Research
Beyond Diagonal State Space Models: Exact Non-Abelian Group Tracking, Solvability Barriers, and Geometric Physical Manifolds
arXiv:2610.00329v1 Announce Type: new Abstract: 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 affi
arXiv:2610.00329v1 Announce Type: new Abstract: 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 580,000x advantage), achieving 0.04 deg dead-reckoning error and active tangent denoising; (4) NC-SSM achieves 74.36% on Dyck-2 and 30.26% on deep AST scope tracking (p = 0.0081); and (5) ablation confirms strict isometry is mathematically necessary for lossless long-range associative memory.
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Source: arXiv cs.LG | 2026-10-02