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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.
Emerging evidence indicates that protein synthesis and degradation are necessary for the remodeling of synapses. These two processes govern cellular protein turnover, are tightly regulated, and are modulated by neuronal activity in time and space. The anisotropic anatomy of the neurons presents a challenge for the study of protein turnover, but the understanding of protein turnover in neurons and its modulation in response to activity can help us to unravel the fine-tuned changes that occur at synapses in response to activity. Here we review the key experimental evidence demonstrating the role of protein synthesis and degradation in synaptic plasticity, as well as the turnover rates of specific neuronal proteins.