Publications

The integration and transfer of information from multiple sources to multiple tar-
gets is a core motive of neural systems. The emerging field of partial information
decomposition (PID) provides a novel information-theoretic lens into these mecha-
nisms by identifying synergistic, redundant, and unique contributions to the mutual
information between one and several variables. While many works have studied
aspects of PID for Gaussian and discrete distributions, the case of general contin-
uous distributions is still uncharted territory. In this work we present a method
for estimating the unique information in continuous distributions, for the case of
one versus two variables. Our method solves the associated optimization problem
over the space of distributions with fixed bivariate marginals by combining copula
decompositions and techniques developed to optimize variational autoencoders.
We obtain excellent agreement with known analytic results for Gaussians, and illus-
trate the power of our new approach in several brain-inspired neural models. Our
method is capable of recovering the effective connectivity of a chaotic network of
rate neurons, and uncovers a complex trade-off between redundancy, synergy and
unique information in recurrent networks trained to solve a generalized XOR task.

We present a theory of neural circuits’ design and function, inspired by the random connectivity of real neural circuits and the mathematical power of random projections. Specifically, we introduce a family of statistical models for large neural population codes, a straightforward neural circuit architecture that would implement these models, and a biologically plausible learning rule for such circuits. The resulting neural architecture suggests a design principle for neural circuit—namely, that they learn to compute the mathematical surprise of their inputs, given past inputs, without an explicit teaching signal. We applied these models to recordings from large neural populations in monkeys’ visual and prefrontal cortices and show them to be highly accurate, efficient, and scalable.

We studied the fine temporal structure of spiking patterns of groups of up to 100 simultaneously recorded units in the prefrontal cortex of monkeys performing a visual discrimination task. We characterized the vocabulary of population activity patterns using 10 ms time bins and found that different sets of population activity patterns (codebooks) are used in different task epochs and that spiking correlations between units play a large role in defining those codebooks. Models that ignore those correlations fail to capture the population codebooks in all task epochs. Further, we show that temporal sequences of population activity patterns have strong history-dependence and are governed by different transition probabilities between patterns and different correlation time scales, in the different task epochs, suggesting different computational dynamics governing each epoch. Together, the large impact of spatial and temporal correlations on the dynamics of the population code makes the observed sequences of activity patterns many orders of magnitude more likely to appear than predicted by models that ignore these correlations and rely only on the population rates. Surprisingly, however, models that ignore these correlations perform quite well for decoding behavior from population responses. The difference of encoding and decoding complexity of the neural codebook suggests that one of the goals of the complex encoding scheme in the prefrontal cortex is to accommodate simple decoders that do not have to learn correlations.

Individual computations and social interactions underlying collective behavior in groups of animals are of great ethological, behavioral, and theoretical interest. While complex individual behaviors have successfully been parsed into small dictionaries of stereotyped behavioral modes, studies of collective behavior largely ignored these findings; instead, their focus was on inferring single, mode-independent social interaction rules that reproduced macroscopic and often qualitative features of group behavior. Here, we bring these two approaches together to predict individual swimming patterns of adult zebrafish in a group. We show that fish alternate between an "active" mode, in which they are sensitive to the swimming patterns of conspecifics, and a "passive" mode, where they ignore them. Using a model that accounts for these two modes explicitly, we predict behaviors of individual fish with high accuracy, outperforming previous approaches that assumed a single continuous computation by individuals and simple metric or topological weighing of neighbors' behavior. At the group level, switching between active and passive modes is uncorrelated among fish, but correlated directional swimming behavior still emerges. Our quantitative approach for studying complex, multi-modal individual behavior jointly with emergent group behavior is readily extensible to additional behavioral modes and their neural correlates as well as to other species.

Social encounters are associated with varying degrees of emotional arousal and stress. The mechanisms underlying adequate socioemotional balance are unknown. The medial amygdala (MeA) is a brain region associated with social behavior in mice. Corticotropin-releasing factor receptor type-2 (CRF-R2) and its specific ligand urocortin-3 (Ucn3), known components of the behavioral stress response system, are highly expressed in the MeA. Here we show that mice deficient in CRF-R2 or Ucn3 exhibit abnormally low preference for novel conspecifics. MeA-specific knockdown of Crfr2 (Crhr2) in adulthood recapitulated this phenotype. In contrast, pharmacological activation of MeA CRF-R2 or optogenetic activation of MeA Ucn3 neurons increased preference for novel mice. Furthermore, chemogenetic inhibition of MeA Ucn3 neurons elicited pro-social behavior in freely behaving groups of mice without affecting their hierarchal structure. These findings collectively suggest that the MeA Ucn3 CRF-R2 system modulates the ability of mice to cope with social challenges.

Information is carried in the brain by the joint spiking patterns of large groups of noisy, unreliable neurons. This noise limits the capacity of the neural code and determines how information can be transmitted and read-out. To accurately decode, the brain must overcome this noise and identify which patterns are semantically similar. We use models of network encoding noise to learn a thesaurus for populations of neurons in the vertebrate retina responding to artificial and natural videos, measuring the similarity between population responses to visual stimuli based on the information they carry. This thesaurus reveals that the code is organized in clusters of synonymous activity patterns that are similar in meaning but may differ considerably in their structure. This organization is highly reminiscent of the design of engineered codes. We suggest that the brain may use this structure and show how it allows accurate decoding of novel stimuli from novel spiking patterns.

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise'' models-being systematic extensions of the previously used pairwise Ising models-provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.

The visual system continually adjusts its sensitivity to the statistical properties of the environment through an adaptation process that starts in the retina. Colour perception and processing is commonly thought to occur mainly in high visual areas, and indeed most evidence for chromatic colour contrast adaptation comes from cortical studies. We show that colour contrast adaptation starts in the retina where ganglion cells adjust their responses to the spectral properties of the environment. We demonstrate that the ganglion cells match their responses to red-blue stimulus combinations according to the relative contrast of each of the input channels by rotating their functional response properties in colour space. Using measurements of the chromatic statistics of natural environments, we show that the retina balances inputs from the two ( red and blue) stimulated colour channels, as would be expected from theoretical optimal behaviour. Our results suggest that colour is encoded in the retina based on the efficient processing of spectral information that matches spectral combinations in natural scenes on the colour processing level.

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. For large populations, direct sampling of these distributions is impossible, and so we must rely on constructing appropriate models. We show here that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. We introduce the stimulus-dependent maximum entropy (SDME) model-a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. We find that the SDME model gives a more accurate account of single cell responses and in particular significantly outperforms uncoupled models in reproducing the distributions of population codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like average surprise and information transmission in a neural population.

Pattern classification learning tasks are commonly used to explore learning strategies in human subjects. The universal and individual traits of learning such tasks reflect our cognitive abilities and have been of interest both psychophysically and clinically. From a computational perspective, these tasks are hard, because the number of patterns and rules one could consider even in simple cases is exponentially large. Thus, when we learn to classify we must use simplifying assumptions and generalize. Studies of human behavior in probabilistic learning tasks have focused on rules in which pattern cues are independent, and also described individual behavior in terms of simple, single-cue, feature-based models. Here, we conducted psychophysical experiments in which people learned to classify binary sequences according to deterministic rules of different complexity, including high-order, multicue-dependent rules. We show that human performance on such tasks is very diverse, but that a class of reinforcement learning-like models that use a mixture of features captures individual learning behavior surprisingly well. These models reflect the important role of subjects' priors, and their reliance on high-order features even when learning a low-order rule. Further, we show that these models predict future individual answers to a high degree of accuracy. We then use these models to build personally optimized teaching sessions and boost learning.

Whisking mediated touch is an active sense whereby whisker movements are modulated by sensory input and behavioral context. Here we studied the effects of touching an object on whisking in head-fixed rats. Simultaneous movements of whiskers C1, C2, and D1 were tracked bilaterally and their movements compared. During free-air whisking, whisker protractions were typically characterized by a single acceleration-deceleration event, whisking amplitude and velocity were correlated, and whisk duration correlated with neither amplitude nor velocity. Upon contact with an object, a second acceleration-deceleration event occurred in about 25% of whisk cycles, involving both contacting (C2) and non-contacting (C1, D1) whiskers ipsilateral to the object. In these cases, the rostral whisker (C2) remained in contact with the object throughout the double-peak phase, which effectively prolonged the duration of C2 contact. These "touch-induced pumps'' (TIPs) were detected, on average, 17.9 ms after contact. On a slower time scale, starting at the cycle following first touch, contralateral amplitude increased while ipsilateral amplitude decreased. Our results demonstrate that sensory-induced motor modulations occur at various timescales, and directly affect object palpation.

The manner in which groups of neurons represent events in the external world is a central question in neuroscience. Estimation of the information encoded by small groups of neurons has shown that in many neural systems, cells carry mildly redundant information. These measures average over all the activity patterns of a neural population. Here, we analyze the population code of the salamander and guinea pig retinas by quantifying the information conveyed by specific multicell activity patterns. Synchronous spikes, even though they are relatively rare and highly informative, convey less information than the sum of either spike alone, making them redundant coding symbols. Instead, patterns of spiking in one cell and silence in others, which are relatively common and often overlooked as special coding symbols, were found to be mostly synergistic. Our results reflect that the mild average redundancy between ganglion cells that was previously reported is actually the result of redundant and synergistic multicell patterns, whose contributions partially cancel each other when taking the average over all patterns. We further show that similar coding properties emerge in a generic model of neural responses, suggesting that this form of combinatorial coding, in which specific compound patterns carry synergistic or redundant information, may exist in other neural circuits.

Collective navigation and swarming have been studied in animal groups, such as fish schools, bird flocks, bacteria, and slime molds. Computer modeling has shown that collective behavior of simple agents can result from simple interactions between the agents, which include short range repulsion, intermediate range alignment, and long range attraction. Here we study collective navigation of bacteria-inspired smart agents in complex terrains, with adaptive interactions that depend on performance. More specifically, each agent adjusts its interactions with the other agents according to its local environment - by decreasing the peers' influence while navigating in a beneficial direction, and increasing it otherwise. We show that inclusion of such performance dependent adaptable interactions significantly improves the collective swarming performance, leading to highly efficient navigation, especially in complex terrains. Notably, to afford such adaptable interactions, each modeled agent requires only simple computational capabilities with short-term memory, which can easily be implemented in simple swarming robots.

In retina and in cortical slice the collective response of spiking neural populations is well described by "maximum-entropy" models in which only pairs of neurons interact. We asked, how should such interactions be organized to maximize the amount of information represented in population responses? To this end, we extended the linear-nonlinear-Poisson model of single neural response to include pairwise interactions, yielding a stimulus-dependent, pairwise maximum-entropy model. We found that as we varied the noise level in single neurons and the distribution of network inputs, the optimal pairwise interactions smoothly interpolated to achieve network functions that are usually regarded as discrete-stimulus decorrelation, error correction, and independent encoding. These functions reflected a trade-off between efficient consumption of finite neural bandwidth and the use of redundancy to mitigate noise. Spontaneous activity in the optimal network reflected stimulus-induced activity patterns, and single-neuron response variability overestimated network noise. Our analysis suggests that rather than having a single coding principle hardwired in their architecture, networks in the brain should adapt their function to changing noise and stimulus correlations.

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the salamander retina responding to natural movies. We show that pairwise interactions between neurons account for observed higher-order correlations, and that for groups of 10 or more neurons pairwise interactions can no longer be regarded as small perturbations in an independent system. We then construct network ensembles that generalize the network instances observed in the experiment, and study their thermodynamic behavior and coding capacity. Based on this construction, we can also create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses. We examine closely two such behaviors that could be relevant for neural code: tuning of the network to the critical point to maximize the ability to encode diverse stimuli, and using the metastable states of the Ising Hamiltonian as neural code words.

Most of our knowledge about how the brain encodes information conies from recordings of single neurons. However, computations in the brain are carried out by large groups of neurons. Modelling the joint activity of many interacting elements is computationally hard because of the large number of possible activity patterns and limited experimental data. Recently it was shown in several different neural systems that maximum entropy pairwise models, which rely only on tiring rates and pairwise correlations of neurons, are excellent models for the distribution of activity patterns of neural populations, and in particular, their responses to natural stimuli. Using simultaneous recordings of large groups of neurons in the vertebrate retina responding to naturalistic stimuli, we show here that the relevant statistics required for finding the pan-wise model can be accurately estimated within seconds. Furthermore, while higher order statistics may, in theory, improve model accuracy, they are, in practice, harmful for times of up to 20 minutes due to sampling noise. Finally, we demonstrate that trading accuracy for entropy may actually improve model performance when data is limited, and suggest an optimization method that automatically adjusts model constraints in order to achieve good performance.

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that describe the correlated spiking activity of populations of 40 neurons in the retina, and show that pairwise interactions account for observed higher-order correlations. By first finding a representative ensemble for observed networks we can create synthetic networks of 120 neurons, and find that with increasing size the networks operate closer to a critical point and start exhibiting collective behaviors reminiscent of spin glasses.

We have explored the manner in which the population of retinal ganglion cells collectively represent the visual world. Ganglion cells in the salamander were recorded simultaneously with a multielectrode array during stimulation with both artificial and natural visual stimuli, and the mutual information that single cells and pairs of cells conveyed about the stimulus was estimated. We found significant redundancy between cells spaced as far as 500 mu m apart. When we used standard methods for defining functional types, only ON-type and OFF-type cells emerged as truly independent information channels. Although the average redundancy between nearby cell pairs was moderate, each ganglion cell shared information with many neighbors, so that visual information was represented 10-fold within the ganglion cell population. This high degree of retinal redundancy suggests that design principles beyond coding efficiency may be important at the population level.

Entropy and information provide natural measures of correlation among elements in a network. We construct here the information theoretic analog of connected correlation functions: irreducible N-point correlation is measured by a decrease in entropy for the joint distribution of N variables relative to the maximum entropy allowed by all the observed N-1 variable distributions. We calculate the "connected information" terms for several examples and show that it also enables the decomposition of the information that is carried by a population of elements about an outside source.

We present a novel pairwise clustering method. Given a proximity matrix of pairwise relations (i.e. pairwise similarity or dissimilarity estimates) between data points, our algorithm extracts the two most prominent clusters in the data set. The algorithm, which is completely nonparametric, iteratively employs a two-step transformation on the proximity matrix. The first step of the transformation represents each point by its relation to all other data points, and the second step re-estimates the pairwise distances using a statistically motivated proximity measure on these representations. Using this transformation, the algorithm iteratively partitions the data points, until it finally converges to two clusters. Although the algorithm is simple and intuitive, it generates a complex dynamics of the proximity matrices. Based on this bipartition procedure we devise a hierarchical clustering algorithm, which employs the basic bipartition algorithm in a straightforward divisive manner. The hierarchical clustering algorithm copes with the model validation problem using a general cross-validation approach, which may be combined with various hierarchical clustering methods.We further present an experimental study of this algorithm. We examine some of the algorithm's properties and performance on some synthetic and 'standard' data sets. The experiments demonstrate the robustness of the algorithm and indicate that it generates a good clustering partition even when the data is noisy or corrupted.

The reliability and accuracy of spike trains have been shown to depend on the nature of the stimulus that the neuron encodes. Adding ion channel stochasticity to neuronal models results in a macroscopic behavior that replicates the input-dependent reliability and precision of real neurons. We calculate the amount of information that an ion channel based stochastic Hodgkin-Huxley (HH) neuron model can encode about a wide set of stimuli. We show that both the information rate and the information per spike of the stochastic model are similar to the values reported experimentally Moreover, the amount of information that the neuron encodes is correlated with the amplitude of fluctuations in the input, and less so with the average firing rate of the neuron. We also show that for the HH ion channel density, the information capacity is robust to changes in the density of ion channels in the membrane, whereas changing the ratio between the Na+ and K+ ion channels has a considerable effect an the information that the neuron can encode. Finally, we suggest that neurons may maximize their information capacity by appropriately balancing the density of the different ion channels that underlie neuronal excitability.

The firing reliability and precision of an isopotential membrane patch consisting of a realistically large number of ion channels is investigated using a stochastic Hodgkin-Huxley (HH) model. In sharp contrast to the deterministic HH model, the biophysically inspired stochastic model reproduces qualitatively the different reliability and precision characteristics of spike firing in response to DC and fluctuating current input in neocortical neurons, as reported by Mainen & Sejnowski (1995). For DC inputs, spike timing is highly unreliable; the reliability and precision are significantly increased for fluctuating current input. This behavior is critically determined by the relatively small number of excitable channels that are opened near threshold for spike firing rather than by the total number of channels that exist in the membrane patch. Channel fluctuations, together with the inherent bistability in the HH equations, give rise to three additional experimentally observed phenomena: subthreshold oscillations in the membrane voltage for DC input, "spontaneous" spikes for subthreshold inputs, and "missing" spikes for suprathreshold inputs. We suggest that the noise inherent in the operation of ion channels enables neurons to act as "smart" encoders. Slowly varying, uncorrelated inputs are coded with low reliability and accuracy and, hence, the information about such inputs is encoded almost exclusively by the spike rate. On the other hand, correlated presynaptic activity produces sharp fluctuations in the input to the postsynaptic cell, which are then encoded with high reliability and accuracy. In this case, information about the input exists in the exact timing of the spikes. We conclude that channel stochasticity should be considered in realistic models of neurons.