{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:A2FTISJW67WZ3RBKHFZTNL5NNC","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":"00ac27a916e441b352f016208ff7082ba33202cc6d7ead5cbdce70ff1e7f8ed6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-02T22:19:26Z","title_canon_sha256":"1101c890c55df2242d9960a1dc41eba873b69453eeb1a5d54cae3221060363a8"},"schema_version":"1.0","source":{"id":"2607.02800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.02800","created_at":"2026-07-07T00:16:17Z"},{"alias_kind":"arxiv_version","alias_value":"2607.02800v1","created_at":"2026-07-07T00:16:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02800","created_at":"2026-07-07T00:16:17Z"},{"alias_kind":"pith_short_12","alias_value":"A2FTISJW67WZ","created_at":"2026-07-07T00:16:17Z"},{"alias_kind":"pith_short_16","alias_value":"A2FTISJW67WZ3RBK","created_at":"2026-07-07T00:16:17Z"},{"alias_kind":"pith_short_8","alias_value":"A2FTISJW","created_at":"2026-07-07T00:16:17Z"}],"graph_snapshots":[{"event_id":"sha256:ebc2dae4b79823370db383fbc91ee074f55ac49997f07c75d2abd6a5a89c1299","target":"graph","created_at":"2026-07-07T00:16:17Z","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/2607.02800/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Induction heads are attention circuits believed to underlie in-context learning in transformers, yet a precise characterization of the estimators they implement remains elusive. We study transformers trained on order-$k$ Markov chains and identify two complementary smoothing mechanisms. First, at finite attention-weight scale, the circuit implements a soft context-matching estimator: it aggregates contributions from exact and partial context matches, weighted exponentially by their overlap, and induces a data-dependent interpolation across context orders analogous to Jelinek-Mercer smoothing. ","authors_text":"Francesco D'Angelo, Nicolas Flammarion, Oguz Kaan Yuksel, Swathi Shree Narashiman","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-02T22:19:26Z","title":"Induction Heads Interpolate N-Grams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02800","kind":"arxiv","version":1},"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:de1f30af7013cb7c84896170032c4acd7ae25da45bea969c53e376d1a5461b8a","target":"record","created_at":"2026-07-07T00:16:17Z","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":"00ac27a916e441b352f016208ff7082ba33202cc6d7ead5cbdce70ff1e7f8ed6","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-02T22:19:26Z","title_canon_sha256":"1101c890c55df2242d9960a1dc41eba873b69453eeb1a5d54cae3221060363a8"},"schema_version":"1.0","source":{"id":"2607.02800","kind":"arxiv","version":1}},"canonical_sha256":"068b344936f7ed9dc42a397336afad68a1b1ebd6de5ceda05d4d91499a7cc43a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"068b344936f7ed9dc42a397336afad68a1b1ebd6de5ceda05d4d91499a7cc43a","first_computed_at":"2026-07-07T00:16:17.945015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T00:16:17.945015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nLDBfEilnVZQzeHLPAJ9S/HGgAbYPTuymztSExjjhpLSOINe8MT2lZJH59vpwAuaBSodJ1TnqNgv8hXOhqLIAw==","signature_status":"signed_v1","signed_at":"2026-07-07T00:16:17.945705Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.02800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de1f30af7013cb7c84896170032c4acd7ae25da45bea969c53e376d1a5461b8a","sha256:ebc2dae4b79823370db383fbc91ee074f55ac49997f07c75d2abd6a5a89c1299"],"state_sha256":"57194b075d79d62751b3ad646f1fd892fff38e70dbe16b960b272d0185f6ae10"}