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, irreversible performance collapse on previously learned tasks upon adaptation to new domains. We introduce the Persistent Integrative Learning Framework (PILF), a biologically inspired paradigm that formally abstracts the irreversible genomic integration mechanism of retroviruses—specifically integrase-mediated permanent insertion of viral cDNA into host chromatin—to enable stable, lifelong knowledge assimilation without destructive interference.PILF rests on three mathematically grounded pillars: (i) a fixed-size core knowledge manifold Kc updated via SVD-projected, bi-Lipschitz feature fusion; (ii) proximal quadratic regularization with an adaptive, monotonically increasing penalty schedule; and (iii) a multi-head attention gate that selectively retrieves and fuses core and task-specific representations. We establish three rigorous guarantees: core-manifold spectral stability with summable increments (Theorem 1), sublinear forgetting bounds of the form E[|P_{t'}(θ^{t+1}) - P_{t'}(θ^t)|] ≤ γ / √(t - t' + 1) (Theorem 2), and O(1/√T) average regret (Theorem 3), all under standard smoothness, monotonicity, and strong convexity assumptions.Comprehensive evaluations on Split-MNIST, Split-CIFAR-10, and DomainBed benchmarks—including comparisons against eight baselines (EWC, SI, GEM, DER, PackNet, CLSER, MEMO, and the recently withdrawn Eidetic Learning)—show PILF outperforms all competitors by up to 10–15% in average accuracy while maintaining backward transfer below 5%. Ablation studies confirm the indispensability of each architectural component. PILF is explicitly distinguished from reversible synaptic consolidation, hippocampal replay, and alternative genetic integration mechanisms by its provably irreversible yet non-destructive assimilation into a fixed-capacity spectral manifold, yielding a scalable, theoretically grounded architecture that unifies biological plausibility with mathematical rigor.