Web: http://arxiv.org/abs/2205.02956

May 9, 2022, 1:11 a.m. | Nadav Dym, Steven J. Gortler

cs.LG updates on arXiv.org arxiv.org

This paper studies separating invariants: mappings on $d$-dimensional
semi-algebraic subsets of $D$ dimensional Euclidean domains which are invariant
to semi-algebraic group actions and separate orbits. The motivation for this
study comes from the usefulness of separating invariants in proving
universality of equivariant neural network architectures.

We observe that in several cases the cardinality of separating invariants
proposed in the machine learning literature is much larger than the ambient
dimension $D$. As a result, the theoretical universal constructions based on
these …

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