{"_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_fb4d4aabaa2bbc40f0eb4db36126473e035e517e402cb0373b2fa644f99d268c","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_fb4d4aabaa2bbc40f0eb4db36126473e035e517e402cb0373b2fa644f99d268c","axiom_type":"AX.OBS","body":{"axiom_subtype":"news.vendor_press.v1","category":"news","fingerprint":"82be1162bb1f779742406fb31d650c9fa5a2cd8d588ddf700943621caea4e9cc","published":"Wed, 27 May 2026 00:00:00 -0400","receipt_hash":"82be1162bb1f779742406fb31d650c9fa5a2cd8d588ddf700943621caea4e9cc","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":"82be1162bb1f779742406fb31d650c9fa5a2cd8d588ddf700943621caea4e9cc","observed_at":"2026-05-27T04:43:18.926230Z","parent_run_hash":"6f581915edab4326e2b95fed7c82c2ee149e978d6d7c2443439442a927c31dfa","published":"Wed, 27 May 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:2605.26895v1 Announce Type: cross \nAbstract: Normalization layers in modern large language models (LLMs) consist of a deterministic normalization operation and a learnable scale vector. While the normalization operation has been extensively studied, the scale vector remains poorly understood despite its ubiquitous use. In this work, we present a systematic study of scale vectors in LLMs from the perspectives of expressivity, optimization, and architectural structure. First, we show empirically that although scale vectors constitute only a negligible fraction of model parameters, removing them substantially degrades LLM pre-training. Our theory further shows that, in Pre-Norm architectures, scale vectors do not increase expressivity; instead, they improve optimization through a self-amplifying preconditioning effect on subsequent linear mappings. Second, we investigate the role of weight decay for scale vectors. By distinguishing Input-Norm and Output-Norm layers, we theoretically","title":"Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models","url":"https://arxiv.org/abs/2605.26895","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.26895v1 Announce Type: cross \nAbstract: Normalization layers in modern large language models (LLMs) consist of a deterministic normalization operation and a learnable scale vector. While the normalization operation has been extensively studied, the scale vector remains poorly understood despite its ubiquitous use. In this work, we present a systematic study of scale vectors in LLMs from the perspectives of expressivity, optimization, and architectural structure. First, we show empirically that although scale vectors constitute only a negligible fraction of model parameters, removing them substantially degrades LLM pre-training. Our theory further shows that, in Pre-Norm architectures, scale vectors do not increase expressivity; instead, they improve optimization through a self-amplifying preconditioning effect on subsequent linear mappings. Second, we investigate the role of weight decay for scale vectors. By distinguishing Input-Norm and Output-Norm layers, we theoretically","title":"Negligible in Size, Significant in Effect: On Scale Vectors in Large Language Models","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-27T04:43:18Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.26895"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:0114f9a20ef2c48dc8ec68fcefa0a88a00d95dab20c95ca62754bd19ac1263125038856d47eadfc1634eb2a361e03fd8ca788da6147ec52637bbb4168c827602","signer":"crovia.substrate","subject":{"observed_at":"2026-05-27T04:43:18Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.26895"},"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":"4568bb7f37014ee1ede04f163f96eb19418e7e8427d75ed8d356aedf30e1e3f6","leaf_index":153756,"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":"5dc7f37f033c0ac5fa7bd94b74e32620a1dcce3b12fcf6b6ed477c094dfb56d4","side":"right"},{"sibling":"3798406cd343cf1b8905df9898f1634b1d4c6894b699707518d8829e91c85d43","side":"right"},{"sibling":"5e8c36359e32fae464f065f1582c8950f356be462149c154af8ed3c0719d87fb","side":"left"},{"sibling":"0bcb8dd38c2d8efba110c66a1309e796ef05a07db440e81cfe63a5c07d5f0b4e","side":"left"},{"sibling":"e2080db2bd462619883f4b377a84eb88817ac8ca9fa807138db8c58cd09f5471","side":"left"},{"sibling":"341a7e88fd1237bdf4d6a0b6b2be9dd845f0a3b5184a146c3314d61c3efc078b","side":"right"},{"sibling":"1471bf5749919a9fc3bde5501a5be14605bb1a8f59a38e7c49e3fd6fa081da33","side":"right"},{"sibling":"dd15059d2d503b45e928c26e84bea4e5b2d187abeace390e61efd18d39e80f21","side":"left"},{"sibling":"c56e46802f42ead6bcf79619c80428b6dc22e9afc9611a87f0d04a5ef9acadd7","side":"right"},{"sibling":"3165125427a29042fc9d02858a59a68858dbdcb2e19d1afa5f6dd6a95cfbce6a","side":"right"},{"sibling":"04b9a68b8ec6fa37251564383c685c23ce69e5e031df4eae69f79a3a334b68bf","side":"right"},{"sibling":"816f233274bb10f5a122aac086a0c8c697b78fec67a4af55190bb596b7506fab","side":"left"},{"sibling":"d415e6939aee710631f5062799379b547d2c3e3d9a68f263bbb5a693285ab2ca","side":"left"},{"sibling":"374c02d15fb12bd356c179c94766043a982052c6132af8bfc15361b431ffa9f7","side":"right"},{"sibling":"35ca36cee447f0ef7064a25d55f59357c66901e31427729c4c1d8b14aa8adb6c","side":"left"},{"sibling":"990705096edf483cc877217308f731dc42d6f6d99f82880167bbdbbfef32560a","side":"right"},{"sibling":"dd265753d95fa2e2fb4f5768e37fab6f691ccff09ad60d0910ff7dc23bac9226","side":"right"},{"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":154065,"merkle_root":"4993cfdc172e7880b60667f16789dc2e831ff000f81bb1ecba248e73f1510eca","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260527T053701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-27T05:37:36Z","sig_algorithm":"ed25519","signature":"76ecf118011540405e96506e6219752df04a2850632f2903dc6f10e08b98bc5a42c8d9e1cb5b7c5bf714479806a403df5f34399afa40c23fbb71493a1f77bd0c","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_fb4d4aabaa2bbc40f0eb4db36126473e035e517e402cb0373b2fa644f99d268c"}}