8 papers
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 d…
Tight Bounds for Logistic Regression with Large Stepsize Gradient Descent in Low Dimension
Michael Crawshaw, Mingrui Liu
We consider the optimization problem of minimizing the logistic loss with gradient descent to train a linear model for binary classification with separable data. With a budget of $…
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…
An Exploration of Non-Euclidean Gradient Descent: Muon and its Many Variants
Michael Crawshaw, Chirag Modi, Mingrui Liu +1
To define a steepest descent method over a neural network, we need to choose a norm for each layer, a way to aggregate these norms across layers, and whether to use normalization.…
Constant Stepsize Local GD for Logistic Regression: Acceleration by Instability
Michael Crawshaw, Blake Woodworth, Mingrui Liu
Existing analysis of Local (Stochastic) Gradient Descent for heterogeneous objectives requires stepsizes where is the communication interval, which ensures monoton…
Complexity Lower Bounds of Adaptive Gradient Algorithms for Non-convex Stochastic Optimization under Relaxed Smoothness
Michael Crawshaw, Mingrui Liu
Recent results in non-convex stochastic optimization demonstrate the convergence of popular adaptive algorithms (e.g., AdaGrad) under the -smoothness condition, but the…