The paper introduces an algorithmic stability framework to analyze catastrophic forgetting in continual learning using SGD, without assuming a specific model architecture. It decomposes forgetting into intra‑task and cross‑task generalization gaps plus empirical forgetting, and derives bounds for different learning‑rate schedules. Experiments on Split CIFAR‑100 and Split MiniImageNet illustrate the theoretical insights.
By Guodong Zheng, Yan Sun, Peng Wang, Enneng Yang, Jiafei Lyu, Xiaochun Cao, Dacheng Tao, Li Shen
arXiv:2601. 13844v3 Announce Type: replace Abstract: We study generalization in an overparameterized continual linear regression setting, where a model is trained with L2 (isotropic) regularization across a sequence of tasks.
By Gilad Karpel, Edward Moroshko, Ran Levinstein, Ron Meir, Daniel Soudry, Itay Evron
The paper introduces Fisher-Shaped EWC (FS‑EWC), a method that extends Elastic Weight Consolidation by controlling Fisher sensitivity over a neighborhood of potential future updates. FS‑EWC minimizes the worst‑case empirical Fisher information trace during task learning, favoring solutions less sensitive to bounded future displacement, and uses trajectory‑based model merging to construct the retained solution. Experiments on multiple benchmarks show that FS‑EWC outperforms standard EWC, achieving a better stability–plasticity balance and greater tolerance to parameter drift.
The paper introduces Fisher-Shaped EWC (FS‑EWC), a replay‑free continual learning method that extends Elastic Weight Consolidation by controlling Fisher sensitivity over a neighborhood of future updates. FS‑EWC minimizes the worst‑case empirical Fisher information trace during task learning, favoring solutions robust to bounded parameter displacement, and uses trajectory‑based model merging to construct the retained solution from multiple optimization states. Experiments on several benchmarks demonstrate that FS‑EWC outperforms standard EWC, achieving a better stability–plasticity balance and higher tolerance to parameter drift.
By Liying Wang, Simone Magistri, Joost van de Weijer
arXiv:2610.32708v1 Announce Type: new
Abstract: Continual learning (CL) aims to learn from sequential tasks while mitigating catastrophic forgetting when historical data are no longer accessible. We...
By Jingyi Guo, Runze Li, Lingzhou Xue
The paper investigates continual linear regression in high-dimensional settings, deriving a closed-form expression for the generalization loss when using gradient descent with a fixed number of steps per task. It shows that the optimal fixed step size decays roughly as “ln T / T” for a single teacher and i.i.d. teachers, matching the performance of optimally tuned L2 regularization. The study also extends to generalized ridge regression with diagonal regularizers, identifies conditions for isotropic optimality, and reveals a regime where the step size stays finite as the number of tasks grows, highlighting a tradeoff between task variability and implicit regularization.
By Gilad Karpel, Daniel Soudry