Blindfold learning of an accurate neural metric

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.

Biological neural networks need to be efficient and compact, as synapses and neurons require space to store and energy to operate and maintain. This favors an optimized network topology that minimizes redundant neurons and connections. Large numbers of extra neurons and synapses are produced during development, and later removed as the brain matures. A key question to understand this process is how neurons determine which synapses are important. We used statistical models of neural networks to simulate developmental pruning. We show that neurons in such networks can use locally available information to measure the importance of their synapses in a biologically plausible way. We demonstrate that this pruning rule, which is motivated by information theoretic considerations, retains network topologies that can efficiently encode sensory inputs. In contrast, pruning at random, or based on synaptic weights alone, was less able to identify redundant neurons.

Restricted Boltzmann Machines as Models of Interacting Variables

We study the type of distributions that restricted Boltzmann machines (RBMs) with different activation functions can express by investigating the effect of the activation function of the hidden nodes on the marginal distribution they impose on observed bi nary nodes. We report an exact expression for these marginals in the form of a model of interacting binary variables with the explicit form of the interactions depending on the hidden node activation function. We study the properties of these interactions in detail and evaluate how the accuracy with which the RBM approximates distributions over binary variables depends on the hidden node activation function and the number of hidden nodes. When the inferred RBM parameters are weak, an intuitive pattern is found for the expression of the interaction terms, which reduces substantially the differences across activation functions. We show that the weak parameter approximation is a good approximation for different RBMs trained on the MNIST data set. Interestingly, in these cases, the mapping reveals that the inferred models are essentially low order interaction models.

Thermodynamic Formalism in Neuronal Dynamics and Spike Train Statistics

The Thermodynamic Formalism provides a rigorous mathematical framework for studying quantitative and qualitative aspects of dynamical systems. At its core, there is a variational principle that corresponds, in its simplest form, to the Maximum Entropy principle. It is used as a statistical inference procedure to represent, by specific probability measures (Gibbs measures), the collective behaviour of complex systems. This framework has found applications in different domains of science. In particular, it has been fruitful and influential in neurosciences. In this article, we review how the Thermodynamic Formalism can be exploited in the field of theoretical neuroscience, as a conceptual and operational tool, in order to link the dynamics of interacting neurons and the statistics of action potentials from either experimental data or mathematical models. We comment on perspectives and open problems in theoretical neuroscience that could be addressed within this formalism.

Modeling a population of retinal ganglion cells with restricted Boltzmann machines

The retina is a complex circuit of the central nervous system whose aim is to encode visual stimuli prior the higher order processing performed in the visual cortex. Due to the importance of its role, modeling the retina to advance in interpreting its spiking activity output is a well studied problem. In particular, it has been shown that latent variable models can be used to model the joint distribution of Retinal Ganglion Cells (RGCs). In this work, we validate the applicability of Restricted Boltzmann Machines to model the spiking activity responses of a large a population of RGCs recorded with high-resolution electrode arrays. In particular, we show that latent variables can encode modes in the RGC activity distribution that are closely related to the visual stimuli. In contrast to previous work, we further validate our findings by comparing results associated with recordings from retinas under normal and altered encoding conditions obtained by pharmacological manipulation. In these conditions, we observe that the model reflects well-known physiological behaviors of the retina. Finally, we show that we can also discover temporal patterns, associated with distinct dynamics of the stimuli.

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.

Measures of Neural Similarity

One fundamental question is what makes two brain states similar. For example, what makes the activity in visual cortex elicited from viewing a robin similar to a sparrow? One common assumption in fMRI analysis is that neural similarity is described by Pearson correlation. However, there are a host of other possibilities, including Minkowski and Mahalanobis measures, with each differing in its mathematical, theoretical, and neural computational assumptions. Moreover, the operable measures may vary across brain regions and tasks. Here, we evaluated which of several competing similarity measures best captured neural similarity. Our technique uses a decoding approach to assess the information present in a brain region, and the similarity measures that best correspond to the classifier’s confusion matrix are preferred. Across two published fMRI datasets, we found the preferred neural similarity measures were common across brain regions but differed across tasks. Moreover, Pearson correlation was consistently surpassed by alternatives.

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.