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

arXiv:2602.07950 · cs.LG · Submitted 2026-02-08 · Read on arXiv

cs.LG

Submitted: 2026-02-08

Updated: 2026-09-06

Comments: 13 pages. Part II of the series. Substantially revised: withdraws the earlier compatible capacity threshold, unconditional volume-monotonicity claim, and universal dissipation-to-forgetting inference; reformulates the analysis around history-dependent reachability and task-conditioned adaptation cost. Includes counterexamples, an exact learning-retention frontier

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Continual Learning — 35× in this paper · explained in 2 episodes
• Adaptation — 10× in this paper · explained in 1 episode
• Adaptability — 7× in this paper · explained in 1 episode
• Catastrophic Forgetting — 5× in this paper · explained in 5 episodes
• Epistemic Speed Limit — 5× in this paper
• Optimal Transport — 5× in this paper · explained in 5 episodes
• Geometric Mismatch — 4× in this paper · explained in 2 episodes
• Degeneracy — 3× in this paper · explained in 3 episodes
• Lyapunov function — 2× in this paper · explained in 2 episodes
• Structural Constraints — 2× in this paper · explained in 2 episodes
• Wasserstein Distance — 2× in this paper · explained in 4 episodes
• Core — 1× in this paper · explained in 2 episodes
• Epistemic Uncertainty — 1× in this paper · explained in 9 episodes
• Fisher Information — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Objective Function — 1× in this paper · explained in 2 episodes
• Parameter Efficiency — 1× in this paper · explained in 3 episodes
• Regularization — 1× in this paper · explained in 3 episodes

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