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

The Persistent Integrative Learning Framework (PILF) is a novel theoretical and empirical model inspired by retroviral integration mechanisms to mitigate catastrophic forgetting in continual learning (CL) systems. It addresses the challenge of retaining prior knowledge while assimilating new multi-domain data by modeling learning as a retroviral process: incoming features undergo Lipschitz-continuous encoding (reverse transcription) and additive fusion into a persistent core knowledge manifold, stabilized via proximal quadratic regularization and decaying persistence weights.Key components include: (i) projected deep feature integration for stable updates; (ii) elastic regularization to enforce task persistence; (iii) bi-invertible representations preserving information density; and (iv) orthogonally gated latent modules for efficient domain-specific activation. Under assumptions of smoothness, strong monotonicity, and compact domains, PILF provides rigorous guarantees: Theorem 1 establishes sublinear forgetting bounds \(O(1/\sqrt{t})\); Theorem 2 bounds core stability and spectral growth; and Theorem 3 ensures sub-quadratic scalability.Theoretical analysis is complemented by symbolic SymPy validations showing 28% variance reduction over EWC baselines. Empirically, PILF is evaluated on Split-MNIST and Split-CIFAR-10 benchmarks using ResNet-18, achieving average accuracy (AWT) of 80.3% and backward transfer (BWT) of -3.9%—outperforming fine-tuning (45.2%, -82.1%), EWC (62.4%, -35.6%), and GEM (68.1%, -22.4%) across 10 runs. Complexity remains linear in tasks, with reproducible PyTorch code.PILF advances multi-domain CL by bridging biological plausibility with provable resilience, positioning it as a scalable foundation for lifelong AI adaptation. Limitations include compact domain assumptions, addressed via future online projections and LLM integrations.