Coherence-Rupture-Regeneration: A Non-Markovian Information-Theoretic Framework for Continual Learning with Empirical Findings

Continual learning systems must acquire new knowledge whilst preserving previouslylearnt information; a challenge that current approaches address through largely Markovianassumptions about task independence. We present the Coherence-Rupture-Regeneration(CRR) framework, which combines rigorous information-theoretic foundations with practicalimplementation for continual learning. Theoretically, we develop the framework fromfirst principles using Fisher information geometry, establish constraint overdeterminationarguments suggesting the necessity of discrete reset cycles, and derive information-theoreticbounds on optimal reset frequency. Empirically, through systematic component ablationstudies and multi-domain validation, we observe consistent improvements over traditionalapproaches in our experimental settings. On Gaussian continual learning benchmarks, CRRattains 76.92% average accuracy compared to 72.24% for EWC (+4.68 pp; +6.48% relativeimprovement), with regeneration contributing +4.78 pp and rupture detection +0.72 pp.Additional synthetic multi-domain tests show CRR achieving 57.9% final average accuracyversus 33.5% for baseline approaches, reducing catastrophic forgetting from 14% to 6% underour protocol. The framework encompasses three interconnected operators: (1) CoherenceIntegration via information-geometric tracking of memory stability, (2) Rupture Detectionvia loss spike analysis with adaptive thresholds, and (3) Regeneration via memory-weightedknowledge distillation. We emphasise that whilst theoretical arguments suggest potentialnecessity of the CRR structure, empirical validation remains limited to small-scale settings (5tasks, synthetic domains) and substantial further investigation is required.