Sparse coding for layered neural networks

We investigate storage capacity of two types of fully connected layered neural networks with sparse coding when binary patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network, in which a transfer function of even layers is different from that of odd layers. The other is a layered network with intra-layer connections, in which the transfer function of inter-layer is different from that of intra-layer, and inter-layered neurons and intra-layered neurons are updated alternately. We derive recursion relations for order parameters by means of the signal-to-noise ratio method, and then apply the self-control threshold method proposed by Dominguez and Bollé to both layered networks with monotonic transfer functions. We find that a critical value αC of storage capacity is about 0.11|alna|−1 (a⪡1) for both layered networks, where a is a neuronal activity. It turns out that the basin of attraction is larger for both layered networks when the self-control threshold method is applied.