Information as Structural Alignment: A Dynamical Theory of Continual Learning

TL;DR

This paper proposes the Informational Buildup Framework (IBF), a dynamical system-based approach to continual learning that inherently reduces forgetting by modeling information as structural alignment rather than stored content.

Contribution

It introduces a novel dynamical theory of continual learning that derives memory and self-correction from learning dynamics without external modules.

Findings

Achieves near-zero forgetting on CIFAR-100 (BT = -0.004)

Attains positive backward transfer in chess (+38.5 cp)

Reduces forgetting by 43% compared to replay in a controlled domain

Abstract

Catastrophic forgetting is not an engineering failure. It is a mathematical consequence of storing knowledge as global parameter superposition. Existing methods, such as regularization, replay, and frozen subnetworks, add external mechanisms to a shared-parameter substrate. None derives retention from the learning dynamics themselves. This paper introduces the Informational Buildup Framework (IBF), an alternative substrate for continual learning, based on the premise that information is the achievement of structural alignment rather than stored content. In IBF, two equations govern the dynamics: a Law of Motion that drives configuration toward higher coherence, and Modification Dynamics that persistently deform the coherence landscape in response to localized discrepancies. Memory, agency, and self-correction arise from these dynamics rather than being added as separate modules. We first demonstrate the full lifecycle in a transparent two-dimensional toy model, then validate across three domains: a controlled non-stationary world, chess evaluated independently by Stockfish, and Split-CIFAR-100 with a frozen ViT encoder. Across all three, IBF achieves replay-superior retention without storing raw data. We observe near-zero forgetting on CIFAR-100 (BT = -0.004), positive backward transfer in chess (+38.5 cp), and 43% less forgetting than replay in the controlled domain. In chess, the framework achieves a mean behavioral advantage of +88.9 +/- 2.8 cp under independent evaluation, exceeding MLP and replay baselines.