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In this work, we identify three structural axioms that any principled relation operator must satisfy, linearity, trace preservation, and complete positivity, and show that they characterize a Kraus channel structure via the Kraus representation theorem. The completeness constraint defining this family is equivalent to these axioms, providing a principled foundation rather than an externally imposed condition. Under this formulation, most existing operator-based KGE models are recoverable as special cases with Kraus rank $\\kappa = 1$ under specific embedding choices. We further generalize this characterization to arbitrary metric geometries by introducing \\mbox{w-Kraus} channels, which satisfy completeness by construction within their respective spaces. Building on this theory, we propose \\textsc{KrausKGE}, a principled KGE mode","title":"Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions","url":"https://arxiv.org/abs/2605.10317","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.10317v1 Announce Type: cross \nAbstract: Knowledge graph embedding (KGE) models typically represent each relation as an operator on entity embeddings. In this work, we identify three structural axioms that any principled relation operator must satisfy, linearity, trace preservation, and complete positivity, and show that they characterize a Kraus channel structure via the Kraus representation theorem. The completeness constraint defining this family is equivalent to these axioms, providing a principled foundation rather than an externally imposed condition. Under this formulation, most existing operator-based KGE models are recoverable as special cases with Kraus rank $\\kappa = 1$ under specific embedding choices. We further generalize this characterization to arbitrary metric geometries by introducing \\mbox{w-Kraus} channels, which satisfy completeness by construction within their respective spaces. Building on this theory, we propose \\textsc{KrausKGE}, a principled KGE mode","title":"Relations Are Channels: Knowledge Graph Embedding via Kraus Decompositions","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-12T04:43:42Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.10317"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:d28b291154811004759f97431caa643ee3ede236a8efe1e65c229a43fb2581cdbd5b9289dd73015c2239ec91c77f881107d4dbd953c191b9838b2710f75ff706","signer":"crovia.substrate","subject":{"observed_at":"2026-05-12T04:43:42Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.10317"},"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":"e74428c8c94f5414a1d5a6f02821d76db0825ff5ffdafd01c9ec3e1a16b0246c","leaf_index":128859,"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":"4b18326067d576ab675a10693fa8f375adffb6bfb4cc5f651fa1d22b387a529a","side":"left"},{"sibling":"0387ae0308a3e7ab11b316573d735e97a72558d78524812d9b76b682e664c118","side":"left"},{"sibling":"743550e69724e98aac1cbc7be2b5784f25d8f55ac129c05c89dce8f09b905e83","side":"right"},{"sibling":"090d939f61421a810aeeb06beaedd058d45d7623654a06c66559cfa2ae6bc2df","side":"left"},{"sibling":"44994356c048f40dd99ab2d25f234abe618e53268c873d1aee1285e843ecb085","side":"left"},{"sibling":"153b5ea7201dd0f711e7e243b09565b35568e59b789bdf4093260eea9b4a8715","side":"right"},{"sibling":"35de91831a229ebffda43a52472669e391dfea2fabdcbb02a5ed218458366227","side":"left"},{"sibling":"17788012ee9d23c33d35ead8be5aa8d08d73dd70833c55b77c06f0f8d286c3ef","side":"right"},{"sibling":"9b7895252355a8c8a373671590682bbf4d36d41befce49b5e889eaf896415156","side":"left"},{"sibling":"1d74b0fb79eace68949b4d82b0e430b1d9eb122c125f67f5be7d50c074c228e7","side":"left"},{"sibling":"c6eaf7a4fcab2db96e9e9423acb6922c80f64882d0f3f50d09e53a4807d23084","side":"left"},{"sibling":"df12eaabc0a370aff5d0488478f48d2b3f90d025c903643f98ea804b017688ec","side":"right"},{"sibling":"ffc4d51379293bc3e1910c7d612f409dc610fd9acf8241793fb89f82e1bad4ef","side":"left"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"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_38dc99d1a19a9fbfd43bb346dec1198ccee6c66754c28f633f7274b4ad8aa836"}}