The optimal value of self-connection

The fact that reducing self-connections improves the performance of the autoassociative networks built by the pseudo-inverse learning rule is known already for quite a while, but is not studied completely yet. In particular , it is known that decreasing of self-connection increases the direct attraction radius of the network, but it also known that it increases the number of spurious dynamic attractors. Thus, it has been concluded that the optimal value of the coeecient of self-connection reduction D lies somewhere in the range (0;0.5). This paper gives an explicit answer to the question what is the optimal value of the self-connection reduction. It shows how the indirect attraction radius increases with the decrease of D. The summary of the results pertaining to the phenomenon is presented. An autoassociative neural network (AANN) is de-ned as a self-organizing network of N mutually interconnected two-state neurons 3, 30, 23], the evolution of which is determined by a synchronous update rule: y i (t + 1) = signns i (t)] = 1; if s i (t) > 0 ?1; otherwise ; (1) where s i (t) = P N j=1 C ji y j (t), or in vector form: ~ Y (t + 1) = signn ~ S(t)]; ~ S(t) = C ~ Y (t): (2) Column vector ~ Y (t) is referred to as the state of the network at time t and C is an NxN weight matrix. The self-organizing nature of the network is attributed to its ability to converge from an arbitrary state to a stable state, which is called an attractor. Theorem 1: As a result of free evolution, an AANN with symmetric weights converges to either a single stable state, called a static at-tractor, or a cycle consisting of exactly two states, called a dynamic attractor. A. Update ow neuro-processing technique Theorem 1 gives us an easy way of identifying dynamic attractors | the indices of the updated neurons should be stored until the next update. If at the next update they are the same, the network is trapped in a dynamic attractor. In 17] the update ow technique for updating the state of an AANN is introduced. It is based on storing only those neurons which have been updated in the last iteration, instead of storing the whole state vector. This technique is proved to be preferable on account of its high evaluation speed and suitability for …