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| { | |
| "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": [] | |
| } | |
| ] | |
| } | |
| } | |