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Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying either a graph-level regression head or a matching-based alignment module. Despite substantial architectural progress, the role of encoder geometry in neural GED estimation remains poorly understood. In this paper, we develop a theoretical framework that connects encoder geometry to GED estimation quality for two broad classes of neural GED estimators: graph similarity predictors and alignment-based methods. On fixed graph collections, where the doubly-stochastic metric $d_{\\mathrm{DS}}$ is comparable to GED, we show that graph-level bi-Lipschitz encoders yield controlled GED surrogates and improved ranking stability; for matching-based estimators, node-level bi-Lipschitz geometry propagates to encoder-i","title":"Towards Metric-Faithful Neural Graph Matching","url":"https://arxiv.org/abs/2605.06588","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.06588v1 Announce Type: cross \nAbstract: Graph Edit Distance (GED) is a fundamental, albeit NP-hard, metric for structural graph similarity. Recent neural graph matching architectures approximate GED by first encoding graphs with a Graph Neural Network (GNN) and then applying either a graph-level regression head or a matching-based alignment module. Despite substantial architectural progress, the role of encoder geometry in neural GED estimation remains poorly understood. In this paper, we develop a theoretical framework that connects encoder geometry to GED estimation quality for two broad classes of neural GED estimators: graph similarity predictors and alignment-based methods. On fixed graph collections, where the doubly-stochastic metric $d_{\\mathrm{DS}}$ is comparable to GED, we show that graph-level bi-Lipschitz encoders yield controlled GED surrogates and improved ranking stability; for matching-based estimators, node-level bi-Lipschitz geometry propagates to encoder-i","title":"Towards Metric-Faithful Neural Graph Matching","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/2605.06588"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:abab4273f36e4ee0eaca1a44ee94408fbe722bf20c3022af2256ed6e836e7bd177db8ce45e76e1e50dc21f5d0905b2dd606ab33fe70c330ca2fcb183a4f81308","signer":"crovia.substrate","subject":{"observed_at":"2026-05-08T04:43:40Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.06588"},"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":"3d8f64f4be0a19db2ec64ffbe9d0cd8f37396d1cc044b6e0840532d473e7ed70","leaf_index":120340,"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":"5f1d32c2ace851617438d51591b68c04f2598cab406615a0c0764f6d48b3c698","side":"right"},{"sibling":"82295e604a667c19c49807f5327f475441d63dabb1f0786a24c9c8588676443e","side":"right"},{"sibling":"5426a62586f7654ca045a8166578a6891f93593d462d2fcb05d2bcd74b415aab","side":"left"},{"sibling":"b7bcb51915563247e2e69ce990eafe2d57447f98d19e8fb6688f93e60bfcac01","side":"right"},{"sibling":"b159aa5b1adb015ec50faabdc3c956d7367237925440c3a548abeabea55d3788","side":"left"},{"sibling":"ee48c805c85a4e43d4a9d14a4f80b704a7a8eb604db6cb321fb8c6fe08a82186","side":"right"},{"sibling":"ff6dfc3e3819926f225fca4697d75146861a953457867e78f1a01b86559feac7","side":"right"},{"sibling":"621ce3a316503da6017cc9f955ea0dca3f50bbc1e8fc10ed72f522e60e814e3f","side":"right"},{"sibling":"7cb9b06d4f6372fac19d788263daadfaf6def57cc0a73d46bed8b284ec0fe014","side":"right"},{"sibling":"42ade783b0aede9d0209c5be94ac7979e635da84dd65ecb4d383719029bbe8f4","side":"left"},{"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_751e16cd577cdee77cfa7084da2084278d16b006efc9c22d7f72bccbde8c70c7"}}