Persistent Integrative Learning Framework: A Retrovirus-Inspired Approach to Mitigating Catastrophic Forgetting in Multi-Domain Artificial Intelligence

Catastrophic forgetting remains a fundamental challenge in continual learning (CL), where neural networks exhibit rapid performance degradation on previously learned tasks upon adaptation to new domains. We introduce the Persistent Integrative Learning Framework (PILF), a biologically inspired paradigm that abstracts the irreversible genomic integration mechanism of retroviruses---specifically the integrase-mediated permanent insertion of viral cDNA into host chromatin---to enable stable, lifelong knowledge assimilation without destructive interference. PILF employs bi-Lipschitz feature fusion with proximal quadratic regularization, establishing rigorous theoretical guarantees for sublinear forgetting bounds under standard smoothness, monotonicity, and strong convexity assumptions. Our formal analysis demonstrates \( \mathcal{O}(1/\sqrt{T}) \) convergence rates and bounded forgetting with explicit constants (Theorems~\ref{thm:stability}--\ref{thm:convergence}, Appendix~\ref{app:proofs}). Comprehensive evaluations on Split-MNIST, Split-CIFAR-10, and DomainBed benchmarks show PILF outperforms strong baselines such as EWC, GEM, and the recently withdrawn Eidetic Learning by up to 15--20% in average accuracy while maintaining backward transfer below 3%. Extensive ablation studies confirm the necessity of both the core manifold and proximal dynamics. PILF distinguishes itself from other biologically inspired methods---including reversible synaptic consolidation, hippocampal replay, and alternative genetic integration mechanisms such as transposon-mediated or CRISPR-like editing---by enforcing irreversible yet non-destructive assimilation into a fixed-size core manifold. The framework provides a scalable, theoretically grounded architecture for resilient multi-domain AI systems, offering both biological plausibility and mathematical rigor.