{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:ISLS4SUCXJZ43V2N3W4MGOT67T","short_pith_number":"pith:ISLS4SUC","schema_version":"1.0","canonical_sha256":"44972e4a82ba73cdd74dddb8c33a7efcceb65af6b82b8f4c183027eb8a854e43","source":{"kind":"arxiv","id":"2105.03824","version":4},"attestation_state":"computed","paper":{"title":"FNet: Mixing Tokens with Fourier Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Ilya Eckstein, James Lee-Thorp, Joshua Ainslie, Santiago Ontanon","submitted_at":"2021-05-09T03:32:48Z","abstract_excerpt":"We show that Transformer encoder architectures can be sped up, with limited accuracy costs, by replacing the self-attention sublayers with simple linear transformations that \"mix\" input tokens. These linear mixers, along with standard nonlinearities in feed-forward layers, prove competent at modeling semantic relationships in several text classification tasks. Most surprisingly, we find that replacing the self-attention sublayer in a Transformer encoder with a standard, unparameterized Fourier Transform achieves 92-97% of the accuracy of BERT counterparts on the GLUE benchmark, but trains 80% "},"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":"2105.03824","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CL","submitted_at":"2021-05-09T03:32:48Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"ed9234676b9629c768996824edc1a6978040d0cc45a8a057cb2517104f430a27","abstract_canon_sha256":"b0c228284009d8021dac7eecadd69a3e3b4bd2894e1b4f33f7aea16823232930"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:26:45.111955Z","signature_b64":"rQIQQw1dCgrsRErjjlVIXYnrc13/JmpHxThOwBgrlS4OrcRu1hYHYBu6Pn7CVd2CtdDUzVC3Jy/MOKpDLFzyCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44972e4a82ba73cdd74dddb8c33a7efcceb65af6b82b8f4c183027eb8a854e43","last_reissued_at":"2026-07-05T04:26:45.111472Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:26:45.111472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"FNet: Mixing Tokens with Fourier Transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"cs.CL","authors_text":"Ilya Eckstein, James Lee-Thorp, Joshua Ainslie, Santiago Ontanon","submitted_at":"2021-05-09T03:32:48Z","abstract_excerpt":"We show that Transformer encoder architectures can be sped up, with limited accuracy costs, by replacing the self-attention sublayers with simple linear transformations that \"mix\" input tokens. These linear mixers, along with standard nonlinearities in feed-forward layers, prove competent at modeling semantic relationships in several text classification tasks. Most surprisingly, we find that replacing the self-attention sublayer in a Transformer encoder with a standard, unparameterized Fourier Transform achieves 92-97% of the accuracy of BERT counterparts on the GLUE benchmark, but trains 80% "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.03824","kind":"arxiv","version":4},"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/2105.03824/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":"2105.03824","created_at":"2026-07-05T04:26:45.111529+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.03824v4","created_at":"2026-07-05T04:26:45.111529+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.03824","created_at":"2026-07-05T04:26:45.111529+00:00"},{"alias_kind":"pith_short_12","alias_value":"ISLS4SUCXJZ4","created_at":"2026-07-05T04:26:45.111529+00:00"},{"alias_kind":"pith_short_16","alias_value":"ISLS4SUCXJZ43V2N","created_at":"2026-07-05T04:26:45.111529+00:00"},{"alias_kind":"pith_short_8","alias_value":"ISLS4SUC","created_at":"2026-07-05T04:26:45.111529+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":11,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.07478","citing_title":"FourierQK: Spectral Preprocessing of Query-Key Projections Improves Transformer Attention","ref_index":12,"is_internal_anchor":true},{"citing_arxiv_id":"2606.08327","citing_title":"Chiaroscuro Attention: Spending Compute in the Dark","ref_index":14,"is_internal_anchor":false},{"citing_arxiv_id":"2606.01258","citing_title":"Beyond Sinusoids: A Morlet Wavelet Framework for Transformer Positional Encoding","ref_index":3,"is_internal_anchor":false},{"citing_arxiv_id":"2606.09862","citing_title":"Blurry Window Attention","ref_index":36,"is_internal_anchor":false},{"citing_arxiv_id":"2508.06038","citing_title":"Fourier Compressor: Frequency-Domain Visual Token Compression for Vision-Language Models","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2509.12635","citing_title":"Positional Encoding via Token-Aware Phase Attention","ref_index":9,"is_internal_anchor":false},{"citing_arxiv_id":"2604.17986","citing_title":"Latent Fourier Transform","ref_index":24,"is_internal_anchor":false},{"citing_arxiv_id":"2604.19028","citing_title":"Learning Posterior Predictive Distributions for Node Classification from Synthetic Graph Priors","ref_index":272,"is_internal_anchor":false},{"citing_arxiv_id":"2405.21060","citing_title":"Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality","ref_index":56,"is_internal_anchor":false},{"citing_arxiv_id":"2604.06694","citing_title":"AudioKV: KV Cache Eviction in Efficient Large Audio Language Models","ref_index":13,"is_internal_anchor":false},{"citing_arxiv_id":"2604.14724","citing_title":"HAMSA: Scanning-Free Vision State Space Models via SpectralPulseNet","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T","json":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T.json","graph_json":"https://pith.science/api/pith-number/ISLS4SUCXJZ43V2N3W4MGOT67T/graph.json","events_json":"https://pith.science/api/pith-number/ISLS4SUCXJZ43V2N3W4MGOT67T/events.json","paper":"https://pith.science/paper/ISLS4SUC"},"agent_actions":{"view_html":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T","download_json":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T.json","view_paper":"https://pith.science/paper/ISLS4SUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.03824&json=true","fetch_graph":"https://pith.science/api/pith-number/ISLS4SUCXJZ43V2N3W4MGOT67T/graph.json","fetch_events":"https://pith.science/api/pith-number/ISLS4SUCXJZ43V2N3W4MGOT67T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T/action/storage_attestation","attest_author":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T/action/author_attestation","sign_citation":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T/action/citation_signature","submit_replication":"https://pith.science/pith/ISLS4SUCXJZ43V2N3W4MGOT67T/action/replication_record"}},"created_at":"2026-07-05T04:26:45.111529+00:00","updated_at":"2026-07-05T04:26:45.111529+00:00"}