Synchronization and Grammatical Inference in an Oscillating Elman Net

We have designed an architecture to span the gap between bio(cid:173) physics and cognitive science to address and explore issues of how a discrete symbol processing system can arise from the continuum, and how complex dynamics like oscillation and synchronization can then be employed in its operation and affect its learning. We show how a discrete-time recurrent "Elman" network architecture can be constructed from recurrently connected oscillatory associative memory modules described by continuous nonlinear ordinary dif(cid:173) ferential equations. The modules can learn connection weights be(cid:173) tween themselves which will cause the system to evolve under a clocked "machine cycle" by a sequence of transitions of attractors within the modules, much as a digital computer evolves by transi(cid:173) tions of its binary flip-flop attractors. The architecture thus em(cid:173) ploys the principle of "computing with attractors" used by macro(cid:173) scopic systems for reliable computation in the presence of noise. We have specifically constructed a system which functions as a finite state automaton that recognizes or generates the infinite set of six symbol strings that are defined by a Reber grammar.