Training the integrate-and-fire model with the informax principle: I

In terms of the informax principle, and the input-output relationship of the integrate-and-fire (IF) model, IF neuron learning rules are developed. For supervised learning and with uniform weight of synapses (the theoretically tractable case), we show that the derived learning rule is stable and the stable state is unique. For unsupervised learning, within physiologically reasonable parameter regions, both long-term potentiation (LTP) and long-term depression (LTD) could happen when the inhibitory input is weak, but LTD cannot be observed when inhibitory input is strong enough. When both LTP and LTD occur, LTD is observable when the output of the postsynaptic neuron is faster than pre-synaptic inputs, otherwise LTP is observable, as observed in recent experiments. Learning rules of general cases are also studied and numerical examples show that the derived learning rule tends to equalize the contribution of different inputs to the output firing rates.

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