Optimal Learning with Excitatory and Inhibitory synapses
This work addresses the fundamental understanding of neural circuit computation, particularly for brain circuits like the cerebellum involved in processing time-dependent signals, but it is incremental as it builds on existing statistical mechanics methods.
The study tackled the problem of storing associations between correlated analog signals in neural circuits, showing that optimal synaptic weight configurations achieve a capacity of 0.5 regardless of the excitatory-inhibitory weight ratio and feature a finite fraction of silent synapses.
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.