Machine Learning and Symmetries
Speaker

Soledad Villar, Johns Hopkins University
Time

2022-03-29 09:00 ~ 10:00, in 4 days (Asia/Shanghai Time)
Venue

Online-Tecent/Zoom
Meeting Info

Zoom link

https://unsw.zoom.us/j/82675301781?pwd=UlJGREFncWtjTWFLQzc4TzNyODlZdz09

Meeting ID: 82675301781

Password: 123456

Tencent Meeting

https://voovmeeting.com/dm/jdL3Buw8g1jH

#VooV Meeting：255-062-645

*No password for voov meeting
Abstract

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 frameworks make use of irreducible representations, some make use of high-order tensor objects, and some apply symmetry-enforcing constraints. Different physical laws obey different combinations of fundamental symmetries, but a large fraction (possibly all) of classical physics is equivariant to translation, rotation, reflection (parity), boost (relativity), and permutations. Here we show that it is simple to parameterize universally approximating polynomial functions that are equivariant under these symmetries, or under the Euclidean, Lorentz, and Poincaré groups, at any dimensionality d. The key observation is that nonlinear O(d)-equivariant (and related-group-equivariant) functions can be universally expressed in terms of a lightweight collection of scalars -- scalar products and scalar contractions of the scalar, vector, and tensor inputs. We complement our theory with numerical examples that show that the scalar-based method is simple, efficient, and scalable.
Bio

Soledad Villar is an assistant professor of applied mathematics and statistics at Johns Hopkins University. She received her PhD in mathematics in 2017 from UT Austin, and was later a research fellow at UC Berkeley, and a Moore-Sloan Research Fellow at NYU. Her honors and awards include delivering a commencement speech at UT Austin representing her graduating PhD class in 2017, a Fulbright Fellowship, and she was named a Rising Stars in Computational and Data Sciences in 2019. Her research has been funded by NSF, The Simons Foundation, ONR, and EOARD.
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