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
arXiv:2606. 08013v1 Announce Type: new Abstract: Catastrophic forgetting, the abrupt loss of previously acquired knowledge upon learning new information, remains the central challenge in Continual Learning.
By Emre Alyamac, Himanshu Janmeda, Shashwat Krishna, Yash Vijay
arXiv:2604.13460v2 Announce Type: replace-cross
Abstract: A central challenge in continual learning is forgetting: the loss of performance on previously learned tasks after learning new ones. Prior t...
By Zonghuan Xu, Xingjun Ma
arXiv:2607. 05609v1 Announce Type: cross Abstract: The Continual Learning (CL) literature has long been driven by the goal of mitigating catastrophic forgetting.
By Giulia Lanzillotta, Mandana Samiei, Doina Precup, Razvan Pascanu, Claire Vernade
arXiv:2609.17026v1 Announce Type: new
Abstract: Continual learning must balance the learning of new knowledge with the retention of previously learned knowledge to incrementally learn tasks from a da...
By Yunxiang Fu, Meng Lou, Zicheng Liao, Yizhou Yu
arXiv:2603. 11201v3 Announce Type: replace-cross Abstract: The world is inherently dynamic, and continual learning aims to enable models to adapt to ever-evolving data streams.
By Haihua Luo, Xuming Ran, Tommi K\"arkk\"ainen, Huiyan Xue, Zhonghua Chen, Qi Xu, Fengyu Cong
The paper introduces Trust Region Continual Learning, a hybrid approach that blends generative replay with a Fisher-metric trust region constraint to address catastrophic forgetting in sequential task learning. It demonstrates that, under local approximations, the update can be interpreted as a single-step Model-Agnostic Meta-Learning (MAML) process, where replay provides an old-task gradient and the Fisher penalty shapes curvature. Experiments on task-incremental diffusion image generation and continual diffusion-policy control show that this method achieves superior final performance, better retention, and faster early-task recovery compared to EWC, replay, and other continual meta-learning baselines.
By Zekun Wang, Anant Gupta, Christopher J. MacLellan