4 papers · 1 filter
PoLoRA: A Preconditioned Orthogonalized LoRA Optimizer
Nikhil Ghosh, Tetiana Parshakova, Robert M. Gower
Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices.…
Muon Does Not Converge on Convex Lipschitz Functions
Tetiana Parshakova, Ahmed Khaled, Michael Crawshaw +2
Muon and its variants have shown strong empirical performance in a variety of deep learning tasks. Existing convergence analyses of Muon rely on smoothness assumptions, though argu…
Non-Euclidean Gradient Descent Operates at the Edge of Stability
Rustem Islamov, Michael Crawshaw, Jeremy Cohen +1
The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian approaches and then hovers near the stability threshold during gradient de…
Step-Size Stability in Stochastic Optimization: A Theoretical Perspective
Fabian Schaipp, Robert M. Gower, Adrien Taylor
We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method,…