{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:6KV3STARSKM2X2SLZFDLVAVBFA","short_pith_number":"pith:6KV3STAR","canonical_record":{"source":{"id":"2509.02981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-03T03:42:22Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"019abf23ef097615c832d773cb54563e213029b0d97d202ad9c6199f2174ead5","abstract_canon_sha256":"302c147a54872ff42186bba3d3947721f26135a3ed09ae5c80e17bb901a94d04"},"schema_version":"1.0"},"canonical_sha256":"f2abb94c119299abea4bc946ba82a12808c85e8f985ae0e49fe59c815b3f6d14","source":{"kind":"arxiv","id":"2509.02981","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02981","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02981v2","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02981","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"6KV3STARSKM2","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"6KV3STARSKM2X2SL","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"6KV3STAR","created_at":"2026-07-05T12:06:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:6KV3STARSKM2X2SLZFDLVAVBFA","target":"record","payload":{"canonical_record":{"source":{"id":"2509.02981","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-03T03:42:22Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"019abf23ef097615c832d773cb54563e213029b0d97d202ad9c6199f2174ead5","abstract_canon_sha256":"302c147a54872ff42186bba3d3947721f26135a3ed09ae5c80e17bb901a94d04"},"schema_version":"1.0"},"canonical_sha256":"f2abb94c119299abea4bc946ba82a12808c85e8f985ae0e49fe59c815b3f6d14","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:20.026793Z","signature_b64":"+Qf9ILr9IJeR2YdzvH0SYFV6OHc8lgqiNx+gxsG4T7P1ddPs+bJSr8u+PqayNVIpcUYri+uEGWaglwQyhvJhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2abb94c119299abea4bc946ba82a12808c85e8f985ae0e49fe59c815b3f6d14","last_reissued_at":"2026-07-05T12:06:20.026263Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:20.026263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.02981","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xXwuIHVxZWlp99SqC6Bf2uCa6Eg4sgB9fF2/IpGPGY3ghEi1GDBVlIHi/chZxnTdJ9nHN/+Z//3aX4om8+daAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:35:32.524109Z"},"content_sha256":"a1dcb0622c3db7db406b25a0f0765e8c043441a57bfabfe29a903a128906cda1","schema_version":"1.0","event_id":"sha256:a1dcb0622c3db7db406b25a0f0765e8c043441a57bfabfe29a903a128906cda1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:6KV3STARSKM2X2SLZFDLVAVBFA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Hayden Schaeffer, Minxin Zhang, Yuxuan Liu","submitted_at":"2025-09-03T03:42:22Z","abstract_excerpt":"The recently proposed Muon optimizer updates weight matrices via orthogonalized momentum and has demonstrated strong empirical success in large language model training. However, it remains unclear how to determine the learning rates for such orthogonalized updates. AdaGrad, by contrast, is a widely used adaptive method that scales stochastic gradients by accumulated past gradients. We propose a new algorithm, AdaGO, which combines a norm-based AdaGrad-type stepsize with an orthogonalized update direction, bringing together the benefits of both approaches. Unlike other adaptive variants of Muon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02981","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.02981/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T12:06:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWn1sj9T4dGW7G/3m2+1eoMYPGIQEjRRskHF0HggSRlwMvMgQWG+Ubf/SBhg3rOEeeQ4XMryT138dTKlqEMpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:35:32.525074Z"},"content_sha256":"317d8de8b0ca54e8fc73ba1af4aa1461a6275bc716b93acd3b5f66625373b930","schema_version":"1.0","event_id":"sha256:317d8de8b0ca54e8fc73ba1af4aa1461a6275bc716b93acd3b5f66625373b930"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KV3STARSKM2X2SLZFDLVAVBFA/bundle.json","state_url":"https://pith.science/pith/6KV3STARSKM2X2SLZFDLVAVBFA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KV3STARSKM2X2SLZFDLVAVBFA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-05T21:35:32Z","links":{"resolver":"https://pith.science/pith/6KV3STARSKM2X2SLZFDLVAVBFA","bundle":"https://pith.science/pith/6KV3STARSKM2X2SLZFDLVAVBFA/bundle.json","state":"https://pith.science/pith/6KV3STARSKM2X2SLZFDLVAVBFA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KV3STARSKM2X2SLZFDLVAVBFA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6KV3STARSKM2X2SLZFDLVAVBFA","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"302c147a54872ff42186bba3d3947721f26135a3ed09ae5c80e17bb901a94d04","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-03T03:42:22Z","title_canon_sha256":"019abf23ef097615c832d773cb54563e213029b0d97d202ad9c6199f2174ead5"},"schema_version":"1.0","source":{"id":"2509.02981","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.02981","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"arxiv_version","alias_value":"2509.02981v2","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.02981","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_12","alias_value":"6KV3STARSKM2","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_16","alias_value":"6KV3STARSKM2X2SL","created_at":"2026-07-05T12:06:20Z"},{"alias_kind":"pith_short_8","alias_value":"6KV3STAR","created_at":"2026-07-05T12:06:20Z"}],"graph_snapshots":[{"event_id":"sha256:317d8de8b0ca54e8fc73ba1af4aa1461a6275bc716b93acd3b5f66625373b930","target":"graph","created_at":"2026-07-05T12:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2509.02981/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The recently proposed Muon optimizer updates weight matrices via orthogonalized momentum and has demonstrated strong empirical success in large language model training. However, it remains unclear how to determine the learning rates for such orthogonalized updates. AdaGrad, by contrast, is a widely used adaptive method that scales stochastic gradients by accumulated past gradients. We propose a new algorithm, AdaGO, which combines a norm-based AdaGrad-type stepsize with an orthogonalized update direction, bringing together the benefits of both approaches. Unlike other adaptive variants of Muon","authors_text":"Hayden Schaeffer, Minxin Zhang, Yuxuan Liu","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-03T03:42:22Z","title":"AdaGrad Meets Muon: Adaptive Stepsizes for Orthogonal Updates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.02981","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a1dcb0622c3db7db406b25a0f0765e8c043441a57bfabfe29a903a128906cda1","target":"record","created_at":"2026-07-05T12:06:20Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"302c147a54872ff42186bba3d3947721f26135a3ed09ae5c80e17bb901a94d04","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2025-09-03T03:42:22Z","title_canon_sha256":"019abf23ef097615c832d773cb54563e213029b0d97d202ad9c6199f2174ead5"},"schema_version":"1.0","source":{"id":"2509.02981","kind":"arxiv","version":2}},"canonical_sha256":"f2abb94c119299abea4bc946ba82a12808c85e8f985ae0e49fe59c815b3f6d14","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2abb94c119299abea4bc946ba82a12808c85e8f985ae0e49fe59c815b3f6d14","first_computed_at":"2026-07-05T12:06:20.026263Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:20.026263Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Qf9ILr9IJeR2YdzvH0SYFV6OHc8lgqiNx+gxsG4T7P1ddPs+bJSr8u+PqayNVIpcUYri+uEGWaglwQyhvJhCg==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:20.026793Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.02981","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a1dcb0622c3db7db406b25a0f0765e8c043441a57bfabfe29a903a128906cda1","sha256:317d8de8b0ca54e8fc73ba1af4aa1461a6275bc716b93acd3b5f66625373b930"],"state_sha256":"0dad8c35c97770dfdc996beff10c48b0b68cc3d54b7e9fad264261d1ae251a3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jjLog2gXlTI7ydzVYeeGOgviU38MRjlEU55Q6PX9WT1esIbDaSVq0JrS4S7/lg9UQDqXeh6aSOb57qI0jo5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T21:35:32.533479Z","bundle_sha256":"9b9155c6a5d05215476f13d0243a599a4b29e51efd3e28464e61aa725bb46888"}}