← 研踪 PaperTrailarXiv:2611.03101 · v1
Diagonal Equivalence in State Space Models: Characterization, Retrieval Rank, and Selective Extensions
首次提交 2026-11-02 21:17
版本更新 2026-11-02 21:17
雷达观测 2026-11-04 23:41
摘要
We classify real and complex state-space models (SSMs) with linear transitions, distinguishing fixed-basis diagonal equivalence from input-output equivalence and tracking coefficient-conditioning windows under coordinate changes. We characterize diagonal equivalence through commuting transition families whose members are diagonalizable over the chosen field. With time-shared token-local matrix maps, we identify this class's state-mediated kernels with unnormalized scalar-mode linear attention with multiplicative masks. Mamba 3's multiple-input, multiple-output (MIMO) construction lifts one value per local interface; SSD-MIMO routes independent values for local retrieval rank above one. HybridMamba combines Mamba 1's per-coordinate decay, Mamba 2-style heads and Mamba 3's complex rotations and two-endpoint writes, mixing real and rotating state blocks with different decay laws. They recover Mamba 1-3 single-input, single-output (SISO) configurations as exact special cases. On five large H100 bfloat16 workloads, our fused GPU kernels improve geometric-mean training time over official Mamba 1/3 in matched SISO recoveries, with Mamba 2 near parity at SSM-core scope. Memory tradeoffs depend on the baseline and metric: saved-for-backward versus peak allocation. In small-model multi-token recall experiments, both designs outperform Mamba 1-3 on the hardest tier; higher routing ranks perform best in gated or phase-diverse configurations. In single-seed language models with about 500M parameters, both improve on Mamba 1/2 in test loss at 2B tokens, but the routing gains do not translate into lower language-model loss. Our best configurations approach Mamba 3 SISO through 10B tokens while remaining behind it and Mamba 3 MIMO in language-model loss.
作者备注：81 pages, 6 figures, 33 tables. Code: https://github.com/d-rochau/OrbitSSM
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v1 · 2026-11-02 21:17 · 最新观测版本
Diagonal Equivalence in State Space Models: Characterization, Retrieval Rank, and Selective Extensions
We classify real and complex state-space models (SSMs) with linear transitions, distinguishing fixed-basis diagonal equivalence from input-output equivalence and tracking coefficient-conditioning windows under coordinate changes. We characterize diagonal equivalence through commuting transition families whose members are diagonalizable over the chosen field. With time-shared token-local matrix maps, we identify this class's state-mediated kernels with unnormalized scalar-mode linear attention with multiplicative masks. Mamba 3's multiple-input, multiple-output (MIMO) construction lifts one value per local interface; SSD-MIMO routes independent values for local retrieval rank above one. HybridMamba combines Mamba 1's per-coordinate decay, Mamba 2-style heads and Mamba 3's complex rotations and two-endpoint writes, mixing real and rotating state blocks with different decay laws. They recover Mamba 1-3 single-input, single-output (SISO) configurations as exact special cases. On five large H100 bfloat16 workloads, our fused GPU kernels improve geometric-mean training time over official Mamba 1/3 in matched SISO recoveries, with Mamba 2 near parity at SSM-core scope. Memory tradeoffs depend on the baseline and metric: saved-for-backward versus peak allocation. In small-model multi-token recall experiments, both designs outperform Mamba 1-3 on the hardest tier; higher routing ranks perform best in gated or phase-diverse configurations. In single-seed language models with about 500M parameters, both improve on Mamba 1/2 in test loss at 2B tokens, but the routing gains do not translate into lower language-model loss. Our best configurations approach Mamba 3 SISO through 10B tokens while remaining behind it and Mamba 3 MIMO in language-model loss.
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