1 citations · 2 across the 14 of their papers we have counts for
16 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…
Adaptive Coordinate Transforms for Neural Operators
Chaoyu Liu, Zhonghao Li, Gaohang Chen +5
Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch betwe…
Diffeomorphism-Equivariant Neural Networks
Josephine Elisabeth Oettinger, Zakhar Shumaylov, Johannes Bostelmann +2
Incorporating group symmetries via equivariance into neural networks has emerged as a robust approach for overcoming the efficiency and data demands of modern deep learning. While…
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…
Learning Regularization Functionals for Inverse Problems: A Comparative Study
Johannes Hertrich, Hok Shing Wong, Alexander Denker +16
In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insig…
On Information Geometry and Iterative Optimization in Model Compression: Operator Factorization
Zakhar Shumaylov, Vasileios Tsiaras, Yannis Stylianou
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the ap…
Data-driven approaches to inverse problems
Carola-Bibiane Schönlieb, Zakhar Shumaylov
Inverse problems are concerned with the reconstruction of unknown physical quantities using indirect measurements and are fundamental across diverse fields such as medical imaging,…
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…
Benchmarking learned algorithms for computed tomography image reconstruction tasks
Maximilian B. Kiss, Ander Biguri, Zakhar Shumaylov +4
Computed tomography (CT) is a widely used non-invasive diagnostic method in various fields, and recent advances in deep learning have led to significant progress in CT image recons…
Symplectic Neural Flows for Modeling and Discovery
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulation…
Hamiltonian Matching for Symplectic Neural Integrators
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical…
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…
Score-based Pullback Riemannian Geometry: Extracting the Data Manifold Geometry using Anisotropic Flows
Willem Diepeveen, Georgios Batzolis, Zakhar Shumaylov +1
Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is cr…
Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation
Zakhar Shumaylov, Jeremy Budd, Subhadip Mukherjee +1
Variational regularisation is the primary method for solving inverse problems, and recently there has been considerable work leveraging deeply learned regularisation for enhanced p…
Provably Convergent Data-Driven Convex-Nonconvex Regularization
Zakhar Shumaylov, Jeremy Budd, Subhadip Mukherjee +1
An emerging new paradigm for solving inverse problems is via the use of deep learning to learn a regularizer from data. This leads to high-quality results, but often at the cost of…