{
  "abstract": "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03101",
  "author_total": 1,
  "authors": [
    {
      "name": "Dennis Rochau"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vdctr4q1fxv9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03101",
  "fulltext_url": null,
  "id": "4vdctr4q1fxv9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03101",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03101",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vdctr4q1fxv9.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03101",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03101"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Diagonal Equivalence in State Space Models: Characterization, Retrieval Rank, and Selective Extensions",
  "title_text": "Diagonal Equivalence in State Space Models: Characterization, Retrieval Rank, and Selective Extensions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:21:16Z",
  "url": "https://research.draconitic.com/paper/4vdctr4q1fxv9",
  "venue": "arXiv",
  "versions": []
}