Optimal population coding by noisy spiking neurons

Abstract

In retina and in cortical slice the collective response of spiking neural populations is well described by "maximum-entropy" models in which only pairs of neurons interact. We asked, how should such interactions be organized to maximize the amount of information represented in population responses? To this end, we extended the linear-nonlinear-Poisson model of single neural response to include pairwise interactions, yielding a stimulus-dependent, pairwise maximum-entropy model. We found that as we varied the noise level in single neurons and the distribution of network inputs, the optimal pairwise interactions smoothly interpolated to achieve network functions that are usually regarded as discrete-stimulus decorrelation, error correction, and independent encoding. These functions reflected a trade-off between efficient consumption of finite neural bandwidth and the use of redundancy to mitigate noise. Spontaneous activity in the optimal network reflected stimulus-induced activity patterns, and single-neuron response variability overestimated network noise. Our analysis suggests that rather than having a single coding principle hardwired in their architecture, networks in the brain should adapt their function to changing noise and stimulus correlations.adaptation | neural networks | Ising model | attractor states P opulations of sensory neurons encode information about stimuli into sequences of action potentials, or spikes (1). Experiments with pairs or small groups of neurons have observed many different coding strategies (2-6): (i) independence, where each neuron responds independently to the stimulus, (ii) decorrelation, where neurons interact to give a decorrelated representation of the stimulus, (iii) error correction, where neurons respond redundantly, in patterns, to combat noise, and (iv) synergistic coding, where population activity patterns carry information unavailable from separate neurons.How should a network arrange its interactions to best represent an ensemble of stimuli? Theoretically, there has been controversy over what is the "correct" design principle for neural population codes (7-11). On the one hand, neurons have a limited repertoire of response patterns, and information is maximized by using each neuron to represent a different aspect of the stimulus. To achieve this, interactions in a network should be organized to remove correlations in network inputs and thus create a decorrelated network response. On the other hand, neurons are noisy, and noise is combatted via redundancy, where different patterns related by noise encode the same stimulus. To achieve this, interactions in a network should be organized to exploit existing correlations in neural inputs to compensate for noise-induced errors. Such a trade-off between decorrelation and noise reduction possibly accounts for the organization of several biological information processing systems, e.g., the adaptation of center-surround receptive fields to ambient light intensity (12-14), the structure of retinal ganglion cell mosaics (15-18),...

Intermediate intrinsic diversity enhances neural population coding

“…First, stimuli might be best encoded by groups of highly similar neurons, suggesting that averaging across the population of recorded neurons can compensate for unreliable spiking in any single neuron (10). Alternatively, stimuli might be best encoded by groups of heterogeneous neurons, suggesting that maximizing the representation of temporal features of the stimuli is important (12,27). We specifically chose to study how diverse groups collectively represent an identical stimulus to mimic features of the olfactory bulb, where 25-50 sister MCs projecting to the same glomerulus (5) each receive highly correlated stimulus-and respiration-driven synaptic input (26,(28)(29)(30).…”

“…In contrast, eliminating redundancy (also referred to as biological degeneracy, ref. 14) may make stimulus coding less robust to noise or damage (15), thus we hypothesized that an optimal coding strategy would require balancing diversity with feature similarity or overlap.Although theorists have previously explored this issue (12,16,17), analysis of the function of the diversity of real populations of neurons requires overcoming methodological hurdles associated with studying cell-to-cell variability (3, 4). Cell-level differences (that are typically averaged away) must be captured and quantified.…”

“…Such populations of neurons could efficiently represent complex stimuli by collectively covering the relevant stimulus space (1,9,10). Network interactions could further increase the efficiency of information transmission by decorrelating neural responses and reducing the redundancy between their outputs (11)(12)(13). In contrast, eliminating redundancy (also referred to as biological degeneracy, ref.…”

“…Although theorists have previously explored this issue (12,16,17), analysis of the function of the diversity of real populations of neurons requires overcoming methodological hurdles associated with studying cell-to-cell variability (3,4). Cell-level differences (that are typically averaged away) must be captured and quantified.…”

Cholinergic shaping of neural correlations

“…In this work, we do not assume that the noise is normally distributed (15,23,25,47); rather, we study a model in which neurons respond to the stimuli in a discrete manner (48) with a Poisson probability distribution (38). This distinction is of importance because theoretical studies show that taking into account the discrete nature of neural activity influences the way the brain encodes stimuli (38,48). When applying this more realistic method to investigate the role of the correlations' slope in neural encoding, we find that, as previous literature suggests (18), the encoding efficiency increases as the correlations' slope decreases.…”