CHMP performance on other compact groups

Determine how the Cycle-Hyperedge Message Passing (CHMP) algorithm performs on compact groups beyond \(SO(2)\) and \(SO(3)\), including \(\mathbb{Z}/2\mathbb{Z}\) and permutation groups \(S_n\).

Background

The theoretical framework is presented for compact groups, but the numerical evaluation is restricted to $SO(2)$ and $SO(3)$. The conclusion explicitly identifies the algorithm’s behavior on other compact groups, such as the binary group and permutation groups, as unresolved.