{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ITFBBX2Y4QTGWPUTJKGRI2AXTF","short_pith_number":"pith:ITFBBX2Y","canonical_record":{"source":{"id":"1912.10077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-12-20T19:49:32Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d7cb441cb479e7a1d4ee538f376ac5a57c869bab985d68cfd418962c549ae22d","abstract_canon_sha256":"fd5747e382e698b86361fdb01a96ed36de82f0f055f4e70dec9b8ad6d1eb1cad"},"schema_version":"1.0"},"canonical_sha256":"44ca10df58e4266b3e934a8d146817994eb89f77ecf5a7d6c068ffd8258a67c0","source":{"kind":"arxiv","id":"1912.10077","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.10077","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1912.10077v2","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.10077","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"ITFBBX2Y4QTG","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"pith_short_16","alias_value":"ITFBBX2Y4QTGWPUT","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"pith_short_8","alias_value":"ITFBBX2Y","created_at":"2026-07-05T00:43:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ITFBBX2Y4QTGWPUTJKGRI2AXTF","target":"record","payload":{"canonical_record":{"source":{"id":"1912.10077","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-12-20T19:49:32Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"d7cb441cb479e7a1d4ee538f376ac5a57c869bab985d68cfd418962c549ae22d","abstract_canon_sha256":"fd5747e382e698b86361fdb01a96ed36de82f0f055f4e70dec9b8ad6d1eb1cad"},"schema_version":"1.0"},"canonical_sha256":"44ca10df58e4266b3e934a8d146817994eb89f77ecf5a7d6c068ffd8258a67c0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:43:21.543694Z","signature_b64":"BPe1VY2OADlrAneYJdD+1Tuob8DxwsEGkr9JOVR/6jXXs84JK3BGEydrjMl3iEjMyHvE3uZR3QRn7Jzo4AKgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44ca10df58e4266b3e934a8d146817994eb89f77ecf5a7d6c068ffd8258a67c0","last_reissued_at":"2026-07-05T00:43:21.543204Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:43:21.543204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.10077","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8AniGL2Nuxj39/+W9nDIMbK4FNVx1TtJNTVG1g6kqERvR7o/BFy25uqHWDxntnhHGTvSevmtk1LuhO9+b28YCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:46:10.616451Z"},"content_sha256":"bbb657d5f1807e2880001d68d60685c600dc9a9b38db0603661a07207080bd7e","schema_version":"1.0","event_id":"sha256:bbb657d5f1807e2880001d68d60685c600dc9a9b38db0603661a07207080bd7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ITFBBX2Y4QTGWPUTJKGRI2AXTF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Are Transformers universal approximators of sequence-to-sequence functions?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Ankit Singh Rawat, Chulhee Yun, Sanjiv Kumar, Sashank J. Reddi, Srinadh Bhojanapalli","submitted_at":"2019-12-20T19:49:32Z","abstract_excerpt":"Despite the widespread adoption of Transformer models for NLP tasks, the expressive power of these models is not well-understood. In this paper, we establish that Transformer models are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, which is quite surprising given the amount of shared parameters in these models. Furthermore, using positional encodings, we circumvent the restriction of permutation equivariance, and show that Transformer models can universally approximate arbitrary continuous sequence-to-sequence functions on a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.10077","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/1912.10077/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:43:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZuLGnyFCG25Bs/RabeUADzwr3SE7K3Mkv6lSyKyJ9C/1Y+nCq4QSryy6J+wTy/PHi7eYtLgs4YMwg08vKvTcAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:46:10.616946Z"},"content_sha256":"6fd69902510edb5270a5450ef865206fd6d359b855528f981309595dd3a8c2c2","schema_version":"1.0","event_id":"sha256:6fd69902510edb5270a5450ef865206fd6d359b855528f981309595dd3a8c2c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF/bundle.json","state_url":"https://pith.science/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T04:46:10Z","links":{"resolver":"https://pith.science/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF","bundle":"https://pith.science/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF/bundle.json","state":"https://pith.science/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITFBBX2Y4QTGWPUTJKGRI2AXTF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ITFBBX2Y4QTGWPUTJKGRI2AXTF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fd5747e382e698b86361fdb01a96ed36de82f0f055f4e70dec9b8ad6d1eb1cad","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-12-20T19:49:32Z","title_canon_sha256":"d7cb441cb479e7a1d4ee538f376ac5a57c869bab985d68cfd418962c549ae22d"},"schema_version":"1.0","source":{"id":"1912.10077","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.10077","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"arxiv_version","alias_value":"1912.10077v2","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.10077","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"pith_short_12","alias_value":"ITFBBX2Y4QTG","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"pith_short_16","alias_value":"ITFBBX2Y4QTGWPUT","created_at":"2026-07-05T00:43:21Z"},{"alias_kind":"pith_short_8","alias_value":"ITFBBX2Y","created_at":"2026-07-05T00:43:21Z"}],"graph_snapshots":[{"event_id":"sha256:6fd69902510edb5270a5450ef865206fd6d359b855528f981309595dd3a8c2c2","target":"graph","created_at":"2026-07-05T00:43:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1912.10077/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Despite the widespread adoption of Transformer models for NLP tasks, the expressive power of these models is not well-understood. In this paper, we establish that Transformer models are universal approximators of continuous permutation equivariant sequence-to-sequence functions with compact support, which is quite surprising given the amount of shared parameters in these models. Furthermore, using positional encodings, we circumvent the restriction of permutation equivariance, and show that Transformer models can universally approximate arbitrary continuous sequence-to-sequence functions on a ","authors_text":"Ankit Singh Rawat, Chulhee Yun, Sanjiv Kumar, Sashank J. Reddi, Srinadh Bhojanapalli","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-12-20T19:49:32Z","title":"Are Transformers universal approximators of sequence-to-sequence functions?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.10077","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bbb657d5f1807e2880001d68d60685c600dc9a9b38db0603661a07207080bd7e","target":"record","created_at":"2026-07-05T00:43:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fd5747e382e698b86361fdb01a96ed36de82f0f055f4e70dec9b8ad6d1eb1cad","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-12-20T19:49:32Z","title_canon_sha256":"d7cb441cb479e7a1d4ee538f376ac5a57c869bab985d68cfd418962c549ae22d"},"schema_version":"1.0","source":{"id":"1912.10077","kind":"arxiv","version":2}},"canonical_sha256":"44ca10df58e4266b3e934a8d146817994eb89f77ecf5a7d6c068ffd8258a67c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44ca10df58e4266b3e934a8d146817994eb89f77ecf5a7d6c068ffd8258a67c0","first_computed_at":"2026-07-05T00:43:21.543204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:43:21.543204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BPe1VY2OADlrAneYJdD+1Tuob8DxwsEGkr9JOVR/6jXXs84JK3BGEydrjMl3iEjMyHvE3uZR3QRn7Jzo4AKgDg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:43:21.543694Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.10077","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbb657d5f1807e2880001d68d60685c600dc9a9b38db0603661a07207080bd7e","sha256:6fd69902510edb5270a5450ef865206fd6d359b855528f981309595dd3a8c2c2"],"state_sha256":"d69f573bf0c5a4a7966ae43680a1c1789a753e320162d0897e254a464f85d579"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lq2gx8PhTpH2ttBRM4vDNZ9bgFmKEwz1R4GzxjUa9gew8I9oFryipD07hGW4FsmBw7qSiG3UzW0ouw5nhqUXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:46:10.621880Z","bundle_sha256":"20bc38d2e126dd2df70fb617cb52c7b28fd50642669c37537d7613f0de44bfe0"}}