| Abstract: |
| Physical systems represented by point clouds tend to be symmetric with respect simultaneously to Euclidean isometries of space and also relabelings of the points. While there are beautiful results from classical invariant theory that characterize functions separately invariant with respect to either of these types of symmetry, there is currently no analogous result for simultaneous invariance under both types of symmetry at once (unless the number of points is small). We review what is known, and discuss workarounds in machine learning contexts for parametrizing the invariant functions in the absence of complete results from the underlying invariant theory. Joint work with Ningyuan (Teresa) Huang, Alexandra Pevzner, and Soledad Villar. |
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