{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SAH3XESM4CCNNG6KAWXAXF5D5H","short_pith_number":"pith:SAH3XESM","canonical_record":{"source":{"id":"2602.09297","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T00:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"81ee95e16ae3ba4d92318d7139e17d4b6c70c2ebeaa1fef635dd73709e30eed4","abstract_canon_sha256":"dc3fd782ca89fbf7dced4a2c33c9570a63fc9516e542b48be878274c8040a072"},"schema_version":"1.0"},"canonical_sha256":"900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12","source":{"kind":"arxiv","id":"2602.09297","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.09297","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"2602.09297v3","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.09297","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"SAH3XESM4CCN","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"pith_short_16","alias_value":"SAH3XESM4CCNNG6K","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"pith_short_8","alias_value":"SAH3XESM","created_at":"2026-05-20T00:00:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SAH3XESM4CCNNG6KAWXAXF5D5H","target":"record","payload":{"canonical_record":{"source":{"id":"2602.09297","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T00:27:45Z","cross_cats_sorted":[],"title_canon_sha256":"81ee95e16ae3ba4d92318d7139e17d4b6c70c2ebeaa1fef635dd73709e30eed4","abstract_canon_sha256":"dc3fd782ca89fbf7dced4a2c33c9570a63fc9516e542b48be878274c8040a072"},"schema_version":"1.0"},"canonical_sha256":"900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:00:34.094861Z","signature_b64":"HznruQ6eJYguhcvSDloRWmJRVGzDvkeHSCz/7vB4nN4NPtdKEaiFiRs3EYs4kL/83s/S0aOQgPT9FRQBD5LjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12","last_reissued_at":"2026-05-20T00:00:34.094185Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:00:34.094185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2602.09297","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:00:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B5TMIVUdQk5xaoGVVU6LIpPffsVcjai72WdJ1232lncwC7oxW4UQz+ytXg5YUTmOGPirdjZFaJL8DZAm5qeGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:29:13.263193Z"},"content_sha256":"cbd42f9dbcd9f8d15442f45c37c57fd19de171465a156e2490ae90ce5dc5b88a","schema_version":"1.0","event_id":"sha256:cbd42f9dbcd9f8d15442f45c37c57fd19de171465a156e2490ae90ce5dc5b88a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SAH3XESM4CCNNG6KAWXAXF5D5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Laplacian Heads Improve Transformers by Smoothing Token Representations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Vardan Papyan, Yuchong Zhang","submitted_at":"2026-02-10T00:27:45Z","abstract_excerpt":"Transformers update token representations through multi-head attention and residual connections as $X \\leftarrow X + \\sum_{i} P^{(i)}XW_{V_i}W_{o_i}$, where $P^{(i)}$ is the softmax attention matrix in head $i$. We propose replacing a subset of $P^{(i)}$'s with the Laplacian $I - P^{(i)}$, giving $X \\leftarrow X + \\sum_{i \\in \\mathcal{A}} P^{(i)}XW_{V_i}W_{o_i} + \\sum_{i \\in \\mathcal{L}} (I - P^{(i)})XW_{V_i}W_{o_i}$. Our proposal has two motivations. First, it allows attention heads to update the mean of token representations, while Laplacian heads can directly control within-sequence varianc"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the performance gains are caused by the smoothing mechanism of the Laplacian heads rather than incidental changes in optimization dynamics or capacity.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Laplacian heads replace some attention matrices with I minus P in Transformers, improving performance by smoothing tokens and challenging the view that oversmoothing is always detrimental.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e881345f8b9b9bd81d3144dc3112e5dedd84537f262765eebd224b425ac7811d"},"source":{"id":"2602.09297","kind":"arxiv","version":3},"verdict":{"id":"15d7ed43-ee0d-42e3-8478-5e2d7cf14c55","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T06:11:12.810571Z","strongest_claim":"We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks.","one_line_summary":"Laplacian heads replace some attention matrices with I minus P in Transformers, improving performance by smoothing tokens and challenging the view that oversmoothing is always detrimental.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the performance gains are caused by the smoothing mechanism of the Laplacian heads rather than incidental changes in optimization dynamics or capacity.","pith_extraction_headline":"Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.09297/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":2,"snapshot_sha256":"4ac687a462bde77cea9bc8bd6e98d73ae86a2377d60b3150c529080fcdff1f67"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"15d7ed43-ee0d-42e3-8478-5e2d7cf14c55"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-20T00:00:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2zOUwi9abvVDbi64JXu2+aMorWklBTE1Y5uGeAzb+S84zA96JGf14bUFfRDfGbtcsFGKOutnRWz0r9bAS7f3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:29:13.263678Z"},"content_sha256":"5d155b0b2177ba7761150e122acf18a762b2f14247a560032973073351e5c26a","schema_version":"1.0","event_id":"sha256:5d155b0b2177ba7761150e122acf18a762b2f14247a560032973073351e5c26a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SAH3XESM4CCNNG6KAWXAXF5D5H/bundle.json","state_url":"https://pith.science/pith/SAH3XESM4CCNNG6KAWXAXF5D5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SAH3XESM4CCNNG6KAWXAXF5D5H/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":"2026-05-28T02:29:13Z","links":{"resolver":"https://pith.science/pith/SAH3XESM4CCNNG6KAWXAXF5D5H","bundle":"https://pith.science/pith/SAH3XESM4CCNNG6KAWXAXF5D5H/bundle.json","state":"https://pith.science/pith/SAH3XESM4CCNNG6KAWXAXF5D5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SAH3XESM4CCNNG6KAWXAXF5D5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SAH3XESM4CCNNG6KAWXAXF5D5H","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":"dc3fd782ca89fbf7dced4a2c33c9570a63fc9516e542b48be878274c8040a072","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T00:27:45Z","title_canon_sha256":"81ee95e16ae3ba4d92318d7139e17d4b6c70c2ebeaa1fef635dd73709e30eed4"},"schema_version":"1.0","source":{"id":"2602.09297","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2602.09297","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"arxiv_version","alias_value":"2602.09297v3","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2602.09297","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"pith_short_12","alias_value":"SAH3XESM4CCN","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"pith_short_16","alias_value":"SAH3XESM4CCNNG6K","created_at":"2026-05-20T00:00:34Z"},{"alias_kind":"pith_short_8","alias_value":"SAH3XESM","created_at":"2026-05-20T00:00:34Z"}],"graph_snapshots":[{"event_id":"sha256:5d155b0b2177ba7761150e122acf18a762b2f14247a560032973073351e5c26a","target":"graph","created_at":"2026-05-20T00:00:34Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That the performance gains are caused by the smoothing mechanism of the Laplacian heads rather than incidental changes in optimization dynamics or capacity."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Laplacian heads replace some attention matrices with I minus P in Transformers, improving performance by smoothing tokens and challenging the view that oversmoothing is always detrimental."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations."}],"snapshot_sha256":"e881345f8b9b9bd81d3144dc3112e5dedd84537f262765eebd224b425ac7811d"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"4ac687a462bde77cea9bc8bd6e98d73ae86a2377d60b3150c529080fcdff1f67"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2602.09297/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transformers update token representations through multi-head attention and residual connections as $X \\leftarrow X + \\sum_{i} P^{(i)}XW_{V_i}W_{o_i}$, where $P^{(i)}$ is the softmax attention matrix in head $i$. We propose replacing a subset of $P^{(i)}$'s with the Laplacian $I - P^{(i)}$, giving $X \\leftarrow X + \\sum_{i \\in \\mathcal{A}} P^{(i)}XW_{V_i}W_{o_i} + \\sum_{i \\in \\mathcal{L}} (I - P^{(i)})XW_{V_i}W_{o_i}$. Our proposal has two motivations. First, it allows attention heads to update the mean of token representations, while Laplacian heads can directly control within-sequence varianc","authors_text":"Vardan Papyan, Yuchong Zhang","cross_cats":[],"headline":"Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T00:27:45Z","title":"Laplacian Heads Improve Transformers by Smoothing Token Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.09297","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-16T06:11:12.810571Z","id":"15d7ed43-ee0d-42e3-8478-5e2d7cf14c55","model_set":{"reader":"grok-4.3"},"one_line_summary":"Laplacian heads replace some attention matrices with I minus P in Transformers, improving performance by smoothing tokens and challenging the view that oversmoothing is always detrimental.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Replacing some attention heads with Laplacian operators improves Transformer performance by enabling beneficial smoothing of token representations.","strongest_claim":"We show that this simple modification improves performance across supervised learning, language modeling, and self-supervised learning tasks.","weakest_assumption":"That the performance gains are caused by the smoothing mechanism of the Laplacian heads rather than incidental changes in optimization dynamics or capacity."}},"verdict_id":"15d7ed43-ee0d-42e3-8478-5e2d7cf14c55"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cbd42f9dbcd9f8d15442f45c37c57fd19de171465a156e2490ae90ce5dc5b88a","target":"record","created_at":"2026-05-20T00:00:34Z","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":"dc3fd782ca89fbf7dced4a2c33c9570a63fc9516e542b48be878274c8040a072","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-02-10T00:27:45Z","title_canon_sha256":"81ee95e16ae3ba4d92318d7139e17d4b6c70c2ebeaa1fef635dd73709e30eed4"},"schema_version":"1.0","source":{"id":"2602.09297","kind":"arxiv","version":3}},"canonical_sha256":"900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"900fbb924ce084d69bca05ae0b97a3e9df2ab81f3a0b8f856e9663f8b3fedd12","first_computed_at":"2026-05-20T00:00:34.094185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:34.094185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HznruQ6eJYguhcvSDloRWmJRVGzDvkeHSCz/7vB4nN4NPtdKEaiFiRs3EYs4kL/83s/S0aOQgPT9FRQBD5LjBQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:34.094861Z","signed_message":"canonical_sha256_bytes"},"source_id":"2602.09297","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbd42f9dbcd9f8d15442f45c37c57fd19de171465a156e2490ae90ce5dc5b88a","sha256:5d155b0b2177ba7761150e122acf18a762b2f14247a560032973073351e5c26a"],"state_sha256":"3e18538af323ce9cb3061c122f781ad4e2b887d6f17acfbed65b495d6dace11f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xPag5Xa6mhHBM2nLRkO24AOz80kdMSMUdo1WkXSzrL2qj8Z40cXbZpZo6NE33Ig4BHI8QjGfE/s8X71p7tG7BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:29:13.266035Z","bundle_sha256":"37a10a93da77177d317aabf2002d3e69ed4954dc7618cf8cec4bd92d27256760"}}