Permutation-Equivariant 2D State Space Models: Theory and Canonical Architecture for Multivariate Time Series
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. We prove that any permutation-equivariant linear 2D state-space system naturally decomposes into local self-dynamics and a global pooled interaction, rendering ordered recurrence...
| Authors | Seungwoo Jeong, Heung-Il Suk |
|---|---|
| Primary category | stat.ML |
| Published | 7 March 2026 |
| Last updated at source | 7 March 2026 |
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