4 papers
Recovery Guarantees for Continual Learning of Dependent Tasks: Memory, Data-Dependent Regularization, and Data-Dependent Weights
Liangzu Peng, Uday Kiran Reddy Tadipatri, Ziqing Xu +2
Continual learning (CL) is concerned with learning multiple tasks sequentially without forgetting previously learned tasks. Despite substantial empirical advances over recent years…
Convergence Rates for Gradient Descent on the Edge of Stability in Overparametrised Least Squares
Lachlan Ewen MacDonald, Hancheng Min, Leandro Palma +3
Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or ``stable", regime. In contrast, gradient desc…
A Local Polyak-Lojasiewicz and Descent Lemma of Gradient Descent For Overparametrized Linear Models
Ziqing Xu, Hancheng Min, Salma Tarmoun +2
Most prior work on the convergence of gradient descent (GD) for overparameterized neural networks relies on strong assumptions on the step size (infinitesimal), the hidden-layer wi…
Understanding the Learning Dynamics of LoRA: A Gradient Flow Perspective on Low-Rank Adaptation in Matrix Factorization
Ziqing Xu, Hancheng Min, Lachlan Ewen MacDonald +4
Despite the empirical success of Low-Rank Adaptation (LoRA) in fine-tuning pre-trained models, there is little theoretical understanding of how first-order methods with carefully c…