Dynamical principles of habituation across substrates and scales

Abstract

Habituation is a basic form of learning in which a system's response to repeated stimulation progressively diminishes but eventually recovers when the stimulus is withheld. Long studied in animals, it has increasingly been observed in unicellular organisms and non-living devices such as electronic circuits and neuromorphic materials, suggesting underlying dynamical principles that recur across domains. This review asks what those principles are: given qualitative constraints imposed by habituation on a system's response, what is the minimal dynamical structure that satisfies them? We formalize the classical hallmarks of habituation as behavioral constraints on input--output behavior, show that linear time-invariant systems are structurally incompatible with these constraints, and construct nonlinear motifs---linear fading-memory dynamics composed with static nonlinearities---that exhibit the hallmarks across diverse settings. We relate these motifs to models of specific biological systems and to physical and algorithmic realizations, from analog circuits to transient computation in machine learning.