Nonlinear Hebbian Learning as a Unifying Principle in Receptive Field Formation

Carlos S N Brito,Wulfram Gerstner,Jeff Beck

doi:10.1371/journal.pcbi.1005070

Abstract

The development of sensory receptive fields has been modeled in the past by a variety of models including normative models such as sparse coding or independent component analysis and bottom-up models such as spike-timing dependent plasticity or the Bienenstock-Cooper-Munro model of synaptic plasticity. Here we show that the above variety of approaches can all be unified into a single common principle, namely nonlinear Hebbian learning. When nonlinear Hebbian learning is applied to natural images, receptive field shapes were strongly constrained by the input statistics and preprocessing, but exhibited only modest variation across different choices of nonlinearities in neuron models or synaptic plasticity rules. Neither overcompleteness nor sparse network activity are necessary for the development of localized receptive fields. The analysis of alternative sensory modalities such as auditory models or V2 development lead to the same conclusions. In all examples, receptive fields can be predicted a priori by reformulating an abstract model as nonlinear Hebbian learning. Thus nonlinear Hebbian learning and natural statistics can account for many aspects of receptive field formation across models and sensory modalities.

Highlights

Neurons in sensory areas of the cortex are optimally driven by stimuli with characteristic features that define the receptive field of the cell
We cut through the jungle of candidate explanations by demonstrating that a single principle is sufficient to explain receptive field development
We reveal that nonlinear Hebbian learning is sufficient for receptive field formation through sensory inputs

Summary

Introduction

Neurons in sensory areas of the cortex are optimally driven by stimuli with characteristic features that define the receptive field of the cell. The characteristic receptive fields of simple cells in V1 have been related to statistical properties of natural images [5]. These findings inspired various models, based on principles as diverse as sparse sensory representations [6], optimal information transmission [7], or synaptic plasticity [8]. Several studies highlighted possible connections between biological and normative justifications of sensory receptive fields [9, 10, 11, 12], in V1, and in other sensory areas [13], such as auditory [14, 15] and secondary visual cortex (V2) [16]

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Discussion

Conclusion