced strongly by the spectrum of eigenvalues of the matrix
describing their synaptic connectivity. In large networks, elements of the synaptic connectivity matrix can
be chosen randomly from appropriate distributions, making results from random matrix theory highly
relevant. Unfortunately, classic results on the eigenvalue spectra of random matrices do not apply to
synaptic connectivity matrices because of the constraint that individual neurons are either excitatory or
inhibitory. Therefore, we compute eigenvalue spectra of large random matrices with excitatory and
inhibitory columns drawn from distributions with different means and equal or different variances.

The spike-triggered average of the integrate-and-fire cell driven by Gaussian white noise

Paninski, L. (2006)

Neural Computation

**18**:2592-2616We compute the exact spike-triggered average (STA) of the voltage for the nonleaky IF cell in continuous time, driven by
Gaussian white noise. The computation is based on techniques from the theory of renewal processes and continuous-time hidden Markov processes
(e.g., the backward and forward Fokker-Planck partial differential equations associated with first-passage time densities). From the STA voltage
it is straightforward to derive the STA input current. The theory also gives an explicit asymptotic approximation for the STA of the leaky IF cell,
valid in the low-noise regime $\sigma \to 0$. We consider both the STA and the conditional average voltage given an observed spike
``doublet'' event, i.e. two spikes separated by some fixed period of silence. In each case, we find that the STA as a function of
time-preceding-spike, $\tau$, has a square-root singularity as $\tau$ approaches zero from below, and scales linearly with the scale of
injected noise current. We close by briefly examining the discrete-time case, where similar phenomena are observed.

Efficient estimation of detailed single-neuron models

Huys, Q., Ahrens, M. Paninski, L. (2006)

Journal of Neurophysiology

**96**:872-890Biophysically accurate multi-compartmental models of individual neurones have signi cantly
advanced our understanding of the input-output function of single cells. These models depend on a large number of parameters which are dif cult to
estimate. In practise, they are often hand tuned to match measured physiological behaviors, thus raising questions of identifiability and
interpretability. We propose a statistical approach to the automatic estimation of various biologically relevant parameters, including 1) the
distribution of channel densities; 2) the spatiotemporal pattern of synaptic input; and 3) axial resistances across extended dendrites.
Recent experimental advances, notably in voltage-sensitive imaging, motivate us to assume access to: a) the spatiotemporal voltage signal in the
dendrite, and b) an approximate description of the channel kinetics of interest. We show here that, given a) and b), the parameters 1)-3) can be
inferred simultaneously by nonnegative linear regression; that this optimization problem possesses a unique solution and is guaranteed to converge
despite the large number of parameters and their complex nonlinear interaction; and that standard optimization algorithms ef ciently reach this
optimum with modest computational and data requirements. We demonstrate that the method leads to accurate estimations on a wide variety of
challenging model data sets that include up to on the order of 10,000 parameters (roughly two orders of magnitude more than previously feasible),
and describe how the method gives insights into the functional interaction of groups of channels.

Dimensional Reduction in Reward-Based Learning

by C Swinehart and L.F. Abbott (2006)

Network: Comp. Neural Sys.

**17**:235-252Reward-based learning in neural systems is challenging because a large number of parameters
that affect network function must be optimized solely on the basis of a reward signal
that indicates improved performance. Searching the parameter space for an optimal solution
is particularly difficult if the network is large. We show that Hebbian forms of synaptic
plasticity applied to synapses between a supervisor circuit and the network it is controlling
can effectively reduce the dimension of the space of parameters being searched to support
efficient reinforcement-based learning in large networks. The critical element is that
the connections between the supervisor units and the network must be reciprocal. Once
the appropriate connections have been set up by Hebbian plasticity, a reinforcement-based
learning procedure leads to rapid learning in a function approximation task. Hebbian plasticity
within the network being supervised ultimately allows the network to perform the
task without input from the supervisor.

Cross-fixation transfer of motion aftereffects with expansion motion

Xin Meng, Pietro Mazzoni and Ning Qian (2006)

Vision Research

**46**:3681-3689It has been shown that motion aftereffect (MAE) not only is present at the adapted location but also partially transfers to nearby non-
adapted locations. However, it is not clear whether MAE transfers across the fixation point. Since cells in area MSTd have receptive
fields that cover both sides of the fixation point and since many MSTd cells, but not cells in earlier visual areas, prefer complex motion
patterns such as expansion, we tested cross-fixation transfer of MAE induced by expanding random-dots stimuli. We also used rightward
translational motion for comparison. Subjects adapted to motion patterns on a fixed side of the fixation point. Dynamic MAE was then
measured with a nulling procedure at both the adapted site and the mirror site across the fixation point. SubjectsÕ eye fixation during
stimulus presentation was monitored with an infrared eye tracker. At the adapted site, both the expansion and the translation patterns
generated strong MAEs, as expected. However, only the expansion pattern, but not translation pattern, generated significant MAE at the
mirror site. This remained true even after we adjusted stimulus parameters to equate the strengths of the expansion MAE and translation
MAE at the adapted site. We conclude that there is cross-fixation transfer of MAE for expansion motion but not for translational
motion.

A Simple Growth Model Constructs Critical Avalanche Networks

by L.F. Abbott and R Rohrkemper (2006)

Prog. Brain Res.

**165**:13-19Neurons recorded from electrode arrays show a remarkable scaling property in their bursts
of spontaneous activity, referred to as "avalanches' (Beggs and Plentz, 2003 & 2004). Such
scaling suggests a critical property in the coupling of these circuits. We show that similar
scaling laws can arise in a simple model for the growth of neuronal processes. In the model
(Van Ooyen and Van Pelt, 1994 & 1996), the spatial range of the processes extending from
each neuron is represented by a circle that grows or shrinks as a function of the average
intracellular calcium concentration. Neurons interact when the circles corresponding to
their processes intersect, with a strength proportional to the area of overlap.

Synaptic Democracy in Active Dendrites

by C.C. Rumsey and L.F. Abbott (2006)

J. Neurophys.

**96**:2307-2318Given the extensive attenuation
that can occur along dendritic cables, location within the dendritic tree
might appear to be a dominant factor in determining the impact of a
synapse on the postsynaptic response. By this reasoning, distal syn-
apses should have a smaller effect than proximal ones. However,
experimental evidence from several types of neurons, such as CA1
pyramidal cells, indicates that a compensatory strengthening of syn-
apses counteracts the effect of location on synaptic efficacy. A form
of spike-timing-dependent plasticity (STDP), called anti-STDP, com-
bined with non-Hebbian activity-dependent plasticity can account for
the equalization of synaptic efficacies. This result, obtained originally
in models with unbranched passive cables, also arises in multi-
compartment models with branched and active dendrites that feature
backpropagating action potentials, including models with CA1 py-
ramidal morphologies. Additionally, when dendrites support the local
generation of action potentials, anti-STDP prevents runaway dendritic
spiking and locally balances the numbers of dendritic and backpropa-
gating action potentials. Thus in multiple ways, anti-STDP eliminates
the location dependence of synapses and allows Hebbian plasticity to
operate in a more "democratic" manner.

A Comparison among some Models of V1 Orientation Selectivity

Andrew F. Teich and Ning Qian (2006)

J. Neurophysiol.

**96**:404-419 Several models
exist for explaining primary visual cortex (V1) orientation tuning. The
modified feedforward model (MFM) and the recurrent model (RM)
are major examples. We have implemented these two models, at the
same level of detail, alongside a few newer variations, and thoroughly
compared their receptive-field structures. We found that antiphase
inhibition in the MFM enhances both spatial phase information and
orientation tuning, producing well-tuned simple cells. This remains
true for a newer version of the MFM that incorporates untuned
complex-cell inhibition. In contrast, when the recurrent connections in
the RM are strong enough to produce typical V1 orientation tuning,
they also eliminate spatial phase information, making the cells com-
plex. Introducing phase specificity into the connections of the RM (as
done in an original version of the RM) can make the cells phase
sensitive, but the cells show an incorrect 90¡ peak shift of orientation
tuning under opposite contrast signs. An inhibition-dominant version
of the RM can generate well-tuned cells across the simpleÐ complex
spectrum, but it predicts that the net effect of cortical interactions is to
suppress feedforward excitation across all orientations in simple cells.
Finally, adding antiphase inhibition used in the MFM into the RM
produces a most general model. We call this new model the modified
recurrent model (MRM) and show that this model can also produce
well-tuned cells throughout the simpleÐ complex spectrum. Unlike the
inhibition-dominant RM, the MRM is consistent with data from cat
V1, suggesting that the net effect of cortical interactions is to boost
simple cell responses at the preferred orientation. These results sug-
gest that the MFM is well suited for explaining orientation tuning in
simple cells, whereas the standard RM is for complex cells. The
assignment of the RM to complex cells also avoids conflicts between
the RM and the experiments of cortical inactivation (done on simple
cells) and the spatial-frequency dependency of orientation tuning
(found in simple cells). Because orientation-tuned V1 cells show a
continuum of simple- to complex-cell behavior, the MRM provides
the best description of V1 data.

Extending the Effects of STDP to Behavioral Timescales

by P.J. Drew and L.F. Abbott (2006)

Proc. Natl. Acad. Sci. USA,

**103**:8876-8881Activity-dependent modification of synaptic strengths due to
spike-timing-dependent plasticity (STDP) is sensitive to correlations
between pre- and postsynaptic firing over timescales of tens
of milliseconds. Temporal associations typically encountered in
behavioral tasks involve times on the order of seconds. To relate
the learning of such temporal associations to STDP, we must
account for this large discrepancy in timescales. We show that the
gap between synaptic and behavioral timescales can be bridged if
the stimuli being associated generate sustained responses that
vary appropriately in time. Synapses between neurons that fire
this way can be modified by STDP in a manner that depends on the
temporal ordering of events separated by several seconds even
though the underlying plasticity has a much smaller temporal
window.

Models and Properties of Power-Law Adaptation in Neural Systems

by P.J. Drew and L.F. Abbott (2006)

J. Neurophysiol.,

**96**:826-833.Many biological systems exhibit complex temporal behavior that cannot be adequately
characterized by a single time constant. This dynamics, observed from single channels up to the level of
human psychophysics, is often better described by power-law rather than exponential dependences on time.
We develop and study the properties of neural models with scale-invariant, power-law adaptation and contrast
them with the more commonly studied exponential case. Responses of an adapting firing-rate model to constant,
pulsed and oscillating inputs in both the power-law and exponential cases are considered. We construct a
spiking model with power-law adaptation based on a nested cascade of processes and show that it can be "programmed"
to produce a wide range of time delays. Finally, within a network model,
we use power-law adaptation to reproduce long-term features of the tilt aftereffect.

An Optimization Principle for Determining Movement Duration

Hirokazu Tanaka, John Krakauer and Ning Qian (2006)

J. Neurophysiol.

**95**:3875-3886Movement duration is an integral com-
ponent of motor control, but nearly all extant optimization models of
motor planning prefix duration instead of explaining it. Here we
propose a new optimization principle that predicts movement dura-
tion. The model assumes that the brain attempts to minimize move-
ment duration under the constraint of meeting an accuracy criterion.
The criterion is task and context dependent but is fixed for a given task
and context. The model determines a unique duration as a trade-off
between speed (time optimality) and accuracy (acceptable endpoint
scatter). We analyzed the model for a linear motor plant, and obtained
a closed-form equation for determining movement duration. By solv-
ing the equation numerically with specific plant parameters for the eye
and arm, we found that the model can reproduce saccade duration as
a function of amplitude (the main sequence), and arm-movement
duration as a function of the ratio of target distance to size (FittsÕs
law). In addition, it explains the dependency of peak saccadic speed
on amplitude and the dependency of saccadic duration on initial eye
position. Furthermore, for arm movements, the model predicts a
scaling relationship between peak velocity and distance and a reduc-
tion in movement duration with a moderate increase in viscosity.
Finally, for a linear plant, our model predicts a neural control signal
identical to that of the minimum-variance model set to the same
movement duration. This control signal is a smooth function of time
(except at the endpoint), in contrast to the discontinuous bangÐ bang
control found in the time-optimal control literature. We suggest that
one aspect of movement planning, as revealed by movement duration,
may be to assign an endpoint accuracy criterion for a given task and
context.

Adaptive filtering enhances information transmission in visual cortex

by Tatyana Sharpee, Hiroki Sugihara, Andrei Kurgansky, Sergei Rebrik, Michael Stryker and Kenneth Miller (2006)

Nature,

**439**February 23, 2006Sensory neuroscience seeks to understand how the brain encodes natural
environments. However, neural coding has largely been studied using
simplified stimuli. In order to assess whether the brain's coding
strategy depends on the stimulus ensemble, we apply a new
information-theoretic method that allows unbiased calculation of
neural filters (receptive fields) from responses to natural scenes or
other complex signals with strong multipoint correlations. In the cat
primary visual cortex we compare responses to natural inputs with
those to noise inputs matched for luminance and contrast. We find that
neural filters adaptively change with the input ensemble so as to
increase the information carried by the neural response about the
filtered stimulus. Adaptation affects the spatial frequency
composition of the filter, enhancing sensitivity to under-represented
frequencies in agreement with optimal encoding arguments. Adaptation
occurs over 40 s to many minutes, longer than most previously reported
forms of adaptation.

Where are the Switches on this Thing?

by L.F. Abbott (2006)

In J.L. van Hemmen and T.J. Sejnowski, eds.

**23 Problems in Systems Neuroscience**(Oxford University Press, Oxford) pp. 423-431.Controlled responses differ from reflexes because they can be turned off and
on. This is a critical part of what distinguishes animals from automatons. How
does the nervous system gate the flow of information so that a sensory
stimulus that elicits a strong response on some occasions, evokes no response
on others? A related question concerns how the flow of sensory information is
altered when we pay close attention to something as opposed to when we
ignore it. Most research in neuroscience focuses on circuits that directly respond
to stimuli or generate motor output. But what of the circuits and
mechanisms that control these direct responses, that modulate them and turn
them off and on?

Self-regulated switching is vital to the operation of complex machines such as computers. The essential building block of a computer is a voltage-gated switch, the transistor, that is turned off and on by the same sorts of currents that it controls. By analogy, the question of my title refers to neural pathways that not only carry the action potentials that arise from neural activity, but are switched off and on by neural activity as well. By what biophysical mechanisms could this occur?

In the spirit of this volume, the point of this contribution is to raise a question, not to answer it. I will discuss three possible mechanisms— neuromodulation, inhibition, and gain modulation—and assess the merits and short-comings of each of them. I have my prejudices, which will become obvious, but I do not want to rule out any of these as candidates, nor do I want to leave the impression that the list is complete or that the problem is in any sense solved.

Self-regulated switching is vital to the operation of complex machines such as computers. The essential building block of a computer is a voltage-gated switch, the transistor, that is turned off and on by the same sorts of currents that it controls. By analogy, the question of my title refers to neural pathways that not only carry the action potentials that arise from neural activity, but are switched off and on by neural activity as well. By what biophysical mechanisms could this occur?

In the spirit of this volume, the point of this contribution is to raise a question, not to answer it. I will discuss three possible mechanisms— neuromodulation, inhibition, and gain modulation—and assess the merits and short-comings of each of them. I have my prejudices, which will become obvious, but I do not want to rule out any of these as candidates, nor do I want to leave the impression that the list is complete or that the problem is in any sense solved.

Signal Propagation and Logic Gating in Networks of Integrate-and-Fire Neurons

by T.P. Vogels and L.F. Abbott (2005)

J. Neurosci.,

**25**:10786-10795.Transmission of signals within the brain is
essential for cognitive function, but it is not clear how neural
circuits support reliable and accurate signal propagation over a
sufficiently large dynamic range. Two modes of propagation have been
studied: synfire chains, in which synchronous activity travels through
feedforward layers of a neuronal network, and the propagation of
fluctuations in firing rate across these layers. In both cases, a
sufficient amount of noise, which was added to previous models from an
external source, had to be included to support stable
propagation. Sparse, randomly connected networks of spiking model
neurons can generate chaotic patterns of activity. We investigate
whether this activity, which is a more realistic noise source, is
sufficient to allow for signal transmission. We find that, for
rate-coded signals but not for synfire chains, such networks support
robust and accurate signal reproduction through up to six layers if
appropriate adjustments are made in synaptic strengths. We investigate
the factors affecting transmission and show that multiple signals can
propagate simultaneously along different pathways. Using this feature,
we show how different types of logic gates can arise within the
architecture of the random network through the strengthening of
specific synapses.

The oblique effect depends on perceived, rather than physical, orientation and direction

Xin Meng and Ning Qian (2005)

Vision Research,

**45**:3402-3413Observers can better discriminate orientation or direction near the cardinal axes than near an oblique axis. We investigated
whether this well-known oblique effect is determined by the physical or the perceived axis of the stimuli. Using the simultaneous
tilt illusion, we generated perceptually different orientations for the same inner (target) grating by contrasting it with differently
oriented outer gratings. Subjects compared the target orientation with a set of reference orientations. If orientation discrimina-
bility was determined by the physical orientations, the psychometric curves for the same target grating would be identical.
Instead, all subjects produced steeper curves when perceiving target gratings near vertically as opposed to more obliquely. This
result of orientation discrimination was confirmed by using adaptation-generated tilt aftereffect to manipulate the perceived ori-
entation of a given physical orientation. Moreover, we obtained the same result in direction discrimination by using motion repul-
sion to alter the perceived direction of a given physical direction. We conclude that when the perceived orientation or direction
differs from the physical orientation or direction, the oblique effect depends on perceived, rather than physical, orientation or
direction. Finally, as a by-product of the study, we found that, around the vertical direction, motion repulsion is much stronger
when the inducing direction is more clockwise to the test direction than when it is more counterclockwise.

Effects of Attention on Motion Repulsion

Yuzhi Chen, Xin Meng, Nestor Matthews, and Ning Qian (2005)

Vision Research,

**45**:1329-1339Motion repulsion involves interaction between two directions of motion. Since attention is known to bias interactions among
different stimuli, we investigated the effect of attentional tasks on motion repulsion. We used two overlapping sets of random dots
moving in different directions. When subjects had to detect a small speed-change or luminance change for dots along one direction,
the repulsive influence from the other direction was significantly reduced compared with the control case without attentional tasks.
However, when the speed-change could occur to either direction such that subjects had to attend both directions to detect the
change, motion repulsion was not different from the control. A further experiment showed that decreasing the difficulty of the atten-
tional task resulted in the disappearance of the attentional effect in the case of attention to one direction. Finally, over a wide range
of contrasts for the unattended direction, attention reduced repulsion measured with the attended direction. These results are con-
sistent with the physiological finding that strong attention to one direction of motion reduces inhibitory effects from the other
direction.

Is Depth Perception of Stereo Plaids Predicted by Intersection of Constraints, Vector Average or Second-order Feature?

Louise Delicato and Ning Qian (2005)

Vision Research,

**45**:75-89Stereo plaid stimuli were created to investigate whether depth perception is determined by an intersection of constraints (IOC) or
vector average (VA) operation on the Fourier components, or by the second-order (non-Fourier) feature in a pattern. We first cre-
ated stereo plaid stimuli where IOC predicted vertical disparity, VA predicted positive diagonal disparity and the second-order fea-
ture predicted negative diagonal disparity. In a depth discrimination task, observers indicated whether they perceived the pattern as
near or far relative to a zero-disparity aperture. Observers perception was consistent with the disparity predicted by VA, indicat-
ing its dominance over IOC and the second-order feature in this condition. Additional stimuli in which VA predicted vertical dis-
parity were created to investigate whether VA would dominate perception when it was a less reliable cue. In this case, observers
performance was consistent with disparity predicted by IOC or the second-order feature, not VA. Finally, in order to determine
whether the second-order feature contributes to depth perception, stimuli were created where IOC and VA predicted positive hor-
izontal disparity while the second-order feature predicted negative horizontal disparity. When the component gratings were oriented
near horizontal (±83 from vertical), depth perception corresponded to that predicted by the second-order feature. However, as the
components moved away from horizontal (±75 and ±65 from vertical), depth perception was increasingly likely to be predicted by
an IOC or VA operation. These experiments suggest that the visual system does not rely exclusively on a single method for com-
puting pattern disparity. Instead, it favours the most reliable method for a given condition.