Finite Filtering Under Continuous Symmetry Reduction

Establish whether a continuous symmetry reduction of a continuum latent multiplier model, formulated as a quotient \(M/G\) by a continuous group acting on the state manifold, can produce a computationally finite filtering procedure and characterize the conditions under which it does so.

Background

The paper’s sector filter exploits a finite permutation symmetry to replace the microscopic MSM state space with an occupation-vector quotient. It proposes extending this idea to continuum latent multiplier models with a continuous group $G$ acting on a state manifold $M$, using the quotient $M/G$ and Lie-algebraic invariants to describe the reduced state. The feasibility of obtaining a finite computational filtering procedure from such a continuous reduction, and the assumptions required for that outcome, are left unresolved.