Learning of Chunking Sequences in Cognition and Behavior
Fig 1
Two-layer network for learning chunking dynamics.
In this example, the input sequence (a, b, c, d, e) is presented repeatedly. Initially, all the synaptic connections within a matrix are similar with small random variations. Through learning distinct elementary modes associate to each of the five patterns through weights of the projection matrix Pki. In the elementary layer, the weights Vii′ in the directions a to b, b to c, and d to e are weakened (arrow thickness denotes coupling strength), while the weights in the opposite direction are strengthened. The Wjj′ follow a similar learning rule to three chunks: ab, c and de. Chunking, i.e. the information specifying the association between CM and EM, is learned in the coupling matrices Qij and Rji. The input in the perceptual layer is represented as non-overlapping binary patterns. For example, element a is the binary pattern sa = [11000100], input b is the binary pattern sb = [00100010], etc. Black circles represent inhibitory couplings, while arrowheads represent excitatory couplings. The number of elementary modes should be larger or equal to the number of patterns in a sequence. Note that there must be at least three units in each layer for a stable heteroclinic cycle to exist. It is not necessary that Ny < Nx, and any value such that Ny > 3, Nx > 3 can be used. i = 1, …, NX; j = 1, …, NY; k = 1…, M; NX ≥ M > 3.