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However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabiliti","title":"Generalizing Graph Foundation Models via Hyperbolic Retrieval-Augmented Generation","url":"https://arxiv.org/abs/2606.03307","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.03307v1 Announce Type: cross \nAbstract: Graph foundation models (GFMs) emerged as a dominant paradigm in graph representation learning by leveraging large-scale pre-training for cross-domain inference. However, the parameterized knowledge encoded within these models is insufficient to cope with distribution shifts, limiting their generalization ability. To mitigate this issue, retrieval-augmented generation (RAG) has been introduced to incorporate external knowledge at inference time. Nevertheless, existing RAG frameworks operating in Euclidean space suffer from a fundamental geometric limitation: the polynomial volume growth of Euclidean space is inherently mismatched with the tree-structured external knowledge bases. This mismatch leads to the loss of semantic granularity in retrieval and gives rise to the hubness phenomenon.To address this limitation, we propose a Hyperbolic Retrieval-Augmented Generation (HyRAG) framework designed to enhance the generalization capabiliti","title":"Generalizing Graph Foundation Models via Hyperbolic Retrieval-Augmented Generation","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-03T04:43:57Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.03307"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:be352bbc6f146381c32f26aaa781d134517461fe06d27a3762883acdc0a2d1aa07e8e72485e93a96a6972aec4b4b8d8e83c8a3bde78dd1772f237941484c620a","signer":"crovia.substrate","subject":{"observed_at":"2026-06-03T04:43:57Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.03307"},"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":"f9f291d70b6d1e39c58e9ee00c475038587860b7e436e7821cbbe409df136770","leaf_index":209202,"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":"3b765a8d3566f8be7b08581584f43035c2f144f3b21856bb330a94243b461c18","side":"right"},{"sibling":"a3c11000199c682b74d62f8518eb1a8e2790d35da0fe73b5c252075d489ef72c","side":"left"},{"sibling":"5e0245b456a1079b3a778568ff3c263f0567d4fe03cd46d4c1ee2c0fec9d0c84","side":"right"},{"sibling":"352970f07d564513d8c75030c80c23ed31e890330e9a870fdfe9c066c40ab652","side":"right"},{"sibling":"218b4187892503cbe70056c2e9f07d379e3857e4c01117fe9dac87c0ec8527d2","side":"left"},{"sibling":"f8476278732bb4d41b8c08d522b3f3fda7a02a51bed0d8aa9461d027be7500a1","side":"left"},{"sibling":"40052708582da742bf088b0c30cd584ba95f867aa32f06040dcfa4b5df18f737","side":"right"},{"sibling":"2ef1f1a576d002b7a433f7807e3e3de79248e5d1145c4394fef6eb45b8063603","side":"right"},{"sibling":"2b9867040ec52d22722edc26b204e15651723dcc66d361cc1af11490a854d461","side":"left"},{"sibling":"2abcec6d14b256f82b270a3141886de6129141dec525543607b760f02588a877","side":"right"},{"sibling":"2b6b45743f97ac502854e489ac38a3366f8ae7ede58a2728b45daadbf29e9d03","side":"right"},{"sibling":"a81babbd79ea0da9e030dd7f43bffb6519d214317decd50727bea4e78189d970","side":"right"},{"sibling":"2dca509b3eb767a47cf215d4315f230ce9103a76264412008ae23a349b519ef1","side":"left"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"8d3baa674a45fd8bc6d3e8d25298f4bec86c72fa8259d576c330d12955c7b4f7","side":"right"},{"sibling":"e32819d1eff909db08066d1703f2db3f091cddac19378b2c0c625ab11e3fdbc0","side":"right"},{"sibling":"c300cf0154c136afc09b1702a0be98f4ba5b6dc5cf57e8cc714ec1eaf4196eff","side":"left"},{"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":209569,"merkle_root":"c852efc8ad7dfffc196c71380f79e6398bcaf566974cbae7c9950b0f600d5bc8","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260603T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-03T05:37:57Z","sig_algorithm":"ed25519","signature":"1ca417607effc813341721cfdade0a2d2d4ba96a90d361dbc3e864b6991b90abc326ec41d9ba3e7110cc04adb29d7b8d95abea7ff2ab8c591b2f864ed7270c03","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_ec91c101f3dc3d818431e52e036db7259a2338e90b79bd4ddbdc0566ac13857d"}}