Dissipative Learning: A Framework for Viable Adaptive Systems

2026-01-25

AI Summary

This work addresses the stability and sustainability of adaptive learning under resource constraints and dynamic environments by proposing the BEDS framework, which models learning as an evolution of compressed belief states subject to dissipation constraints, integrating information theory, thermodynamics, and information geometry. The core contributions include establishing a conditional optimality theorem that identifies Fisher–Rao regularization as the thermodynamically optimal strategy, unifying existing methods as special cases of a single dynamical equation, and introducing a novel classification of continual learning challenges into “crystallizable” and “sustainable” problems. The study further reveals the structural suboptimality of Euclidean regularization, interpreting overfitting as excessive crystallization and catastrophic forgetting as insufficient dissipation control, and proposes a new optimization criterion for continual learning grounded in system feasibility.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Life-Long and Continual Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

We propose a perspective in which learning is an intrinsically dissipative process. Forgetting and regularization are not heuristic add-ons but structural requirements for adaptive systems. Drawing on information theory, thermodynamics, and information geometry, we introduce the BEDS (Bayesian Emergent Dissipative Structures) framework, modeling learning as the evolution of compressed belief states under dissipation constraints. A central contribution is the Conditional Optimality Theorem, showing that Fisher-Rao regularization measuring change via information divergence rather than Euclidean distance is the unique thermodynamically optimal regularization strategy, achieving minimal dissipation. Euclidean regularization is shown to be structurally suboptimal. The framework unifies existing methods (Ridge, SIGReg, EMA, SAC) as special cases of a single governing equation. Within this view, overfitting corresponds to over-crystallization, while catastrophic forgetting reflects insufficient dissipation control. The framework distinguishes BEDS-crystallizable problems, where beliefs converge to stable equilibria, from BEDS-maintainable problems, which require continual adaptation. It extends naturally to continual and multi-agent systems, where viability, stability under adaptation and finite resources replaces asymptotic optimality as the primary criterion. Overall, this work reframes learning as maintaining viable belief states under dissipation constraints, providing a principled lens on forgetting, regularization, and stability.

Problem

• dissipative learning
• adaptive systems
• regularization
• catastrophic forgetting
• overfitting

Innovation

• Dissipative Learning
• Fisher-Rao Regularization
• Bayesian Emergent Dissipative Structures
• Conditional Optimality Theorem
• Continual Adaptation