Noise-Robust Modes of the Retinal Population Code Have the Geometry of "Ridges" and Correspond to Neuronal Communities

Optimal Encoding in Stochastic Latent-Variable Models

In this work we explore encoding strategies learned by statistical models of sensory coding in noisy spiking networks. Early stages of sensory communication in neural systems can be viewed as encoding channels in the information-theoretic sense. However, neural populations face constraints not commonly considered in communications theory. Using restricted Boltzmann machines as a model of sensory encoding, we find that networks with sufficient capacity learn to balance precision and noise-robustness in order to adaptively communicate stimuli with varying information content. Mirroring variability suppression observed in sensory systems, informative stimuli are encoded with high precision, at the cost of more variable responses to frequent, hence less informative stimuli. Curiously, we also find that statistical criticality in the neural population code emerges at model sizes where the input statistics are well captured. These phenomena have well-defined thermodynamic interpretations, and we discuss their connection to prevailing theories of coding and statistical criticality in neural populations.

Clustering of Neural Activity: A Design Principle for Population Codes

We propose that correlations among neurons are generically strong enough to organize neural activity patterns into a discrete set of clusters, which can each be viewed as a population codeword. Our reasoning starts with the analysis of retinal ganglion cell data using maximum entropy models, showing that the population is robustly in a frustrated, marginally sub-critical, or glassy, state. This leads to an argument that neural populations in many other brain areas might share this structure. Next, we use latent variable models to show that this glassy state possesses well-defined clusters of neural activity. Clusters have three appealing properties: (i) clusters exhibit error correction, i.e., they are reproducibly elicited by the same stimulus despite variability at the level of constituent neurons; (ii) clusters encode qualitatively different visual features than their constituent neurons; and (iii) clusters can be learned by downstream neural circuits in an unsupervised fashion. We hypothesize that these properties give rise to a "learnable" neural code which the cortical hierarchy uses to extract increasingly complex features without supervision or reinforcement.

Modeling the Correlated Activity of Neural Populations: A Review

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the importance of collective effects in populations of neurons, only in the past two decades has it become possible to record from many cells simultaneously using advanced experimental techniques with single-spike resolution and to relate these correlations to function and behavior. This review focuses on the modeling and inference approaches that have been recently developed to describe the correlated spiking activity of populations of neurons. We cover a variety of models describing correlations between pairs of neurons, as well as between larger groups, synchronous or delayed in time, with or without the explicit influence of the stimulus, and including or not latent variables. We discuss the advantages and drawbacks or each method, as well as the computational challenges related to their application to recordings of ever larger populations.

The structured 'low temperature' phase of the retinal population code

Recent advances in experimental techniques have allowed the simultaneous recordings of populations of hundreds of neurons, fostering a debate about the nature of the collective structure of population neural activity. Much of this debate has focused on the empirical findings of a phase transition in the parameter space of maximum entropy models describing the measured neural probability distributions, interpreting this phase transition to indicate a critical tuning of the neural code. Here, we instead focus on the possibility that this is a first-order phase transition which provides evidence that the real neural population is in a 'structured', collective state. We show that this collective state is robust to changes in stimulus ensemble and adaptive state. We find that the pattern of pairwise correlations between neurons has a strength that is well within the strongly correlated regime and does not require fine tuning, suggesting that this state is generic for populations of 100+ neurons. We find a clear correspondence between the emergence of a phase transition, and the emergence of attractor-like structure in the inferred energy landscape. A collective state in the neural population, in which neural activity patterns naturally form clusters, provides a consistent interpretation for our results.