On the design of artificial auto-associative neuronal networks

In this paper, we consider the problem of how to construct an artificial neuronal network such that it reproduces a given set of patterns in an exact manner. It turns out that the structure of the weight matrix of the network represents the structure of the set of patterns it is acting on, not the patterns themselves. Conditions are discussed under which the associative network memorizes a certain subset of these patterns. Our formal approach is based on the simple observation that neural networks are structured sets of neurons. By regarding recurrent neural networks as dynamical systems with symmetry, the category of G-sets and G-morphisms appears as a natural framework for evaluating their structure and functioning analytically.