{"_canonicalization":{"envelope_id":"axm_ + sha256(envelope minus {signature, axiom_id, anchors})","envelope_signature":"ed25519(envelope minus {signature, axiom_id})","json":"sort_keys=True, separators=(',',':'), ensure_ascii=False, allow_nan=False, utf-8","leaf_hash":"sha256(0x00 || canonical_json(envelope_full))","seal_signature":"ed25519(seal minus {signature, sig_algorithm})"},"axiom_id":"axm_64cbb8a9991fa185b84813dc5cb0746477b9be2f6e0ebeafe345ca74e54c6c6c","bitcoin_anchor":{"bitcoin_attestations":[],"calendar_attestations":[],"ots_url":"","stamped_at":"","status":"pending_next_stamp"},"envelope":{"anchors":[{"chain":"crovia.axiom_graph","height":0,"merkle_proof":"spider_vendor_press_v1","root_at_anchor":"spider_vendor_press_v1"}],"axiom_id":"axm_64cbb8a9991fa185b84813dc5cb0746477b9be2f6e0ebeafe345ca74e54c6c6c","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"000ff2ab03b26281571b3cc1dec1c85a515cfdb85a7db8b82c1942119b235d8f","published":"Thu, 04 Jun 2026 00:00:00 -0400","receipt_hash":"000ff2ab03b26281571b3cc1dec1c85a515cfdb85a7db8b82c1942119b235d8f","schema":"spider.news.vendor_press.v1","spider":"vendor_press","spider_record":{"axiom_subtype":"news.vendor_press.v1","category":"news","decision_hint":"POSITIVE","envelope_target":"AX.OBS","fingerprint":"000ff2ab03b26281571b3cc1dec1c85a515cfdb85a7db8b82c1942119b235d8f","observed_at":"2026-06-04T04:43:08.243501Z","parent_run_hash":"298818240313a3c9ce3ace3750dbf55845013dc3bc59aeced6331eccefdb61ac","published":"Thu, 04 Jun 2026 00:00:00 -0400","runtime_version":"0.1.0","schema":"spider.news.vendor_press.v1","source_status":200,"source_url":"https://export.arxiv.org/rss/cs.AI","spider":"vendor_press","summary_excerpt":"arXiv:2606.04058v1 Announce Type: cross \nAbstract: Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon. To keep these updates tractable, Muon performs the orthonormalization with the Newton--Schulz (NS) iteration. Since NS is only approximate, directions with small singular values fail to be orthonormalized. In Muon, NS is applied to the momentum matrix at every step, yet little is known about how the singular value spectrum of these momentum matrices behaves during training, or how that behavior changes with model size. We present the first systematic study of this question. Tracking singular value quantiles of the momentum buffer across layers in models ranging from 77M to 2.8B parameters, we observe a consistent picture: after a short burn-in, the quantiles stabilize at a value determined by the layer type and model size. These stabilization values follow rema","title":"Spectral Scaling Laws of Muon","url":"https://arxiv.org/abs/2606.04058","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.04058v1 Announce Type: cross \nAbstract: Orthonormalized update rules have rapidly become a leading choice of optimizer for training large language models, with recent open-source state-of-the-art models adopting Muon. To keep these updates tractable, Muon performs the orthonormalization with the Newton--Schulz (NS) iteration. Since NS is only approximate, directions with small singular values fail to be orthonormalized. In Muon, NS is applied to the momentum matrix at every step, yet little is known about how the singular value spectrum of these momentum matrices behaves during training, or how that behavior changes with model size. We present the first systematic study of this question. Tracking singular value quantiles of the momentum buffer across layers in models ranging from 77M to 2.8B parameters, we observe a consistent picture: after a short burn-in, the quantiles stabilize at a value determined by the layer type and model size. These stabilization values follow rema","title":"Spectral Scaling Laws of Muon","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-06-04T04:43:08Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2606.04058"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:86c1d25f13266a48744036b85ed47a2521917bde205fca70ecfaca6438e6cd82e30e2fb662816b1ccd4115dca003da6bd35042108ee340a815254edd05cddb0a","signer":"crovia.substrate","subject":{"observed_at":"2026-06-04T04:43:08Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2606.04058"},"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":"b9512842f9026e01bb77bb045a560303e7a99d96af4173c2f8e0f0bb7aba9525","leaf_index":212621,"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":"cecf7a702d4b898cff4d7256a992b31329d2223c2e365842960f7e8332878290","side":"left"},{"sibling":"3f92dc458779f6f0e27993f6092422c7e098d20d686929c295d9c19781699727","side":"right"},{"sibling":"57ed2d8e7fcc4b9a7f0357833acb80375fa6118c73eb7301a7a2df54e9a1f1b8","side":"left"},{"sibling":"cc5b8d3c21a9b90b2aca60659a450d08de9b0f4bb8a6b0ca06fac0d68c994ad5","side":"left"},{"sibling":"8f90c56270924f8b15ac4c93191df9965ea2222ffe04275973932730c12c462c","side":"right"},{"sibling":"e45a00123eb622a9e74504132e353e625e4bbbd90046168a18f3faf0a8c32548","side":"right"},{"sibling":"d2014279f61fb9e0da911cabc2d3a32664afdbd198aebf9c06cb2b3f9176da97","side":"right"},{"sibling":"2943aa232ba1099978a3aeee29e3e0c39faa6231597512d9c82160e7a5a2db32","side":"left"},{"sibling":"c78f0d662697b816291c956749c41d06c16e4dc4c3d390f9a90590e3f2821765","side":"right"},{"sibling":"cfb460164a914d1f96a36aa17124b45bb5417829d2adbe5ca48375dbd842ec44","side":"left"},{"sibling":"a84ebc8e894a9893ee34d1afc942d15f28243b926f1e5f9d7f10a3de1e795262","side":"left"},{"sibling":"f8f6bd9da448fa097e2115b71146f61691d9f8807aca291c87c633192a7224e9","side":"left"},{"sibling":"2dca509b3eb767a47cf215d4315f230ce9103a76264412008ae23a349b519ef1","side":"left"},{"sibling":"24d1bb4b13e0e46131b27b70a48e65fcf4e2e14b95e3bb83ade821e9df530f6b","side":"left"},{"sibling":"422bcf7e281ca3a607f3726a5e6b8fabdb85e8b32199b4a86356998e260a0b34","side":"right"},{"sibling":"54a99163a4a62374c3ca6fb46294222f1d4b1a9d0b636e27256b0e093e98239a","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":213053,"merkle_root":"19d104b92c4d7299881c447fb8422611fc9cb8615d37a538959e34a2da7ef55f","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260604T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-06-04T05:37:49Z","sig_algorithm":"ed25519","signature":"630748e88645187aa3b4d4cb8c872cc146180d0301e4c6656f15f99081d7776432715cea2a997b32b7b3a5216f215d19c1b536c0b093100ec843fa0bd65f2101","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_64cbb8a9991fa185b84813dc5cb0746477b9be2f6e0ebeafe345ca74e54c6c6c"}}