Self-organizing maps based on limit cycle attractors

Recent efforts to develop large-scale brain and neurocognitive architectures have paid relatively little attention to the use of self-organizing maps (SOMs). Part of the reason for this is that most conventional SOMs use a static encoding representation: each input pattern or sequence is effectively represented as a fixed point activation pattern in the map layer, something that is inconsistent with the rhythmic oscillatory activity observed in the brain. Here we develop and study an alternative encoding scheme that instead uses sparsely-coded limit cycles to represent external input patterns/sequences. We establish conditions under which learned limit cycle representations arise reliably and dominate the dynamics in a SOM. These limit cycles tend to be relatively unique for different inputs, robust to perturbations, and fairly insensitive to timing. In spite of the continually changing activity in the map layer when a limit cycle representation is used, map formation continues to occur reliably. In a two-SOM architecture where each SOM represents a different sensory modality, we also show that after learning, limit cycles in one SOM can correctly evoke corresponding limit cycles in the other, and thus there is the potential for multi-SOM systems using limit cycles to work effectively as hetero-associative memories. While the results presented here are only first steps, they establish the viability of SOM models based on limit cycle activity patterns, and suggest that such models merit further study.