Quantifying information stored in synaptic connections rather than in firing activities of neural networks

TL;DR

This paper introduces a theoretical framework to quantify the information stored in synaptic connections of neural networks, complementing existing measures based on neural firing activity.

Contribution

It develops analytical tools to measure mutual information in synaptic distributions, revealing synergistic interactions and formalizing heterogeneity in information encoding.

Findings

Supports the principle of distributed coding in neural firing activities.

Corroborates established insights on pattern storage capacity.

Discovers synergistic interactions among synapses, where joint information exceeds the sum of individual parts.

Abstract

A cornerstone of our understanding of both biological and artificial neural networks is that they store information in the strengths of synaptic connections among the neurons. However, in contrast to the well-established theory for quantifying information encoded by the firing activity of neural networks, there does not exist a framework for quantifying information stored in the network's connection distribution itself. Here, we develop a theoretical framework for synaptic information by using densely connected Hebbian networks performing autoassociative memory tasks and by modeling data patterns to be stored as log-normal distributions. Specifically, we derive analytical approximations for Shannon mutual information between the data and singletons, pairs, and arbitrary n-tuples of synaptic connections within the network. Our framework corroborates well-established insights regarding pattern storage capacity, supports the principle of distributed coding in neural firing activities, and formalizes the heterogeneity inherent in information encoding across synapses in a network. Notably, it discovers synergistic interactions among synapses, revealing that the information encoded jointly by all the synapses exceeds the 'sum of its parts'. Taken together, this study introduces a powerful, interpretable framework for quantitatively understanding information storage in the synapses of neural networks, one that illustrates the duality of synaptic connectivity and neural population activity in learning and memory.