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Beyond Diagonal State Space Models: Exact Non-Abelian Group Tracking, Solvability Barriers, and Geometric Physical Manifolds
Selective state space models (SSMs), such as Mamba, S4D, and LRU, are bounded by transition matrix commutativity (A_t A_t' = A_t' A_t) and solvable affine transformation groups (Aff_D of derived length <= 2). Consequently, stacked multi-layer diagonal networks face severe optimization degradation on
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