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Unstructured transition matrices enable maximal expressivity, as measured by their ability to model finite-state automaton (FSA) transitions, but come at a prohibitively high compute and memory cost. In contrast, most structured transition matrix forms are highly efficient both in runtime and memory consumption, but suffer from limited expressivity. Building on recent work on structured sparse SSMs, we propose Flash PD-SSM, a novel SSM that achieves comparable throughput to widely-used structured SSMs with significantly better expressivity guarantees. Flash PD-SSM maintains a trainable set of structured sparse matrices, a single one of which is discretely selected at each time-step, enabling FSA expressiveness at the level of unstructured matrices while maintaining the eff","title":"Flash PD-SSM: Memory-Optimized Structured Sparse State-Space Models","url":"https://arxiv.org/abs/2605.19150","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.19150v1 Announce Type: cross \nAbstract: State-space models (SSMs) face a fundamental trade-off between efficiency and expressivity that is mainly dictated by the structure of the model's transition matrix. Unstructured transition matrices enable maximal expressivity, as measured by their ability to model finite-state automaton (FSA) transitions, but come at a prohibitively high compute and memory cost. In contrast, most structured transition matrix forms are highly efficient both in runtime and memory consumption, but suffer from limited expressivity. Building on recent work on structured sparse SSMs, we propose Flash PD-SSM, a novel SSM that achieves comparable throughput to widely-used structured SSMs with significantly better expressivity guarantees. Flash PD-SSM maintains a trainable set of structured sparse matrices, a single one of which is discretely selected at each time-step, enabling FSA expressiveness at the level of unstructured matrices while maintaining the eff","title":"Flash PD-SSM: Memory-Optimized Structured Sparse State-Space Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-20T04:43:44Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.19150"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:09dcb45897814bba538874f8ca0a294cb8607b2f67c0dd0f12d0a084bf5b76939d7d9df4138c712d5d6207d3d3520a71dd0fa7ea6f15c0b66521611d036ca305","signer":"crovia.substrate","subject":{"observed_at":"2026-05-20T04:43:44Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.19150"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"68fd6393f44f410682c00299700d972f1681c3df27c7377aaebe8a7720b3aebc","leaf_index":145084,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"53ec3271309f64b7291a1305431b4ae944a4c8edbd47980965c91d95cd386d91","side":"right"},{"sibling":"91cfdbf6cda6353c12c9931c2ff9fab91a9edcf1336d117d36d7be427945a8d9","side":"right"},{"sibling":"70bb782e9ad669b2b4e2a91ee630035512397fed9fee601414ef1351f33f4803","side":"left"},{"sibling":"9cf4a0e9ee02e6d8cca45a64d2e0810236fcbc986fa412ce0439039255d39cfa","side":"left"},{"sibling":"224bed9cafef62f1104019003daf8283dc33b820202293989f0d7d19434d49cf","side":"left"},{"sibling":"6498b36e278698012393fb252639299d44ff76d3bbc2b98f93604927ea46e4ae","side":"left"},{"sibling":"3c054fc9610e75398c84d6602026026e93d4cc85db18f6da86b0e99184718c59","side":"right"},{"sibling":"3047d0cbdc103ff93a1a073ea940e12ff062595dae419513748ed63fbcb3359c","side":"left"},{"sibling":"9db04d2181fb869f16a5baf7dcfe999cc93a7e9beef8493d0cc71f57470fe5e1","side":"right"},{"sibling":"1526885f19d1fadf6955cf519dbc4e62d593a4bba99d741e8c301740a7068233","side":"left"},{"sibling":"e3a7d5c07f161682d61bd453ffc02ecdf87cfeda70f986d6650017f9d2d6b265","side":"left"},{"sibling":"edbc49f08e5b92291934c05c9e6efd270a6b0698d8d2fa474006366027dfe098","side":"right"},{"sibling":"3e4df6e7457cecbf36f350375e72dcab336a3984422e4c406ef809e4e2944e96","side":"left"},{"sibling":"8f4c0fbe56b6c010fbb8c782ebcd478079bb3f991d8704e2534209a075d9163c","side":"left"},{"sibling":"be08fedc4e72a6fb56606f66812fae7317e09690b9acb18385f4ab117a981238","side":"right"},{"sibling":"0534329a7475dc9df51998c83c16892126679dade0fa34182f21e869599386c7","side":"right"},{"sibling":"2d24720928ead0e7670650eb55f558c4f20e4c18df376f47ba72cfa8cf0ed344","side":"right"},{"sibling":"d841ad93efda0869e5eb97678f348f03f5caab4353e05ff4bf18f47fb945b822","side":"left"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":147301,"merkle_root":"08903d7159c3b38eeeeafc09eab15139ea417f1d94f02f1fbc87296b37db840a","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260521T183701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-21T18:37:33Z","sig_algorithm":"ed25519","signature":"905f2924632dfa2970c8690285f5b5d4a1d891d0e0ef1cbc404ebec2fd937215ac768e16f0a9f28b18977a55ae0bfd226db6833ae7ef588729054117d2da7303","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_5d3844286216492a4eb88f1a80cf3e3c6d4e38eae9b7021e099e0f3fc799766f"}}