34 citations · 63 across the 8 of their papers we have counts for
9 papers
Warm-starting PDE solvers with any-dimensional machine learning
Wilson G. Gregory, George A. Kevrekidis, Ben Blum-Smith +1
Any-dimensional machine learning models, such as graph neural networks (GNNs), can be naturally trained and evaluated on inputs of different sizes and dimensions. Inspired by the G…
If you can distinguish, you can express: Galois theory, Stone--Weierstrass, machine learning, and linguistics
Ben Blum-Smith, Claudia Brugman, Thomas Conners +1
This essay develops a parallel between the Fundamental Theorem of Galois Theory and the Stone--Weierstrass theorem: both can be viewed as assertions that tie the distinguishing pow…
A Galois theorem for machine learning: Functions on symmetric matrices and point clouds via lightweight invariant features
Ben Blum-Smith, Ningyuan Huang, Marco Cuturi +1
In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by con…
Equivariant geometric convolutions for emulation of dynamical systems
Wilson G. Gregory, David W. Hogg, Ben Blum-Smith +3
Machine learning methods are increasingly being employed as surrogate models in place of computationally expensive and slow numerical integrators for a bevy of applications in the…
Machine learning and invariant theory
Ben Blum-Smith, Soledad Villar
Inspired by constraints from physical law, equivariant machine learning restricts the learning to a hypothesis class where all the functions are equivariant with respect to some gr…
Dimensionless machine learning: Imposing exact units equivariance
Soledad Villar, Weichi Yao, David W. Hogg +2
Units equivariance (or units covariance) is the exact symmetry that follows from the requirement that relationships among measured quantities of physics relevance must obey self-co…
Scalars are universal: Equivariant machine learning, structured like classical physics
Soledad Villar, David W. Hogg, Kate Storey-Fisher +2
There has been enormous progress in the last few years in designing neural networks that respect the fundamental symmetries and coordinate freedoms of physical law. Some of these f…
A rotation group whose subspace arrangement is not from a real reflection group
Ben Blum-Smith
We exhibit a family of real rotation groups whose subspace arrangements are not contained in that of any real reflection group, answering a question of Martino and Singh.
Purely noncommuting groups
Ben Blum-Smith, Fedor Bogomolov
In this paper we define and investigate a class of groups characterized by a representation-theoretic property we call purely noncommuting or PNC. This property guarantees that the…