Permutation-Equivariant 2D State Space Models: Theory and Canonical Architecture for Multivariate Time Series

ArXi:2603.08753v1 Announce Type: cross Multivariate time series (MTS) modeling often implicitly imposes an artificial ordering over variables, violating the inherent exchangeability found in many real-world systems where no canonical variable axis exists. We formalize this limitation as a violation of the permutation symmetry principle and require state-space dynamics to be permutation-equivariant along the variable axis. In this work, we theoretically characterize the complete canonical form of linear variable coupling under this symmetry constraint.