{"paper":{"title":"Higher-Order Transformer Derivative Estimates for Explicit Pathwise Learning Guarantees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","cs.NE","math.NA","math.PR","stat.ML"],"primary_cat":"cs.LG","authors_text":"Anastasis Kratsios, Blanka Horvath, Raeid Saqur, Xuwei Yang, Yannick Limmer","submitted_at":"2024-05-26T13:19:32Z","abstract_excerpt":"An inherent challenge in computing fully-explicit generalization bounds for transformers involves obtaining covering number estimates for the given transformer class $T$. Crude estimates rely on a uniform upper bound on the local-Lipschitz constants of transformers in $T$, and finer estimates require an analysis of their higher-order partial derivatives. Unfortunately, these precise higher-order derivative estimates for (realistic) transformer models are not currently available in the literature as they are combinatorially delicate due to the intricate compositional structure of transformer bl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16563","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/2405.16563/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"}