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The Fisher information constitutes a natural measure for the sensitivity of a probability distribution with respect to a set of parameters. An implementation of the stationarity principle for synaptic learning in terms of the Fisher information results in a Hebbian self-limiting learning rule for synaptic plasticity. In the present work, we study the dependence of the solutions to this rule in terms of the moments of the input probability distribution and find a preference for non-Gaussian directions, making it a suitable candidate for independent component analysis (ICA). We confirm in a numerical experiment that a neuron trained under these rules is able to find the independent components in the non-linear bars problem. The specific form of the plasticity rule depends on the transfer function used, becoming a simple cubic polynomial of the membrane potential for the case of the rescaled error function. The cubic learning rule is also an excellent approximation for other transfer functions, as the standard sigmoidal, and can be used to show analytically that the proposed plasticity rules are selective for directions in the space of presynaptic neural activities characterized by a negative excess kurtosis.
We present an effective model for timing-dependent synaptic plasticity (STDP) in terms of two interacting traces, corresponding to the fraction of activated NMDA receptors and the concentration in the dendritic spine of the postsynaptic neuron. This model intends to bridge the worlds of existing simplistic phenomenological rules and highly detailed models, thus constituting a practical tool for the study of the interplay of neural activity and synaptic plasticity in extended spiking neural networks. For isolated pairs of pre- and postsynaptic spikes, the standard pairwise STDP rule is reproduced, with appropriate parameters determining the respective weights and timescales for the causal and the anticausal contributions. The model contains otherwise only three free parameters, which can be adjusted to reproduce triplet nonlinearities in hippocampal culture and cortical slices. We also investigate the transition from time-dependent to rate-dependent plasticity occurring for both correlated and uncorrelated spike patterns.