Abstract
Visual cortical neurons often exhibit an approximately exponential distribution of their firing rates in response to natural stimulation (Baddeley et al., 1997). This may be motivated by a desire to maximize information carrying capacity given a fixed mean firing rate constraint, corresponding to a desired level of metabolic costs. However, it is not clear through what mechanisms cortical neurons may achieve this goal. One important candidate mechanism is intrinsic plasticity, i.e. the ability of a neuron to change its excitability through the adaptation of membrane properties. We have recently proposed a new model of intrinsic plasticity where a model neuron adapts its nonlinear activation function to obtain an approximately exponential distribution of its firing rate (Triesch, 2004). In combination with Hebbian learning at the synapses, we have shown that this leads to the discovery of sparse directions in the input.
In this work we apply the model to learning on natural images. We show that a single model neuron exposed to natural image patches that are processed by a simple LGN model, develops receptive fields that are localized and oriented and resemble Gabor wavelets. The model accounts for the approximately exponential distribution of firing rates observed in visual cortical neurons and the formation of simple-cell-like receptive fields.
When a two-dimensional layer of such model neurons with short ranging excitation and longer ranging inhibition is exposed to natural image input, we observe the formation of orientation maps with smoothly varying orientations between neighboring neurons.
BaddeleyR.AbbottL.F.BoothM.C.A.SengpielF.FreemanT.WakemanE.A.RollsE.T. (1997). Responses of neurons in primary and inferior temporal visual cortices to natural scenes. Proc. R. Soc. Lon. Ser. B, 264.
TrieschJ. (2004). Synergies between intrinsic and synaptic plasticity in individual model neurons. Advances in Neural Information Processing Systems (NIPS) 2004.