A Thermodynamic Theory of Learning Part II: History-Dependent Reachability and Continual Learning

תקציר מקורי באנגליתarXiv:2602.07950v3 Announce Type: replace Abstract: We formulate plasticity as target-dependent, finite-horizon reachability under history-dependent dynamics, using standard minimum-energy control theory. An extended state includes parameters and internal variables that affect future updates. Around a reference trajectory, the input-to-endpoint response and its controllability Gramian determine the minimum input energy for each reachable displacement. Minimizing this energy over the joint task target defines a task-conditioned adaptation cost, exact for the arbitrary-input linear model. A solvable learning-retention example shows that this cost can increase without any rank loss, and distinguishes small directional gain from an inaccessible direction. Wasserstein transport supplies a compl