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MWIS encompasses many combinatorial challenges, including optimal assignment, scheduling, set packing, and MAP inference in discrete Markov Random Fields. Unlike Belief Propagation, we prove GN always converges to a binary indicator of a Maximum Independent Set. GN realizes a fast quasi-Newton descent through an exact Majorization-Minimization step, systematically improving the MWIS relaxed primal objective. We establish an equivalence between GN and the Replicator Dynamics of a nonlinear evolutionary game, where vertices compete for inclusion in an independent set. While a non-potential game, the GN game follows Fisher's Fundamental Theorem of Natural Selection, where the average fitness equals the MWIS primal objective and strictly increases.","title":"Graph Normalization: Fast Binarizing Dynamics for Differentiable MWIS","url":"https://arxiv.org/abs/2605.05330","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.05330v1 Announce Type: cross \nAbstract: We introduce Graph Normalization (GN), a principled dynamical system on graphs that serves as a differentiable approximation engine for the NP-hard Maximum Weight Independent Set (MWIS) problem. MWIS encompasses many combinatorial challenges, including optimal assignment, scheduling, set packing, and MAP inference in discrete Markov Random Fields. Unlike Belief Propagation, we prove GN always converges to a binary indicator of a Maximum Independent Set. GN realizes a fast quasi-Newton descent through an exact Majorization-Minimization step, systematically improving the MWIS relaxed primal objective. We establish an equivalence between GN and the Replicator Dynamics of a nonlinear evolutionary game, where vertices compete for inclusion in an independent set. While a non-potential game, the GN game follows Fisher's Fundamental Theorem of Natural Selection, where the average fitness equals the MWIS primal objective and strictly increases.","title":"Graph Normalization: Fast Binarizing Dynamics for Differentiable MWIS","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-08T04:43:40Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.05330"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:4c9f121d64bb2af4ee3ea65a4a1d8a47860f11c8b2f1febf9a218374e4d360a37e404748ec9f822387945361a45cc2766d6b319b53f29de41cc500a63f6bca0f","signer":"crovia.substrate","subject":{"observed_at":"2026-05-08T04:43:40Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.05330"},"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":"91a313e25a3bc356f49e3df2ea8bb40913007175dc2f5a1239e79fe9ec58c30e","leaf_index":120173,"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":"13b91b4c0acc48bc5143329301a6a394d3a3a3926385d5a37425a44acb880a5d","side":"left"},{"sibling":"6075b7559273639315fc1320930df9c940cc7c968f4ce562507e1d0044742e00","side":"right"},{"sibling":"f6dbca98a05367119bca1b0d8231081c1274cd871575cd25b8f60f195bbacc5e","side":"left"},{"sibling":"99600aaefd7ea30c0713331404bdfa2999631a4d113964d588ac718de452216e","side":"left"},{"sibling":"0b91a2183a8485ec2ea3b3402b3a398ecbe6b5c8c9806da19360d21a61bc18a0","side":"right"},{"sibling":"55c2fe9ae9c677eb542780acf595acf6df2e8cf81924322ae0460b003293be7a","side":"left"},{"sibling":"fbc97c8ffc4e0529c02cda4ab186b044b09b474182fb9fbd8e687b59c97e08b2","side":"left"},{"sibling":"b1a469ecc2c62da181fb78fb052d1f4d059aafbe92dbb6d04682090381d419fd","side":"right"},{"sibling":"34e93c6f591cc4fb93a4c29771210eb73573b454d2c5329963f437f1309fe46f","side":"left"},{"sibling":"b9834433f5bd1deeaab4ced2b3bcc0d91d19763a5d0981fb299d124b63459eb3","side":"right"},{"sibling":"143f33d3924b3840fd6dd8ba12566fc35bf86189e663ef0ad4884d676f295e3a","side":"left"},{"sibling":"b1ed99341c327c7c9ab2489f40af2547ab3b3b4b6a74fb684210164fb891a413","side":"right"},{"sibling":"6ee3be9bdfc9bee55d32f7dbb0075f02fe87d20887d563d3e300caf36b1b88c7","side":"left"},{"sibling":"8ccd9937a2c0d5c04044d07d1557791b7d07bb31eac41a39a675608d44b38f23","side":"right"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"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":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","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_3ef3c0bfd6da1a8af0c67fff8e048b90f5b60697327ebf82effd8ead375b707d"}}