Degeneracy and Redundancy in Active Inference

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.