Computational Models Relevant For Visual Cortex

Ann With Inhibitory Feedback-Loop Giving Infomax Outputs

The Harpur & Prager (1996) model is illustrated in Figure 1(a). It performs infomax by an unique ICA-like process without any explicit phase-processing. It anyway achieves statistical independence by recurrent opposite-weighted connections and by the resulting competition between “neurons”. Output weight-vectors represent Gabor-like wavelets.

The input vector is = (x₁,..., x_m); the output vector is = (a₁,..., a_n); feedforward (j -to-i) connection-weights are elements in the vector (= w_i1,..., w_im); their feedback (i-to-j) parallels are their negatives: -w_ij.

The ANN “algorithm”, which (iteratively) processes images by minimizing the discrepancy ||², is as follows:

• (index i belongs to the output “neuron(s)”);

• , 0<μ≤1 (µ is adjustable learning rate);

• (η is learning rate).

Comparing the model’s connectivity with an experimental report on the rat visual cortex¹, one can see similarities which suggest to relate with V1 and with the extrastriate cortex. Namely, it is reported that feedback connections from the extrastriate cortex “provide input directly to [V1’s pyramidal] neurons which make the reciprocal forward connection, and that feedback-recipient forward-projecting neurons are strongly interconnected”. However, Harpur & Prager (1996) neglect the direct intra-layer connections, so there is just indirect (although essential) mutual influence between “neurons” of the ”V1”-layer. The Baird (1990) model of networks of oscillators incorporates the reported extrastriate-to-striate “top-down” modulatory connectivity and the reported interconnections of forward-projecting excitatory neurons of V1, possibly.

Network Of Units With Coupled Oscillatory Activities, Embedded In Neuropil

By comparing subfigures of Figure 1, one sees that the Baird (1990) oscillatory ANN model has a loop-structure similar to the Olshausen & Field (1997) net and to the Harpur & Prager (1996) net, and fits the experimentally found striate–extrastriate loop. However, Baird considers the sources of inhibitory feedback as interneurons without (significant) connections other than with their excitatory partner in the main layer. Baird claims that he obeyed biological data and that his net, which can realize oscillatory content-addressable memory, could be relevant for modelling visual cortex (as well as the olfactory bulb). Baird’s model might reveal something about (Gabor) wavelet formation, but even more about formation of temporal sequences of images (visual episodes).

Figure 1.

(a) The Harpur & Prager (1996, p. 278) ANN. / (b) The Baird (1990, p. 370) oscillatory ANN. / (c) The Olshausen & Field (1997, p. 3317) net