For feature-lifted dynamical systems with unknown finite-group symmetry, the paper proves a representation-theoretic characterization of the minimal identification trajectory length and gives a random-generator algorithm that discovers the symmetry from the same trajectory.
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abstract
Given a faithful finite-dimensional representation $V$ of a finite group $G$ over any field $\mathbb{F}$, we show that any irreducible ${\mathbb{F}}G$-module $W$ appears, as a submodule or a quotient, in $\mathrm{Sym}^m(V)$ for some integer $1 \leq m \leq |G|$ (that may depend on $W$).
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cs.LG 1years
2026 1verdicts
REJECT 1representative citing papers
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Adaptive Symmetry Discovery for Dynamical System Identification
For feature-lifted dynamical systems with unknown finite-group symmetry, the paper proves a representation-theoretic characterization of the minimal identification trajectory length and gives a random-generator algorithm that discovers the symmetry from the same trajectory.