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

Catastrophic forgetting remains a fundamental open challenge in continual learning (CL): neural networks exhibit rapid performance collapse 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—integrase-mediated permanent insertion of viral cDNA into host chromatin—into a computational architecture for stable, lifelong knowledge assimilation. PILF rests on three mathematically grounded components: (i) a fixed-capacity core knowledge manifold Kc updated by an SVD-projected, spectrally bounded rank-one integration step; (ii) proximal-elastic regularization with a monotonically increasing penalty schedule; and (iii) a bi-Lipschitz feature encoder with a scaled dot-product attention gate. We prove three results under standard smoothness, monotonicity, and strong-convexity assumptions: core-manifold spectral stability with summable increments for a decay exponent ϵ > 1 (Theorem 1); a per-step forgetting bound of order O(t^−γ) yielding O(√T) cumulative forgetting (Theorem 2); and O(1/√T) average regret (Theorem 3). We evaluate PILF on a controlled, fully reproducible domain-incremental benchmark against fine-tuning and four baselines (Elastic Weight Consolidation, online ℓ2 anchoring, a rehearsal buffer, and an ablated variant). PILF attains the strongest accuracy–retention trade-off—final average accuracy 75.8% (95% CI ±1.3), improving over fine-tuning by +13.9 points and over the best regularization baseline by +7.7 points, and matching a rehearsal baseline while storing no past data, with backward transfer of only −5.8%—the smallest in magnitude of any method (baselines span −8.1% to −39.2%). Candid ablations attribute most of this retention to the proximal-elastic schedule and the bi-Lipschitz constraint, with the persistent manifold contributing a smaller but consistent backward-transfer benefit. As the task count grows from 3 to 11, PILF's backward transfer degrades only from −5.1% to −9.0%, whereas fine-tuning remains near −40% throughout, empirically corroborating the sublinear-forgetting bound. All numerical results, tables, and figures are reproduced exactly by the embedded reference implementation.