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We study logistic regression for continual learning with linear predictors in a high-dimensional statistical setting. Existing theoretical work has largely focused on continual linear regression with...
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.
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.
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...
arXiv:2606. 26629v1 Announce Type: new Abstract: Weight-space regularization methods such as Elastic Weight Consolidation (EWC) are the standard approach to catastrophic forgetting in continual learning.
arXiv:2606. 30559v1 Announce Type: new Abstract: We characterize weakly regularized continual classification in homogeneous models as sequential projections onto task margin sets.