# Contrasting information theoretic decompositions of modulatory and arithmetic interactions in neural information processing systems

## TL;DR

This paper applies an information theoretic framework to analyze how local neural processors use contextual input to modulate information transmission, revealing unique properties of contextual modulation compared to simple arithmetic operations.

## Contribution

It introduces a novel information decomposition method to characterize contextual modulation in neural systems, highlighting its distinct properties and potential applications.

## Key findings

- Contextual modulation differs from basic arithmetic operations in information processing.
- The decomposition reveals various forms of contextual modulation.
- Previous neural network models effectively utilize these properties for enhanced processing.

## Abstract

Biological and artificial neural systems are composed of many local processors, and their capabilities depend upon the transfer function that relates each local processor's outputs to its inputs. This paper uses a recent advance in the foundations of information theory to study the properties of local processors that use contextual input to amplify or attenuate transmission of information about their driving inputs. This advance enables the information transmitted by processors with two distinct inputs to be decomposed into those components unique to each input, that shared between the two inputs, and that which depends on both though it is in neither, i.e. synergy. The decompositions that we report here show that contextual modulation has information processing properties that contrast with those of all four simple arithmetic operators, that it can take various forms, and that the form used in our previous studies of artificial neural nets composed of local processors with both driving and contextual inputs is particularly well-suited to provide the distinctive capabilities of contextual modulation under a wide range of conditions. We argue that the decompositions reported here could be compared with those obtained from empirical neurobiological and psychophysical data under conditions thought to reflect contextual modulation. That would then shed new light on the underlying processes involved. Finally, we suggest that such decompositions could aid the design of context-sensitive machine learning algorithms.