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: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.
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:2406. 04425v2 Announce Type: replace Abstract: A fundamental problem in machine learning is understanding the effect of early stopping on the parameters obtained and the generalization capabilities of the model.
arXiv:2510. 12249v2 Announce Type: replace Abstract: In performative learning, the data distribution reacts to the deployed model - for example, because strategic users adapt their features to game it - which creates a more complex dynamic than in classical supervised learning.
arXiv:2601. 19791v4 Announce Type: replace Abstract: We study grokking, the onset of generalization long after overfitting, in a classical ridge regression setting.
arXiv:2608. 15901v1 Announce Type: cross Abstract: Continual learning regularizers like EWC fight forgetting by penalizing changes from previous-task parameters with per-parameter importance, typically diagonal Fisher values.
arXiv:2606. 30559v1 Announce Type: new Abstract: We characterize weakly regularized continual classification in homogeneous models as sequential projections onto task margin sets.
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.
The paper investigates the performance cost, termed the sequential price, incurred by sequential task updates in continual learning. In an overparameterized linear‑regression setting with i.i.d. task sampling, the authors prove that distribution‑level forgetting and population loss converge to a stationary limit that splits into the intrinsic loss of joint training and an additional sequential price. They further analyze elastic weight consolidation (EWC), showing how its regularization strength affects the stationary sequential price and demonstrate the theory on the Jester joke‑rating dataset.
arXiv:2502. 11665v3 Announce Type: replace-cross Abstract: The classical kernel ridge regression problem aims to find the best fit for the output $Y$ as a function of the input data $X\in \mathbb{R}^d$, with a fixed choice of regularization term imposed by a given choice of a reproducing kernel Hilbert space, such as a Sobolev space.
arXiv:2505. 21423v3 Announce Type: replace Abstract: The remarkable generalization properties of overparameterized networks are often attributed to implicit biases, such as norm minimization at small learning rates and low sharpness in the Edge-of-Stability regime.
Continual training of deep neural networks under non-stationarity often leads to a progressive loss of plasticity, eventually limiting further learning. We relate plasticity to the empirical Neural Tangent Kernel, and identify dynamical isometry (the condition that layer-wise Jacobian singular values remain close to one) as a key mechanism for preserving plasticity in continual learning.