arXiv Machine Learning
Oct 16

Optimal Explicit and Implicit Regularization Strengths in High-Dimensional Continual Linear Regression

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 Machine Learning
Oct 23

Fine-Grained Analysis of Catastrophic Forgetting in Continual Learning via Algorithmic Stability

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 Machine Learning
Aug 28

Unifying Detection and Adaptation in Task-Free Continual Learning

The paper introduces FiUni, a Fisher-guided unified framework that performs batch-level task detection and parameter-efficient continual adaptation for large language models. By exploiting orthogonality in the Fisher information matrix’s Kronecker-Factored Approximate Curvature subspaces, FiUni constructs frozen subspaces to guide low-rank adaptation and matches incoming batch windows to historical subspaces. This approach allows the model to decide whether to reuse, expand, or create new subspaces, balancing knowledge sharing and task isolation while achieving competitive performance with fewer trainable parameters.

By Dezheng Han, Anbang Zhang, Zhihao Zhu, Shuaishuai Guo