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

Catastrophic forgetting poses a significant challenge in continual learning (CL), where neural networks rapidly degrade on prior tasks upon learning new ones. This paper introduces the Persistent Integrative Learning Framework (PILF), a biologically inspired method drawing from retroviral genome integration mechanisms, such as those in HIV, to enable stable, lifelong knowledge retention in multi-domain AI systems. PILF features a core knowledge manifold that acts as a persistent "host genome," integrating new domain features via bi-Lipschitz mappings to preserve geometric structures, while proximal quadratic regularization and spectral normalization prevent destructive updates. The framework provides rigorous theoretical guarantees, including sublinear forgetting bounds of \(\mathbb{E}[|P_{t'}(\theta^{t+1}) - P_{t'}(\theta^t)|] \leq \gamma / \sqrt{t - t' + 1}\) and \(\mathcal{O}(1/\sqrt{T})\) convergence rates under smoothness, bounded gradients, and strong convexity assumptions. Empirical evaluations on Split-MNIST, Split-CIFAR-10, and DomainBed benchmarks demonstrate PILF outperforming baselines like EWC, GEM, and Eidetic Learning by 15–20% in average accuracy, with backward transfer below 3%. Ablations confirm the essential roles of the core manifold, proximal dynamics, and bi-Lipschitz constraints. The paper bridges biological plausibility with mathematical rigor, offering a scalable architecture for resilient AI, alongside implementation details and proofs.