无示例连续学习的状态空间模型
Exemplar-Free Continual Learning for State Space Models
AI总结：
本文提出Inf-SSM，通过利用无限维Grassmannian的几何结构，约束状态空间模型在连续学习中的状态演化，有效减少灾难性遗忘并提升准确率。
摘要：
状态空间模型（SSMs）擅长捕捉长期依赖关系，但其动态内部状态在连续学习中适应困难，尤其在无示例设置下更甚。为解决此问题，本文提出Inf-SSM，一种基于无限维Grassmannian几何的正则化方法，通过求解Sylvester方程实现对SSM无限时间 horizon演化的正则化。该方法通过利用SSM的结构特性，将复杂度从O(n^3)降低至O(n^2)，并能无缝集成到现有连续学习方法中。在ImageNet-R和Caltech-256等挑战性基准测试中，显著减少了遗忘并提高了连续任务的准确率。
英文摘要：
State-Space Models (SSMs) excel at capturing long-range dependencies with structured recurrence, making them well-suited for sequence modeling. However, their evolving internal states pose challenges in adapting them under Continual Learning (CL). This is particularly difficult in exemplar-free settings, where the absence of prior data leaves updates to the dynamic SSM states unconstrained, resulting in catastrophic forgetting. To address this, we propose Inf-SSM, a novel and simple geometry-aware regularization method that utilizes the geometry of the infinite-dimensional Grassmannian to constrain state evolution during CL. Unlike classical continual learning methods that constrain weight updates, Inf-SSM regularizes the infinite-horizon evolution of SSMs encoded in their extended observability subspace. We show that enforcing this regularization requires solving a matrix equation known as the Sylvester equation, which typically incurs $\mathcal{O}(n^3)$ complexity. We develop a $\mathcal{O}(n^2)$ solution by exploiting the structure and properties of SSMs. This leads to an efficient regularization mechanism that can be seamlessly integrated into existing CL methods. Comprehensive experiments on challenging benchmarks, including ImageNet-R and Caltech-256, demonstrate a significant reduction in forgetting while improving accuracy across sequential tasks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
