Temporal receptive fields, spikes, and Hebbian delay selection

The intriguing concept of a receptive field evolving through Hebbian learning, mostly during ontogeny, has been discussed extensively in the context of the visual cortex receiving spatial input from the retina. Here, we analyze an extension of this idea to the temporal domain. In doing so, we indicate how a particular spike-based learning rule can be described by means of a mean-field learning equation and present a solution for a couple of illustrative examples. We argue that the success of the learning procedure strongly depends on an interplay of, in particular, the temporal parameters of neuron (model) and learning window, and show under what conditions the noisy synaptic dynamics can be regarded as a diffusion process.