{"paper":{"title":"Linformer: Self-Attention with Linear Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Self-attention in transformers can be approximated by a low-rank matrix to reduce complexity to linear in sequence length.","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Belinda Z. Li, Han Fang, Hao Ma, Madian Khabsa, Sinong Wang","submitted_at":"2020-06-08T17:37:52Z","abstract_excerpt":"Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences, as the standard self-attention mechanism of the Transformer uses $O(n^2)$ time and space with respect to sequence length. In this paper, we demonstrate that the self-attention mechanism can be approximated by a low-rank matrix. We further exploit this finding to propose a new self-attention mechanism, which reduces the overall self-attention complexity from $"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We demonstrate that the self-attention mechanism can be approximated by a low-rank matrix... The resulting linear transformer, the Linformer, performs on par with standard Transformer models, while being much more memory- and time-efficient.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the low-rank projection matrices learned or fixed during training preserve enough information for downstream tasks across the full range of sequence lengths and domains the model will encounter.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Linformer approximates self-attention with a low-rank projection to achieve O(n) time and space complexity while matching Transformer accuracy on standard NLP tasks.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Self-attention in transformers can be approximated by a low-rank matrix to reduce complexity to linear in sequence length.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a487fe0efcf41a99445598c202731d9fbab80e318271895095e67dae94cf6208"},"source":{"id":"2006.04768","kind":"arxiv","version":3},"verdict":{"id":"0a08b9c0-8e77-493b-8931-242caa882ea7","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T00:29:37.213350Z","strongest_claim":"We demonstrate that the self-attention mechanism can be approximated by a low-rank matrix... The resulting linear transformer, the Linformer, performs on par with standard Transformer models, while being much more memory- and time-efficient.","one_line_summary":"Linformer approximates self-attention with a low-rank projection to achieve O(n) time and space complexity while matching Transformer accuracy on standard NLP tasks.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the low-rank projection matrices learned or fixed during training preserve enough information for downstream tasks across the full range of sequence lengths and domains the model will encounter.","pith_extraction_headline":"Self-attention in transformers can be approximated by a low-rank matrix to reduce complexity to linear in sequence length."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.04768/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":19,"sample":[{"doi":"","year":2004,"title":"Longformer: The Long-Document Transformer","work_id":"abea7a44-6668-4de7-aab6-f53a6e5aa088","ref_index":1,"cited_arxiv_id":"2004.05150","is_internal_anchor":true},{"doi":"","year":2005,"title":"Language Models are Few-Shot Learners","work_id":"214732c0-2edd-44a0-af9e-28184a2b8279","ref_index":2,"cited_arxiv_id":"2005.14165","is_internal_anchor":true},{"doi":"","year":null,"title":"Training Deep Nets with Sublinear Memory Cost","work_id":"f2c5c287-a500-40e4-a136-e7e3172db1d7","ref_index":3,"cited_arxiv_id":"1604.06174","is_internal_anchor":true},{"doi":"","year":1904,"title":"Generating Long Sequences with Sparse Transformers","work_id":"c5b81688-45ee-4a9a-b095-e6290f45cb6c","ref_index":4,"cited_arxiv_id":"1904.10509","is_internal_anchor":true},{"doi":"","year":2019,"title":"Bert: Pre-training of deep bidirectional transformers for language understanding","work_id":"693b70ad-3022-4615-938e-7752341ec181","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":19,"snapshot_sha256":"d7ab771ae1b9b3bcd851ffe57f3a2ee32c9ae27ca7672a6d6b9c0d536b970ec6","internal_anchors":11},"formal_canon":{"evidence_count":3,"snapshot_sha256":"2b22cdf79b79855b10388867a1a43a9d35d290d2b3eb673140f21aa4e921a432"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}