{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:BZ7WVKG2WGK4RTW52GSPGRWKGG","short_pith_number":"pith:BZ7WVKG2","schema_version":"1.0","canonical_sha256":"0e7f6aa8dab195c8ceddd1a4f346ca31bbced225246e905e05bcd1cb75b85731","source":{"kind":"arxiv","id":"2606.19379","version":1},"attestation_state":"computed","paper":{"title":"How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architectural","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Stuart Whipp","submitted_at":"2026-06-12T10:39:39Z","abstract_excerpt":"Transformer feed-forward networks (FFNs) are often treated as nonlinear stores of computation, yet how nonlinear a trained FFN block actually is has rarely been measured. We treat each FFN as a position-wise input-to-output map and split it into the exact least-squares linear approximation plus a residual. The held-out variance the closed-form linear map explains defines a block's linear recoverability (R^2_lin), an optimiser-free measure of its linearity.\n  Across all twelve blocks of GPT-2, Pythia-160m, and llama-160m, R^2_lin is highly heterogeneous and non-monotone with depth, ranging from"},"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":"2606.19379","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2026-06-12T10:39:39Z","cross_cats_sorted":["cs.AI","cs.CL"],"title_canon_sha256":"e20b4df8eb6d80255a5357a292d6ce2e666258f6da96b1e36f07d8bf51aa714d","abstract_canon_sha256":"33ecd2d53a88730d5f4efdc5f04bf51b9db2b4551867a92d2ebbd45eb227cf3f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:23.633167Z","signature_b64":"kQhTyYYwEyI9vglm5sLEGXbT+k+nD42GPeH81Cm28JlHEcHg0inHEFYVz9m8eY4Lq++eaJ7l1e+wx13rBCvuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e7f6aa8dab195c8ceddd1a4f346ca31bbced225246e905e05bcd1cb75b85731","last_reissued_at":"2026-06-19T16:12:23.632788Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:23.632788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How Linear Is a Transformer Feed-Forward Block? Per-Block Linear Recoverability Is Learned, Not Architectural","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.CL"],"primary_cat":"cs.LG","authors_text":"Stuart Whipp","submitted_at":"2026-06-12T10:39:39Z","abstract_excerpt":"Transformer feed-forward networks (FFNs) are often treated as nonlinear stores of computation, yet how nonlinear a trained FFN block actually is has rarely been measured. We treat each FFN as a position-wise input-to-output map and split it into the exact least-squares linear approximation plus a residual. The held-out variance the closed-form linear map explains defines a block's linear recoverability (R^2_lin), an optimiser-free measure of its linearity.\n  Across all twelve blocks of GPT-2, Pythia-160m, and llama-160m, R^2_lin is highly heterogeneous and non-monotone with depth, ranging from"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19379","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/2606.19379/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":"2606.19379","created_at":"2026-06-19T16:12:23.632842+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.19379v1","created_at":"2026-06-19T16:12:23.632842+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19379","created_at":"2026-06-19T16:12:23.632842+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZ7WVKG2WGK4","created_at":"2026-06-19T16:12:23.632842+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZ7WVKG2WGK4RTW5","created_at":"2026-06-19T16:12:23.632842+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZ7WVKG2","created_at":"2026-06-19T16:12:23.632842+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG","json":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG.json","graph_json":"https://pith.science/api/pith-number/BZ7WVKG2WGK4RTW52GSPGRWKGG/graph.json","events_json":"https://pith.science/api/pith-number/BZ7WVKG2WGK4RTW52GSPGRWKGG/events.json","paper":"https://pith.science/paper/BZ7WVKG2"},"agent_actions":{"view_html":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG","download_json":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG.json","view_paper":"https://pith.science/paper/BZ7WVKG2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.19379&json=true","fetch_graph":"https://pith.science/api/pith-number/BZ7WVKG2WGK4RTW52GSPGRWKGG/graph.json","fetch_events":"https://pith.science/api/pith-number/BZ7WVKG2WGK4RTW52GSPGRWKGG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG/action/storage_attestation","attest_author":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG/action/author_attestation","sign_citation":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG/action/citation_signature","submit_replication":"https://pith.science/pith/BZ7WVKG2WGK4RTW52GSPGRWKGG/action/replication_record"}},"created_at":"2026-06-19T16:12:23.632842+00:00","updated_at":"2026-06-19T16:12:23.632842+00:00"}