Synaptic organizations and dynamical properties of weakly connected neural oscillators.
II. Learning phase information

Biological Cybernetics (1996) 75:129--135

Frank C. Hoppensteadt and Eugene M. Izhikevich

Systems Science Center, Box 7606,
Arizona State University,
Tempe, AZ 85287-7606.

Abstract. This is the second of two articles devoted to analyzing the relationship between synaptic organizations (anatomy) and dynamical properties (function) of networks of neural oscillators near multiple supercritical Andronov-Hopf bifurcation points. Here we analyze learning processes in such networks.

Regarding learning dynamics, we assume
1) Learning is local (i.e. synaptic modification depends on pre- and post-synaptic neurons but not on others).
2) Synapses modify slowly relative to characteristic neuron response times.
3) In absence of either pre- or post-synaptic activity, the synapse weakens (forgets).

Our major goal is to analyze all synaptic organizations of oscillatory neural networks that can memorize and retrieve phase information or time delays. We show that such networks have the following attributes

• The rate of synaptic plasticity connected with learning is determined locally by the pre-synaptic neurons.
  
• The excitatory neurons must be long-axon relay neurons capable of forming distant connections with other excitatory and inhibitory neurons.
  
• If inhibitory neurons have long axons, then the network can learn, passively forget and actively unlearn information by adjusting synaptic plasticity rates.

Keywords: Weakly connected neural networks -- Neural oscillators -- Multiple Andronov-Hopf bifurcation -- Canonical model -- Phase differences -- Synchronization -- Memory -- Unlearning -- Synaptic organizations -- Dale's principle -- Local circuit neurons

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