{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JYRBSRP2A354X3KJTPBJG57ZRL","short_pith_number":"pith:JYRBSRP2","schema_version":"1.0","canonical_sha256":"4e221945fa06fbcbed499bc29377f98adaa430a320fdde3d978fda23c0ec3fdc","source":{"kind":"arxiv","id":"2503.10251","version":2},"attestation_state":"computed","paper":{"title":"Numerical stability analysis of large language models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Longbin Zeng, Philipp Petersen, Stanislav Budzinskiy, Wenyi Fang","submitted_at":"2025-03-13T10:53:17Z","abstract_excerpt":"Transformers are the state-of-the-art architecture for large language models, and a key to their scalability is the strategic usage of low-precision arithmetic. We develop a mixed-precision analysis of transformer inference, deriving bounds for the condition numbers and forward error of the architecture's constituent parts. Notably, we compare the numerical stability of LayerNorm and RMSNorm in the massive-outlier regime, tighten the error bound of softmax in the presence of attention sinks, and quantify the impact of its shifted evaluation on the sensitivity to perturbations. Furthermore, we "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2503.10251","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2025-03-13T10:53:17Z","cross_cats_sorted":["cs.LG","cs.NA","stat.ML"],"title_canon_sha256":"dc8e6e0c6e7b40d276f42363b543da657b2a2267411258c7d1823301a2ac664e","abstract_canon_sha256":"a5bc879f4a2adb98010f830bf8138fbf3e7d0b0a7108c31593e9ee98ab25e18d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:13:44.721088Z","signature_b64":"5tqxZgYpMAaJJ0GthcK6KYIBoqEty1OwXL6Zz/eDx+/gmAH/a40UK0c/7jMU8Rd69M34FgJPmjAhGzuCoDKxCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e221945fa06fbcbed499bc29377f98adaa430a320fdde3d978fda23c0ec3fdc","last_reissued_at":"2026-06-23T03:13:44.720592Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:13:44.720592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Numerical stability analysis of large language models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","cs.NA","stat.ML"],"primary_cat":"math.NA","authors_text":"Longbin Zeng, Philipp Petersen, Stanislav Budzinskiy, Wenyi Fang","submitted_at":"2025-03-13T10:53:17Z","abstract_excerpt":"Transformers are the state-of-the-art architecture for large language models, and a key to their scalability is the strategic usage of low-precision arithmetic. We develop a mixed-precision analysis of transformer inference, deriving bounds for the condition numbers and forward error of the architecture's constituent parts. Notably, we compare the numerical stability of LayerNorm and RMSNorm in the massive-outlier regime, tighten the error bound of softmax in the presence of attention sinks, and quantify the impact of its shifted evaluation on the sensitivity to perturbations. Furthermore, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.10251","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/2503.10251/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2503.10251","created_at":"2026-06-23T03:13:44.720650+00:00"},{"alias_kind":"arxiv_version","alias_value":"2503.10251v2","created_at":"2026-06-23T03:13:44.720650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.10251","created_at":"2026-06-23T03:13:44.720650+00:00"},{"alias_kind":"pith_short_12","alias_value":"JYRBSRP2A354","created_at":"2026-06-23T03:13:44.720650+00:00"},{"alias_kind":"pith_short_16","alias_value":"JYRBSRP2A354X3KJ","created_at":"2026-06-23T03:13:44.720650+00:00"},{"alias_kind":"pith_short_8","alias_value":"JYRBSRP2","created_at":"2026-06-23T03:13:44.720650+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2505.06708","citing_title":"Gated Attention for Large Language Models: Non-linearity, Sparsity, and Attention-Sink-Free","ref_index":2,"is_internal_anchor":true},{"citing_arxiv_id":"2604.23505","citing_title":"Uncertainty Propagation in LLM-Based Systems","ref_index":45,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL","json":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL.json","graph_json":"https://pith.science/api/pith-number/JYRBSRP2A354X3KJTPBJG57ZRL/graph.json","events_json":"https://pith.science/api/pith-number/JYRBSRP2A354X3KJTPBJG57ZRL/events.json","paper":"https://pith.science/paper/JYRBSRP2"},"agent_actions":{"view_html":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL","download_json":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL.json","view_paper":"https://pith.science/paper/JYRBSRP2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2503.10251&json=true","fetch_graph":"https://pith.science/api/pith-number/JYRBSRP2A354X3KJTPBJG57ZRL/graph.json","fetch_events":"https://pith.science/api/pith-number/JYRBSRP2A354X3KJTPBJG57ZRL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL/action/storage_attestation","attest_author":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL/action/author_attestation","sign_citation":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL/action/citation_signature","submit_replication":"https://pith.science/pith/JYRBSRP2A354X3KJTPBJG57ZRL/action/replication_record"}},"created_at":"2026-06-23T03:13:44.720650+00:00","updated_at":"2026-06-23T03:13:44.720650+00:00"}