Elements for a general memory structure: properties of recurrent neural networks used to form situation models

Abstract

We study how individual memory items are stored assuming that situations given in the environment can be represented in the form of synaptic-like couplings in recurrent neural networks. Previous numerical investigations have shown that specific architectures based on suppression or max units can successfully learn static or dynamic stimuli (situations). Here we provide a theoretical basis concerning the learning process convergence and the network response to a novel stimulus. We show that, besides learning "simple" static situations, a nD network can learn and replicate a sequence of up to n different vectors or frames. We find limits on the learning rate and show coupling matrices developing during training in different cases including expansion of the network into the case of nonlinear interunit coupling. Furthermore, we show that a specific coupling matrix provides low-pass-filter properties to the units, thus connecting networks constructed by static summation units with continuous-time networks. We also show under which conditions such networks can be used to perform arithmetic calculations by means of pattern completion.

Compact Internal Representation as a Functional Basis for Protocognitive Exploration of Dynamic Environments

“…As we shall show further the network can learn different static and time-evolving situations by an appropriate adjustment of the coupling matrix W. Learning rules can be described as teacher forcing based on the classical delta rule using the mismatch between the internal and external inputs (K'uhn et al, 2007;Makarov et al, 2008):…”

“…In (Makarov et al, 2008) we have shown that such a dynamic situation can be learned by using the following learning rule:…”

“…Thus the minimal training sequence of vectors consists of four time steps: ξ(1),...,ξ(4). Then the limit matrix is given by (Makarov et al, 2008;Villacorta-Atienza et al, 2010):…”

“…6). At each learning step k the network is exposed to one of the vectors and the learning follows the rule for static cases (K'uhn et al, 2007;Makarov et al, 2008):…”

“…It has been shown (Makarov et al, 2008) that the learning of static situations (i.e. of CIRs) can be always achieved by using a small enough learning rate satisfying to:…”