Efficient computation and cue integration with noisy population codes

Abstract

The brain represents sensory and motor variables through the activity of large populations of neurons. It is not understood how the nervous system computes with these population codes, given that individual neurons are noisy and thus unreliable. We focus here on two general types of computation, function approximation and cue integration, as these are powerful enough to handle a range of tasks, including sensorimotor transformations, feature extraction in sensory systems and multisensory integration. We demonstrate that a particular class of neural networks, basis function networks with multidimensional attractors, can perform both types of computation optimally with noisy neurons. Moreover, neurons in the intermediate layers of our model show response properties similar to those observed in several multimodal cortical areas. Thus, basis function networks with multidimensional attractors may be used by the brain to compute efficiently with population codes.

Optimal computation with attractor networks

“…In a subsequent study, we extended this finding to networks encoding multiple independent variables [6]. More recently, we presented simulations suggesting an even more general result: networks encoding multiple variables, related to one another through nonlinear transformations, can be tuned to perform optimal computation even when the reliability of the input variables change from trial to trial [7].…”

“…Let us consider a network in which several stimuli are encoded in hills of activity, and the noise among different hills is independent; networks of this type were shown by Deneve et al [7] to be able to perform a broad range of computations optimally. In this type of network, the tuning curve, fðsÞ, is concatenated into p tuning curves, fðsÞ ¼ ðf 1 ðsÞ; f 2 ðsÞ; .…”

A neural mechanism for coordinate transformation predicts pre-saccadic remapping

“…This type of modulation generates spatial representations that consist of localized, self-stabilizing activity peaks. A similar mechanism has been used by Denève et al (2001), while many previous descriptions and models of gain-modulated neurons had assumed linear or planar modulation based on a linear eye position signal A B Fig. 7 Modulation of visual response by gaze direction in the transformation field.…”

“…Pouget and colleagues presented a number of radial basis function models that successfully account for of reference frame transformations with population codes (Pouget and Sejnowski 1997) and provide a mechanism for sensor fusion by bidirectional transformations (Denève et al 2001;Pouget et al 2002). These models do not, however, address saccadic remapping.…”

“…In a neural network model, Zipser and Andersen (1988) have shown how a population of such gain-modulated neurons could perform a transformation of eye-centered visual input into a head-centered reference frame, given the current eye position. This mechanism has later been formalized and extended to multi-directional transformations by Pouget and colleagues (Pouget and Sejnowski 1997;Denève et al 2001).…”