Available phase space and robustness of the layered feed-forward neural network

Abstract

We have studied numerically the basin of attraction of learned patterns and the phase-space fraction available to them in a layered feed-forward model with iterated learning rule. We observe a new transition at α∓ 0.03, apart from the discontinuous one at α∓0.18 reported earlier for the model (α is the fraction of the number of learned patterns to the number of neurons in a layer). These two transitions are speculated to be identical to the corresponding transitions at α∓0.05 and α∓0.14 (discontinuous) in the Hopfield model, which occurs in the first few layers, and finally shift in position due to amplification (and filtration) effect of the layered systems. The robustness of such a layered network against the loss of neurons in some intermediate layers is also studied.