{"paper":{"title":"Theoretical limitations of multi-layer Transformer","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI","cs.CC","cs.DS"],"primary_cat":"cs.LG","authors_text":"Binghui Peng, Hongxun Wu, Lijie Chen","submitted_at":"2024-12-04T02:37:31Z","abstract_excerpt":"Transformers, especially the decoder-only variants, are the backbone of most modern large language models; yet we do not have much understanding of their expressive power except for the simple $1$-layer case.\n  Due to the difficulty of analyzing multi-layer models, all previous work relies on unproven complexity conjectures to show limitations for multi-layer Transformers. In this work, we prove the first $\\textit{unconditional}$ lower bound against multi-layer decoder-only transformers. For any constant $L$, we prove that any $L$-layer decoder-only transformer needs a polynomial model dimensi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.02975","kind":"arxiv","version":1},"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/2412.02975/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"}