Information as Structural Alignment: A Dynamical Theory of Continual Learning

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.

• The paper introduces IBF, showing that memory emerges from persistent local deformations of a coherence landscape rather than from stored parameters.
• It proposes two coupled dynamical equations—one for motion and one for localized modification—validated across synthetic, strategic, and high-dimensional benchmarks.
• Empirical results demonstrate IBF’s superior retention and transfer performance, effectively mitigating catastrophic forgetting without data replay.

Information as Structural Alignment: A Dynamical Theory of Continual Learning

Introduction

The paper "Information as Structural Alignment: A Dynamical Theory of Continual Learning" (2604.07108) introduces the Informational Buildup Framework (IBF), a theoretically principled alternative to conventional continual learning substrates. The key premise is that information is instantiated not as stored content, but as persistent structural alignment—the geometric correspondence between an agent's internal configuration and the external environment. From this, the paper derives a novel formalism that provides mechanisms for memory, agency, and self-correction as emergent properties, rather than as engineered add-ons.

Catastrophic forgetting is rigorously characterized as an inevitable consequence of parameter superposition in current deep architectures. All canonical countermeasures (regularization, replay, capacity expansion) operate around this substrate and cannot eliminate the problem at its root. IBF proposes an orthogonal substrate, where learning, retention, and behavioral deployment are governed by two coupled dynamical equations: a Law of Motion over a configuration space, and localized Modification Dynamics driven by discrepancy signals.

Theoretical Foundations

At the heart of IBF is the proposition that memory emerges from persistent local deformation of a coherence landscape—a scalar field quantifying alignment with environmental structure—rather than as distributed parameter encodings. The formalism is grounded in four axioms and a modification postulate:

• Axioms establish the existence of an informational domain, a coherence field over configuration space, the presence of informational gravity (gradient ascent on coherence), and a Law of Motion dictating system evolution as gradient flow modulated by a responsiveness field.
• Modification Dynamics stipulate that the effective coherence landscape deforms persistently wherever localized discrepancy signals are detected, subject to thermodynamic constraints (e.g., slow modification rates, bounded capacity, and passively decaying structure).

These dynamics yield distinct empirical consequences: memory as persistent local structure, agency as spatially modulated trajectory selection, and self-correction as thermodynamic dissolution of misaligned modifications under sustained contradiction.

Universal Engine and Lifecycle

The computational realization of IBF is a domain-agnostic engine operating over a finite latent space supplied by a frozen encoder and evaluator. Modifications are stored as kernel-localized particles (correction and responsiveness populations), each characterized by location, amplitude, decay rate, and a history of discrepancy signals.

• Learning proceeds by nucleating new particles at regions of persistent discrepancy, which accumulate corrections. Stability transitions (crystallization) occur when local discrepancy signals converge, reducing decay and yielding long-lived memory.
• Retention is achieved by context-dependent gating: dormant (inactive) memory is preserved and can be reactivated across contexts after cross-verification.
• Self-correction (Crucible mechanism) revokes or dissolves corrections whose validity is contradicted by subsequent experience.
• Agency emerges through responsiveness modulation, where responsiveness amplitudes are modulated by the variance of local discrepancy signals, yielding spatially heterogenous exploration/exploitation.

The discrete implementation, justified by a convergence claim, faithfully approximates the continuous theoretical dynamics.

Validation Domains and Experimental Design

Three distinct domains validate IBF's continuous learning dynamics and test the theoretical claims across increasingly challenging regimes:

1. Rotating Rules World (RRW): A synthetic, analytically controlled environment designed to maximize explicit cross-context contradiction. Here, mechanisms can be transparently dissected and attributed.
2. Chess: High-complexity, externally evaluated by Stockfish. Strategic regularity, hierarchical structure, and context-switches provide a stringent test of agency and self-correction.
3. Split-CIFAR-100: Standard continual learning benchmark with a strong baseline, high dimensionality, and minimal inter-task overlap, serving as a stress test for non-destructive memory at scale.

A geometric calibration protocol sets the kernel bandwidth directly from the latent configuration geometry, precluding the need for hyperparameter search.

Empirical Results

Strong numerical results and regime-dependent behaviors validate the core claims:

• RRW: IBF achieves $43\%$ less forgetting than replay MLPs, without storing past data. No-Crucible ablation confirms perfect context isolation (no forgetting, but no transfer). Agency is mildly harmful in contradiction-heavy environments due to increased exposure to contradicting signals.
• Chess: IBF achieves a statistically significant mean advantage of $+88.9 \pm 2.8$ centipawns over the passive baseline at the prescribed geometric scale, with backward transfer $\mathrm{BT}_A = +35.4 \pm 2.9$ centipawns (versus replay’s $+26.8$), all with zero stored raw data. Ablations show agency is crucial for activating self-correction: removal collapses Crucible activity by three orders of magnitude and significantly weakens performance.
• CIFAR-100: Retention is near-perfect with $\mathrm{BT} = -0.004$ (versus replay MLP’s $-.234$ and EWC's catastrophic degradation). Class-IL performance remains strong with $52.8\%$ accuracy, whereas replay MLP degrades to $39.2\%$. Here, higher-order mechanisms (Crucible, agency) are behaviorally redundant due to natural geometric separation; spatial isolation alone suffices.

The regime dependence is crucial: the same agency mechanism is harmful in RRW, essential in chess, and neutral in CIFAR, consistent with the theory’s predictions about alignment structure and discrepancy regimes.

Theoretical Implications and Relation to Prior Work

IBF contrasts sharply with parameter-centric paradigms such as EWC, replay, and progressive networks, which address forgetting only in the context of superposed global parameters. By relocating memory to persistent local landscape deformations and assimilating agency/self-correction as dynamical consequences, IBF provides a radical substrate-level alternative.

The methodology bears conceptual similarity to kernel methods, ART, and episodic-control strategies, but IBF introduces distinct thermodynamic transitions (crystallization, dissolution), self-organizing agency, and a formal convergence bridge to continuous alignment dynamics.

Relation to the Free Energy Principle (FEP) is primarily at the level of ambition—formulating adaptive behavior via mismatch minimization—but IBF eschews the requirement of an explicit generative model, instead shifting the focus to geometric deformation and relational coherence in state space.

Practical Implications and Future Directions

The practical implications of IBF are significant for AI systems that must adapt under non-stationarity without catastrophic interference. The substrate is compatible with frozen representations, requires no raw data storage, and achieves transfer/retention superior to data-replaying neural methods. The fact that geometric calibration is sufficient to set critical parameters eliminates substantial tuning burden.

Future investigations should target:

• Scaling to higher-dimensional latent spaces (e.g., full-scale LLMs, vision transformer backbones).
• Continuous, autonomous operation without explicit context cues, enabling seamless adaptation in open-task or streaming regimes.
• Multi-agent and world-model settings, where discrepancy signals are interdependent and mutual landscape deformation becomes a major driver of emergent communication and coordination.
• Hardware alignment: Given the substrate’s event-driven, local structure deformation model, neuromorphic or analog implementations might realize efficiency or functional advantages not accessible in dense digital architectures.

Conclusion

The Informational Buildup Framework supplies a theoretically rigorous alternative to traditional continual learning architectures, deriving memory, agency, and self-correction from a minimal dynamical substrate where information is instantiated as structural alignment. Across synthetic, strategic, and high-dimensional benchmarks, IBF achieves replay-superior retention and demonstrates regime-dependent emergence of higher-order mechanisms—all without storing raw experience. The substrate claim is substantiated both by robust empirical evidence and by a principled theory predicting when and how the mechanisms activate. This positions IBF as a promising foundation for continual, adaptive artificial intelligence beyond the limits of globally superposed parameter systems (2604.07108).