Dynamical principles of habituation across substrates and scales

What the math gives to ML

The paper identifies a minimal mechanism for habituation: a nonlinear static input-output transformation driven by a linear fading-memory state. Its key negative result is that a linear time-invariant system cannot satisfy both response decrement under repeated stimulation and recovery after stimulus withdrawal, whereas a nonlinear gain or output nonlinearity can. A direct neural-network transfer is a stateful habituating layer that tracks recent feature or token exposure and suppresses its response through a bounded nonlinear gain, while exponential decay produces recovery. The mechanism makes falsifiable predictions about response decay, exponential recovery time, and the contrast with an otherwise matched LTI baseline.