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 when adapting to new domains. We introduce the Persistent Integrative Learning Framework (PILF), a biologically inspired paradigm that mimics retroviral integration mechanisms to enable stable, lifelong knowledge assimilation. PILF employs bi-Lipschitz feature fusion with proximal quadratic regularization, establishing theoretical guarantees for sublinear forgetting bounds under standard smoothness, monotonicity, and convexity assumptions. Our formal analysis demonstrates \( \mathcal{O}(1/\sqrt{T}) \) convergence rates and bounded forgetting with explicit constants. Comprehensive evaluations on Split-MNIST, Split-CIFAR-10, and DomainBed benchmarks show PILF outperforms state-of-the-art methods like EWC, GEM, and Eidetic Learning by 15--20% in average accuracy while maintaining backward transfer below 3%. Ablation studies confirm the necessity of both the core manifold and proximal dynamics. The framework provides a scalable, theoretically grounded architecture for resilient multi-domain AI systems, bridging biological plausibility with rigorous mathematical foundations.灾难性遗忘（Catastrophic Forgetting）仍是持续学习（Continual Learning, CL）领域的核心挑战——神经网络在适配新领域时，会在已习得的任务上出现性能的快速退化。本文提出持久整合学习框架（Persistent Integrative Learning Framework, PILF），这是一种受生物启发的范式，通过模拟逆转录病毒整合机制，实现稳定的终身知识同化。PILF采用双李普希茨（bi-Lipschitz）特征融合结合近端二次正则化（proximal quadratic regularization），在标准光滑性、单调性与凸性假设下，为次线性遗忘界提供了理论保证。本文的形式化分析证明了$mathcal{O}(1/sqrt{T})$级别的收敛速率，以及带有显式常数的有界遗忘性能。在Split-MNIST、Split-CIFAR-10与DomainBed基准数据集上的全面评估表明，PILF在平均准确率上优于EWC、GEM、遗觉学习（Eidetic Learning）等当前最优方法15%至20%，同时将反向迁移率控制在3%以下。消融实验验证了核心流形与近端动力学二者的必要性。该框架为鲁棒多领域人工智能系统提供了一种可扩展、具备理论支撑的架构，实现了生物合理性与严格数学基础的有机结合。