Score-Preserving Continual Lasso under Task Shift
Read the original on arXiv Statistics ML →The Flow has not summarised this story yet — read it at arXiv Statistics ML.
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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...
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.
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.
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: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.
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.