BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Soledad Villar (Mathematical Institute for Data Science at Johns H opkins University) DTSTART:20211202T170000Z DTEND:20211202T180000Z DTSTAMP:20260423T021032Z UID:MPML/60 DESCRIPTION:Title: Eq uivariant machine learning structure like classical physics\nby Soleda d Villar (Mathematical Institute for Data Science at Johns Hopkins Univers ity) as part of Mathematics\, Physics and Machine Learning (IST\, Lisbon)\ n\n\nAbstract\nThere has been enormous progress in the last few years in d esigning neural networks that respect the fundamental symmetries and coord inate freedoms of physical law. Some of these frameworks make use of irred ucible representations\, some make use of high-order tensor objects\, and some apply symmetry-enforcing constraints. Different physical laws obey di fferent combinations of fundamental symmetries\, but a large fraction (pos sibly 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 fu nctions that are equivariant under these symmetries\, or under the Euclide an\, Lorentz\, and Poincare groups\, at any dimensionality d. The key obse rvation is that nonlinear O(d)-equivariant (and related-group-equivariant) functions can be expressed in terms of a lightweight collection of scalar s---scalar products and scalar contractions of the scalar\, vector\, and t ensor inputs. These results demonstrate theoretically that gauge-invariant deep learning models for classical physics with good scaling for large pr oblems are feasible right now.\n LOCATION:https://researchseminars.org/talk/MPML/60/ END:VEVENT END:VCALENDAR