提出新方法缓解状态空间模型在无样本持续学习中的灾难性遗忘。
Exemplar-Free Continual Learning for State Space Models
- 基于无限维格拉斯曼流形几何，约束状态空间模型的长期演化路径。
- 在ImageNet-R和Caltech-256上显著降低遗忘率，提升多任务准确率。
- 效率高，复杂度从O(n³)降至O(n²)，可无缝融入现有持续学习框架。
状态空间模型（SSMs）凭借结构化循环机制擅长捕捉长程依赖，适用于序列建模。然而，其动态内部状态在持续学习（CL）中难以适应，尤其在无样本设置下，缺乏历史数据导致状态更新无约束，引发灾难性遗忘。为此，我们提出Inf-SSM，一种新颖且简单的几何感知正则化方法，利用无限维格拉斯曼流形的几何特性，约束SSM在持续学习中的状态演化。不同于传统方法约束权重更新，Inf-SSM通过扩展可观测子空间编码的无限时域演化进行正则化。我们证明该约束需求解西尔维斯特方程，通常具有$/mathcal{O}(n^3)$复杂度；通过挖掘SSM的结构与性质，我们设计出$/mathcal{O}(n^2)$求解方案，实现高效正则化机制，并可无缝集成至现有持续学习方法中。在ImageNet-R与Caltech-256等挑战性基准上的全面实验表明，该方法显著减少遗忘，同时提升跨任务准确率。
原文摘要 · Abstract (English)
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.
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