{
  "schema_version": 1,
  "title": "Reproduction: On Structured State-Space Duality",
  "emoji": "🔁",
  "space_id": "snaykey/repro-ssm-duality",
  "paper": {
    "arxiv_id": "2510.04944",
    "openreview_id": "DKathyl3XN"
  },
  "tags": [
    "icml2026-repro",
    "paper-DKathyl3XN"
  ],
  "updated_at": "2026-07-28T00:00:00+00:00",
  "root": {
    "slug": "index",
    "title": "Reproduction: On Structured State-Space Duality",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-prop-3-1-scalar-identity",
        "title": "Proposition 3.1 establishes the scalar-identity case, showing SSMs with state matrices A_t = a_t I_N are equivalent to 1-semiseparable masked attention with a causal mask (Section 3.2).",
        "file": "pages/claim-1-prop-3-1-scalar-identity/page.md",
        "children": []
      },
      {
        "slug": "claim-2-thm-4-1-necessary-sufficient",
        "title": "Theorem 4.1 gives a necessary and sufficient condition for an N-dimensional SSM to admit a 1-semiseparable masked-attention dual: its corresponding N-semiseparable matrix must have diagonal blocks each containing at most N new columns (Section 4.4, Definition 4.2).",
        "file": "pages/claim-2-thm-4-1-necessary-sufficient/page.md",
        "children": []
      },
      {
        "slug": "claim-3-diagonal-ssd-complexity",
        "title": "General diagonal SSMs are shown to preserve the same O(NTd) training complexity as the scalar-identity case (Algorithm 1) while supporting richer, per-channel dynamics (Section 4.3).",
        "file": "pages/claim-3-diagonal-ssd-complexity/page.md",
        "children": []
      },
      {
        "slug": "claim-4-prop-4-1-nss-nsss",
        "title": "Proposition 4.1 proves the equivalence between N-semiseparable matrices and N-SSS (sequentially semiseparable) representable matrices (Section 4.4).",
        "file": "pages/claim-4-prop-4-1-nss-nsss/page.md",
        "children": []
      },
      {
        "slug": "claim-5-sec-5-softmax-general-ssm",
        "title": "Section 5 demonstrates a limitation: softmax attention is incompatible with the semiseparable-matrix duality framework due to rank explosion, and general (non-diagonal) SSMs may lack any attention dual despite having low state dimension (Section 5).",
        "file": "pages/claim-5-sec-5-softmax-general-ssm/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}