Optimal learning with excitatory and inhibitory synapses

Alessandro Ingrosso

PLOS Computational Biology, 2020, vol. 16, issue 12, 1-24

Abstract: Characterizing the relation between weight structure and input/output statistics is fundamental for understanding the computational capabilities of neural circuits. In this work, I study the problem of storing associations between analog signals in the presence of correlations, using methods from statistical mechanics. I characterize the typical learning performance in terms of the power spectrum of random input and output processes. I show that optimal synaptic weight configurations reach a capacity of 0.5 for any fraction of excitatory to inhibitory weights and have a peculiar synaptic distribution with a finite fraction of silent synapses. I further provide a link between typical learning performance and principal components analysis in single cases. These results may shed light on the synaptic profile of brain circuits, such as cerebellar structures, that are thought to engage in processing time-dependent signals and performing on-line prediction.Author summary: A general analysis of learning with biological synaptic constraints in the presence of statistically structured signals is lacking. Here, analytical techniques from statistical mechanics are leveraged to analyze association storage between analog inputs and outputs with excitatory and inhibitory synaptic weights. The linear perceptron performance is characterized and a link is provided between the weight distribution and the correlations of input/output signals. This formalism can be used to predict the typical properties of perceptron solutions for single learning instances in terms of the principal component analysis of input and output data. This study provides a mean-field theory for sign-constrained regression of practical importance in neuroscience as well as in adaptive control applications.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pcbi00:1008536

DOI: 10.1371/journal.pcbi.1008536

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