Neural Population Coding Is Optimized by Discrete Tuning Curves

Abstract

The sigmoidal tuning curve that maximizes the mutual information for a Poisson neuron, or population of Poisson neurons, is obtained. The optimal tuning curve is found to have a discrete structure that results in a quantization of the input signal. The number of quantization levels undergoes a hierarchy of phase transitions as the length of the coding window is varied. We postulate, using the mammalian auditory system as an example, that the presence of a subpopulation structure within a neural population is consistent with an optimal neural code.

Role of Homeostasis in Learning Sparse Representations

“…This is, for instance, perfectly illustrated by the binary nature of the neural code in the auditory cortex of rats (DeWeese et al, 2003). Binary codes also emerge as optimal neural codes for rapid signal transmission (Bethge, Rotermund, & Pawelzik, 2003;Nikitin, Stocks, Morse, & McDonnell, 2009). With a binary event-based code, the cost is incremented only when a new neuron becomes active, regardless of the analog value.…”

Optimizing Neural Information Capacity through Discretization

“…Several theoretical groups have analyzed precisely this problem over the past 20 years (Brinkman et al, 2016; Brunel and Nadal, 1998; Ganguli and Simoncelli, 2014; Gjorgjieva et al, 2014; Harper and McAlpine, 2004; Kastner et al, 2015; McDonnell et al, 2006; Nikitin et al, 2009; Pitkow and Meister, 2012; Sharpee, 2014; Wei and Stocker, 2016). For the sake of specificity, our initial discussion will be for the case where discretization occurs at the level of single neurons, with neurons acting as threshold-like devices processing the same analogue inputs.…”

“…The answer depends on the reliability of individual neurons. When this reliability is low, redundant coding based on a single neuronal type provides more information about the stimulus compared to distributed coding using staggered thresholds (Kastner et al, 2015; McDonnell et al, 2006; Nikitin et al, 2009; Sharpee, 2014). When the reliability increases beyond a certain threshold, a distributed coding based on multiple thresholds, and therefore multiple neuronal types, transmits more information (Figure 1D).…”

“…It also depends upon metabolic constraints, such as the average spike rate across the population or its maximum. Considering the case where all neurons have the same noise level, we know that in the limit of very large noise, it will be optimal for all neurons to have the same threshold (Kastner et al, 2015; McDonnell et al, 2006; Nikitin et al, 2009; Sharpee, 2014). In the opposite limit of very small noise, the threshold distribution should match the input distribution.…”

Toward Functional Classification of Neuronal Types

“…Here, however, an interesting complication arises. It turns out that when multiple neurons encode the same input dimension, it might be optimal (in the sense of maximizing the Shannon mutual information about this input dimension) to assign these neurons different thresholds (Kastner et al, 2014; McDonnell et al, 2006; Nikitin et al, 2009). In this case, the neurons that encode the same dimensions would belong to separate classes, as has been observed in the retina (Kastner and Baccus, 2011).…”