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

Ising-like model replicating time-averaged spiking behaviour of in vitro neuronal networks

We analyze time-averaged experimental data from in vitro activities of neuronal networks. Through a Pairwise Maximum-Entropy method, we identify through an inverse binary Ising-like model the local fields and interaction couplings which best reproduce the average activities of each neuron as well as the statistical correlations between the activities of each pair of neurons in the system. The specific information about the type of neurons is mainly stored in the local fields, while a symmetric distribution of interaction constants seems generic. Our findings demonstrate that, despite not being directly incorporated into the inference approach, the experimentally observed correlations among groups of three neurons are accurately captured by the derived Ising-like model. Within the context of the thermodynamic analogy inherent to the Ising-like models developed in this study, our findings additionally indicate that these models demonstrate characteristics of second-order phase transitions between ferromagnetic and paramagnetic states at temperatures above, but close to, unity. Considering that the operating temperature utilized in the Maximum-Entropy method isT o = 1 , this observation further expands the thermodynamic conceptual parallelism postulated in this work for the manifestation of criticality in neuronal network behavior.

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.

Ensemble inhibition and excitation in the human cortex: An Ising-model analysis with uncertainties

The pairwise maximum entropy model, also known as the Ising model, has been widely used to analyze the collective activity of neurons. However, controversy persists in the literature about seemingly inconsistent findings, whose significance is unclear due to lack of reliable error estimates. We therefore develop a method for accurately estimating parameter uncertainty based on random walks in parameter space using adaptive Markov-chain Monte Carlo after the convergence of the main optimization algorithm. We apply our method to the activity patterns of excitatory and inhibitory neurons recorded with multielectrode arrays in the human temporal cortex during the wake-sleep cycle. Our analysis shows that the Ising model captures neuronal collective behavior much better than the independent model during wakefulness, light sleep, and deep sleep when both excitatory (E) and inhibitory (I) neurons are modeled; ignoring the inhibitory effects of I neurons dramatically overestimates synchrony among E neurons. Furthermore, information-theoretic measures reveal that the Ising model explains about 80-95% of the correlations, depending on sleep state and neuron type. Thermodynamic measures show signatures of criticality, although we take this with a grain of salt as it may be merely a reflection of long-range neural correlations.

Clinical Impact of Spontaneous Hyperactivity in Degenerating Retinas: Significance for Diagnosis, Symptoms, and Treatment

Hereditary retinal degenerations result from varied pathophysiologic mechanisms, all ultimately characterized by photoreceptor dysfunction and death. Hence, much research on these diseases has concentrated on the outer retina. Over the past decade or so increasing attention has focused on concomitant changes in complex inner retinal neural circuits that process visual signals for transmission to the brain. One striking abnormality develops before the ultimately profound anatomic disruption of the inner retina. Highly elevated spontaneous activity was first demonstrated in central nervous system visual centers in vivo by Dräger and Hubel (1978), and subsequently has been confirmed in vitro, now in multiple animal models and by multiple investigators (see other contributions to this Research Topic). What evidence exists that this phenomenon occurs in human patients with retinal degeneration, and what is the ultimate effect of spontaneous hyperactivity in the output neurons, the retinal ganglion cells? Here I summarize abnormalities of visual perception among patients with retinal degeneration that may arise from hyperactivity. Next, I consider the disruption of neural encoding and anatomic connectivity that may result within the retina and in downstream visual centers of the brain. I then consider how specific characteristics of hyperactivity may distinguish various forms or stages of retinal degeneration, potentially helping in the near future to refine diagnosis and/or treatment choices for different patients. Finally, I review how consideration of these features may help optimize pharmacologic, gene, stem cell, prosthetic or other therapies to forestall visual loss or restore sight.