Degeneracy and Redundancy in Active Inference.

Noor Sajid,Karl J Friston,Cathy J Price,Thomas Parr,Thomas M Hope

doi:10.1093/cercor/bhaa148

Abstract

The notions of degeneracy and redundancy are important constructs in many areas, ranging from genomics through to network science. Degeneracy finds a powerful role in neuroscience, explaining key aspects of distributed processing and structure–function relationships in the brain. For example, degeneracy accounts for the superadditive effect of lesions on functional deficits in terms of a “many-to-one” structure–function mapping. In this paper, we offer a principled account of degeneracy and redundancy, when function is operationalized in terms of active inference, namely, a formulation of perception and action as belief updating under generative models of the world. In brief, “degeneracy” is quantified by the “entropy” of posterior beliefs about the causes of sensations, while “redundancy” is the “complexity” cost incurred by forming those beliefs. From this perspective, degeneracy and redundancy are complementary: Active inference tries to minimize redundancy while maintaining degeneracy. This formulation is substantiated using statistical and mathematical notions of degenerate mappings and statistical efficiency. We then illustrate changes in degeneracy and redundancy during the learning of a word repetition task. Finally, we characterize the effects of lesions—to intrinsic and extrinsic connections—using in silico disconnections. These numerical analyses highlight the fundamental difference between degeneracy and redundancy—and how they score distinct imperatives for perceptual inference and structure learning that are relevant to synthetic and biological intelligence.

Highlights

Degenerate functional architectures generally feature multiple pathways that are available to fulfill a particular functional endpoint (Tononi et al 1999; Price and Friston 2002; Friston and Price 2003)
We offer a principled account of degeneracy and redundancy, when function is operationalized in terms of active inference, namely, a formulation of perception and action as belief updating under generative models of the world
We investigated the relationship between redundancy and degeneracy in a generative model of word repetition

Summary

Introduction

Degenerate functional architectures generally feature multiple pathways that are available to fulfill a particular functional endpoint (Tononi et al 1999; Price and Friston 2002; Friston and Price 2003). A simple example would be that either the left or right hand could be used to “lift a cup.”. This provides a degenerate structure–function relationship that preserves function following damage because, in this example, the ability to lift a cup is conserved if only one hand is damaged. Being able to lift a cup with the right or left hand keeps “options open,” while using both hands would be redundant. When multiple functions can be supported by the same structures (i.e., when there is a many-to-many mapping between structure and function), the trade-off between degeneracy and redundancy becomes even more pronounced. When conducting fine-control tasks like painting or surgery, is it more efficient for both hands to be dextrous or is one “preferred hand” sufficient? In what follows, we try to answer this question using notions of Bayes optimality inherent in active inference (Friston, FitzGerald, et al 2017a)

Objectives

Conclusion