Basins of attraction in a perceptron-like neural network

We st udy the perfor mance of a neu ral net work of the per­ cept ron typ e. We isolate two important set s of pa rameters which ren ­ der t he network fau lt tolerant (existence of large basins of attraction ) in both hetero-as sociative and auto-associative systems and study t he size of the bas ins of attraction (the maximal allowable noise level still ens uring recognition ) for sets of random patterns. The releva nce of ou r result s to t he pe rcept ron's ability t o gene ralize are pointed out, as is t he role of diagonal couplings in t he fully connected Hopfield model.