Publications

The architectures of biological neural networks result from developmental processes shaped by genetically encoded rules, biophysical constraints, stochasticity, and learning. Understanding these processes is crucial for comprehending neural circuits’ structure and function. The ability to reconstruct neural circuits, and even entire nervous systems, at the neuron and synapse level, facilitates the study of the design principles of neural systems and their developmental plan. Here, we investigate the developing connectome of C. elegans using statistical generative models based on simple biological features: neuronal cell type, neuron birth time, cell body distance, reciprocity, and synaptic pruning. Our models accurately predict synapse existence, degree profiles of individual neurons, and statistics of small network motifs. Importantly, these models require a surprisingly small number of neuronal cell types, which we infer and characterize. We further show that to replicate the experimentally-observed developmental path, multiple developmental epochs are necessary. Validation of our model’s predictions of the synaptic connections using multiple reconstructions of adult worms suggests that our model identified the fundamental “backbone” of the connectivity graph. The accuracy of the generative statistical models we use here offers a general framework for studying how connectomes develop and the underlying principles of their design.

Dale’s principle implies that biological neural networks are composed of neurons that are either excitatory or inhibitory. While the number of possible architectures of such Daleian networks is exponentially smaller than the number of non-Daleian ones, the computational and functional implications of using Daleian networks by the brain are mostly unknown. Here, we use models of recurrent spiking neural networks and rate-based ones to show, surprisingly, that despite the structural limitations on Daleian networks, they can approximate the computation performed by non-Daleian networks to a very high degree of accuracy. Moreover, we find that Daleian networks are more functionally robust to synaptic noise. We then show that unlike non-Daleian networks, Daleian ones can learn efficiently by tuning of single neuron features, nearly as well as learning by tuning individual synaptic weights. Importantly, this suggests a simpler and more biologically plausible learning mechanisms. We therefore suggest that in addition to architectural simplicity, Dale's principle confers computational and learning benefits for biological networks, and offer new directions for constructing and training biologically-inspired artificial neural networks.

The mapping of the wiring diagrams of neural circuits promises to allow us to link the structure and function of neural networks. Current approaches to analyzing such connectomes rely mainly on graph-theoretical tools, but these may downplay the complex nonlinear dynamics of single neurons and the way networks respond to their inputs. Here, we measure the functional similarity of simulated networks of neurons, by quantifying the similitude of their spiking patterns in response to the same stimuli. We find that common graph-theory metrics convey little information about the similarity of networks’ responses. Instead, we learn a functional metric between networks based on their synaptic differences and show that it accurately predicts the similarity of novel networks, for a wide range of stimuli. We then show that a sparse set of architectural features—the sum of synaptic inputs that each neuron receives and the sum of each neuron’s synaptic outputs—predicts the functional similarity of networks of up to 1000 neurons, with high accuracy. We thus suggest new architectural design principles that shape the function of neural networks. These architectural features conform with experimental evidence of homeostatic synaptic mechanisms.

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.

The social interactions underlying group foraging and their benefits have been mostly studied using mechanistic models replicating qualitative features of group behavior, and focused on a single resource or a few clustered ones. Here, we tracked groups of freely foraging adult zebrafish with spatially dispersed food items and found that fish perform stereotypical maneuvers when consuming food, which attract neighboring fish. We then present a mathematical model, based on inferred functional interactions between fish, which accurately describes individual and group foraging of real fish. We show that these interactions allow fish to combine individual and social information to achieve near-optimal foraging efficiency and promote income equality within groups. We further show that the interactions that would maximize efficiency in these social foraging models depend on group size, but not on food distribution - suggesting that fish may adaptively pick the subgroup of neighbors they 'listen to' to determine their own behavior.

The prefrontal cortex (PFC) plays an important role in regulating social functions in mammals, and its dysfunction has been linked to social deficits in neurodevelopmental disorders. Yet little is known of how the PFC encodes social information and how social representations may be altered in such disorders. Here, we show that neurons in the medial PFC of freely behaving male mice preferentially respond to socially relevant olfactory cues. Population activity patterns in this region differed between social and nonsocial stimuli and underwent experience-dependent refinement. In mice lacking the autism-associated gene Cntnap2, both the categorization of sensory stimuli and the refinement of social representations were impaired. Noise levels in spontaneous population activity were higher in Cntnap2 knockouts and correlated with the degree to which social representations were disrupted. Our findings elucidate the encoding of social sensory cues in the medial PFC and provide a link between altered prefrontal dynamics and autism-associated social dysfunction.

Recent developments in automated tracking allow uninterrupted, high-resolution recording of animal trajectories, sometimes coupled with the identification of stereotyped changes of body pose or other behaviors of interest. Analysis and interpretation of such data represents a challenge: the timing of animal behaviors may be stochastic and modulated by kinematic variables, by the interaction with the environment or with the conspecifics within the animal group, and dependent on internal cognitive or behavioral state of the individual. Existing models for collective motion typically fail to incorporate the discrete, stochastic, and internal-state- dependent aspects of behavior, while models focusing on individual animal behavior typically ignore the spatial aspects of the problem. Here we propose a probabilistic modeling framework to address this gap. Each animal can switch stochastically between different behavioral states, with each state resulting in a possibly different law of motion through space. Switching rates for behavioral transitions can depend in a very general way, which we seek to identify from data, on the effects of the environment as well as the interaction between the animals. We represent the switching dynamics as a Generalized Linear Model and show that: (i) forward simulation of multiple interacting animals is possible using a variant of the Gillespie's Stochastic Simulation Algorithm; (ii) formulated properly, the maximum likelihood inference of switching rate functions is tractably solvable by gradient descent; (iii) model selection can be used to identify factors that modulate behavioral state switching and to appropriately adjust model complexity to data. To illustrate our framework, we apply it to two synthetic models of animal motion and to real zebrafish tracking data.

Individual behavior, in biology, economics, and computer science, is often described in terms of balancing exploration and exploitation. Foraging has been a canonical setting for studying reward seeking and information gathering, from bacteria to humans, mostly focusing on individual behavior. Inspired by the gradient-climbing nature of chemotaxis, the infotaxis algorithm showed that locally maximizing the expected information gain leads to efficient and ethological individual foraging. In nature, as well as in theoretical settings, conspecifics can be a valuable source of information about the environment. Whereas the nature and role of interactions between animals have been studied extensively, the design principles of information processing in such groups are mostly unknown. We present an algorithm for group foraging, which we term "socialtaxis," that unifies infotaxis and social interactions, where each individual in the group simultaneously maximizes its own sensory information and a social information term. Surprisingly, we show that when individuals aim to increase their information diversity, efficient collective behavior emerges in groups of opportunistic agents, which is comparable to the optimal group behavior. Importantly, we show the high efficiency of biologically plausible socialtaxis settings, where agents share little or no information and rely on simple computations to infer information from the behavior of their conspecifics. Moreover, socialtaxis does not require parameter tuning and is highly robust to sensory and behavioral noise. We use socialtaxis to predict distinct optimal couplings in groups of selfish vs. altruistic agents, reflecting how it can be naturally extended to study social dynamics and collective computation in general settings.

The ability to record the joint activity of large groups of neurons would allow for direct study of information representation and computation at the level of whole circuits in the brain. The combinatorial space of potential population activity patterns and neural noise imply that-it would be impossible to directly map the relations between stimuli and population responses. Understanding of large neural population codes therefore depends on identifying simplifying design principles. We review recent results showing that strongly correlated population codes can be explained using minimal models that rely on low order relations among cells. We discuss the implications for large populations, and how such models allow for mapping the semantic organization of the neural codebook and stimulus space, and decoding.

Adaptation in the retina is thought to optimize the encoding of natural light signals into sequences of spikes sent to the brain. While adaptive changes in retinal processing to the variations of the mean luminance level and second-order stimulus statistics have been documented before, no such measurements have been performed when higher-order moments of the light distribution change. We therefore measured the ganglion cell responses in the tiger salamander retina to controlled changes in the second (contrast), third (skew) and fourth (kurtosis) moments of the light intensity distribution of spatially uniform temporally independent stimuli. The skew and kurtosis of the stimuli were chosen to cover the range observed in natural scenes. We quantified adaptation in ganglion cells by studying linear-nonlinear models that capture well the retinal encoding properties across all stimuli. We found that the encoding properties of retinal ganglion cells change only marginally when higher-order statistics change, compared to the changes observed in response to the variation in contrast. By analyzing optimal coding in LN-type models, we showed that neurons can maintain a high information rate without large dynamic adaptation to changes in skew or kurtosis. This is because, for uncorrelated stimuli, spatio-temporal summation within the receptive field averages away non-gaussian aspects of the light intensity distribution.

Social behavior in mammals is often studied in pairs under artificial conditions, yet groups may rely on more complicated social structures. Here, we use a novel system for tracking multiple animals in a rich environment to characterize the nature of group behavior and interactions, and show strongly correlated group behavior in mice. We have found that the minimal models that rely only on individual traits and pairwise correlations between animals are not enough to capture group behavior, but that models that include third-order interactions give a very accurate description of the group. These models allow us to infer social interaction maps for individual groups. Using this approach, we show that environmental complexity during adolescence affects the collective group behavior of adult mice, in particular altering the role of high-order structure. Our results provide new experimental and mathematical frameworks for studying group behavior and social interactions.

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.

In vision, two mixtures, each containing an independent set of many different wavelengths, may produce a common color percept termed "white." In audition, two mixtures, each containing an independent set of many different frequencies, may produce a common perceptual hum termed "white noise." Visual and auditory whites emerge upon two conditions: when the mixture components span stimulus space, and when they are of equal intensity. We hypothesized that if we apply these same conditions to odorant mixtures, "whiteness" may emerge in olfaction as well. We selected 86 molecules that span olfactory stimulus space and individually diluted them to a point of about equal intensity. We then prepared various odorant mixtures, each containing various numbers of molecular components, and asked human participants to rate the perceptual similarity of such mixture pairs. We found that as we increased the number of nonoverlapping, equal-intensity components in odorant mixtures, the mixtures became more similar to each other, despite not having a single component in common. With similar to 30 components, most mixtures smelled alike. After participants were acquainted with a novel, arbitrarily named mixture of similar to 30 equal-intensity components, they later applied this name more readily to other novel mixtures of similar to 30 equal-intensity components spanning stimulus space, but not to mixtures containing fewer components or to mixtures that did not span stimulus space. We conclude that a common olfactory percept, "olfactory white," is associated with mixtures of similar to 30 or more equal-intensity components that span stimulus space, implying that olfactory representations are of features of molecules rather than of molecular identity.

The way information is represented by sequences of action potentials of spiking neurons is determined by the input each neuron receives, but also by its biophysics, and the specifics of the circuit in which it is embedded. Even the "code" of identified neurons can vary considerably from individual to individual. Here we compared the neural codes of the identified H1 neuron in the visual systems of two families of flies, blow flies and flesh flies, and explored the effect of the sensory environment that the flies were exposed to during development on the H1 code. We found that the two families differed considerably in the temporal structure of the code, its content and energetic efficiency, as well as the temporal delay of neural response. The differences in the environmental conditions during the flies' development had no significant effect. Our results may thus reflect an instance of a family-specific design of the neural code. They may also suggest that individual variability in information processing by this specific neuron, in terms of both form and content, is regulated genetically.

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.

Information is carried in the brain by the joint activity patterns of large groups of neurons. Understanding the structure and function of population neural codes is challenging because of the exponential number of possible activity patterns and dependencies among neurons. We report here that for groups of similar to 100 retinal neurons responding to natural stimuli, pairwise-based models, which were highly accurate for small networks, are no longer sufficient. We show that because of the sparse nature of the neural code, the higher-order interactions can be easily learned using a novel model and that a very sparse low-order interaction network underlies the code of large populations of neurons. Additionally, we show that the interaction network is organized in a hierarchical and modular manner, which hints at scalability. Our results suggest that learnability may be a key feature of the neural code.

Odor identity is coded in spatiotemporal patterns of neural activity in the olfactory bulb. Here we asked whether meaningful olfactory information could also be read from the global olfactory neural population response. We applied standard statistical methods of dimensionality-reduction to neural activity from 12 previously published studies using seven different species. Four studies reported olfactory receptor activity, seven reported glomerulus activity, and one reported the activity of projection-neurons. We found two linear axes of neural population activity that accounted for more than half of the variance in neural response across species. The first axis was correlated with the total sum of odor-induced neural activity, and reflected the behavior of approach or withdrawal in animals, and odorant pleasantness in humans. The second and orthogonal axis reflected odorant toxicity across species. We conclude that in parallel with spatiotemporal pattern coding, the olfactory system can use simple global computations to read vital olfactory information from the neural population response.

LElectroolfactograms (EOGs) are the summated generator potentials of olfactory receptor neurons measured directly from the olfactory epithelium. To validate the sensory origin of the human EOG, we set out to ask whether EOGs measured in humans were odorant concentration dependent. Each of 22 subjects (12 women, mean age = 23.3 yr) was tested with two odorants, either valeric acid and linalool (n = 12) or isovaleric acid and l-carvone (n = 10), each delivered at four concentrations diluted with warm (37°C) and humidified (80%) odorless air. In behavior, increased odorant concentration was associated with increased perceived intensity (all F > 5, all P < 0.001). In EOG, increased odorant concentration was associated with increased area under the EOG curve (all F > 8, all P < 0.001). These findings substantiate EOG as a tool for probing olfactory coding directly at the level of olfactory receptor neurons in humans.

The concerted action of saccades and fixational eye movements are crucial for seeing stationary objects in the visual world. We studied how these eye movements contribute to retinal coding of visual information using the archer fish as a model system. We quantified the animal's ability to distinguish among objects of different sizes and measured its eye movements. We recorded from populations of retinal ganglion cells with a multielectrode array, while presenting visual stimuli matched to the behavioral task. We found that the beginning of fixation, namely the time immediately after the saccade, provided the most visual information about object size, with fixational eye movements, which consist of tremor and drift in the archer fish, yielding only a minor contribution. A simple decoder that combined information from

Biological networks have so many possible states that exhaustive sampling is impossible. Successful analysis thus depends on simplifying hypotheses, but experiments on many systems hint that complicated, higher-order interactions among large groups of elements have an important role. Here we show, in the vertebrate retina, that weak correlations between pairs of neurons coexist with strongly collective behaviour in the responses of ten or more neurons. We find that this collective behaviour is described quantitatively by models that capture the observed pairwise correlations but assume no higher-order interactions. These maximum entropy models are equivalent to Ising models, and predict that larger networks are completely dominated by correlation effects. This suggests that the neural code has associative or error-correcting properties, and we provide preliminary evidence for such behaviour. As a first test for the generality of these ideas, we show that similar results are obtained from networks of cultured cortical neurons.

A key issue in understanding the neural code for an ensemble of neurons is the nature and strength of correlations between neurons and how these correlations are related to the stimulus. The issue is complicated by the fact that there is not a single notion of independence or lack of correlation. We distinguish three kinds: ( 1) activity independence; ( 2) conditional independence; and ( 3) information independence. Each notion is related to an information measure: the information between cells, the information between cells given the stimulus, and the synergy of cells about the stimulus, respectively. We show that these measures form an interrelated framework for evaluating contributions of signal and noise correlations to the joint information conveyed about the stimulus and that at least two of the three measures must be calculated to characterize a population code. This framework is compared with others recently proposed in the literature. In addition, we distinguish questions about how information is encoded by a population of neurons from how that information can be decoded. Although information theory is natural and powerful for questions of encoding, it is not sufficient for characterizing the process of decoding. Decoding fundamentally requires an error measure that quantifies the importance of the deviations of estimated stimuli from actual stimuli. Because there is no a priori choice of error measure, questions about decoding cannot be put on the same level of generality as for encoding.

A population of neurons typically exhibits a broad diversity of responsesto sensory inputs. The intuitive notion of functional classification is thatcells can be clustered so that most of the diversity is captured by the identity of the clusters rather than by individuals within clusters. We showhow this intuition can be made precise using information theory, without any need to introduce a metric on the space of stimuli or responses.Applied to the retinal ganglion cells of the salamander, this approach recovers classical results, but also provides clear evidence for subclassesbeyond those identified previously. Further, we find that each of the ganglion cells is functionally unique, and that even within the same subclassonly a few spikes are needed to reliably distinguish between cells.

The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used by different neurons, or by corresponding neurons in different individuals. We present a quantitative formulation of this problem using ideas from information theory, and apply this approach to the analysis of experiments in the fly visual system. We find significant individual differences in the structure of the code, particularly in the way that temporal patterns of spikes are used to convey information beyond that available from variations in spike rate. On the other hand, all the flies in our ensemble exhibit a high coding efficiency, so that every spike carries the same amount of information in all the individuals. Thus the neural code has a quantifiable mixture of individuality and universality.

Derailed models of single neurons are typically focused on the dendritic tree and ignore the axonal tree, assuming that the axon is a simple transmission line. In the last 40 years, however, several theoretical and experimental studies have suggested that axone could implement information processing tasks by exploiting: 1) the time delay in action potential (AP) propagation along the axon; 2) the differential filtering of APs into the axonal subtrees; and 3) their activity-dependent excitability. Models for axonal trees have attempted to examine the feasibility of these ideas. However, because the physiological and anatomical data on axons are seriously limited, realistic models of axone have not been developed. The present paper summarizes the main insights that were gained from simplified models of axons; it also highlights the stochastic nature of axone, a topic that was largely neglected in classical models of axons. The advance of new experimental techniques makes it now possible to pay a very close experimental visit to axons. Theoretical tools and fast computers enable to go beyond the simplified models and to construct realistic models of axons. When tightly linked, experiments and theory will help to unravel how axons share the information processing tasks that single neurons implement.