1 citations · 1 across the 4 of their papers we have counts for
5 papers
Non-Euclidean Gradient Descent Has Many Edges of Stability
Peter Zaika, Zakhar Shumaylov
Recent observations that deep learning models train at the edge of stability have renewed interest in understanding stability properties of classical optimization algorithms. For q…
Muon is Not That Special: Random or Inverted Spectra Work Just as Well
Zakhar Shumaylov, Nathaël Da Costa, Peter Zaika +6
The recent empirical success of the Muon optimizer has renewed interest in non-Euclidean optimization, typically justified by similarities with second-order methods, and linear min…
When is a System Discoverable from Data? Discovery Requires Chaos
Zakhar Shumaylov, Peter Zaika, Philipp Scholl +3
The deep learning revolution has enabled major AI advances in physical sciences, particularly in discovering dynamical systems from observational data. Yet the reliability of learn…
Generalized Lie Symmetries in Physics-Informed Neural Operators
Amy Xiang Wang, Zakhar Shumaylov, Peter Zaika +2
Physics-informed neural operators (PINOs) have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). Recent research has demonstrated…
Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups
Zakhar Shumaylov, Peter Zaika, James Rowbottom +3
The quest for robust and generalizable machine learning models has driven recent interest in exploiting symmetries through equivariant neural networks. In the context of PDE solver…