{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:JOVJU5JALXNBHUW4QG2ENTYSXU","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":"cdeb8d84d67909fa4d7ca2b803cc79e098ffbf8b1ea90b19e09ba4b6ccac8c32","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-11T08:55:17Z","title_canon_sha256":"448b0bd0febfb18dfc84fa556aa49fdca8806ea8007219392fc5d14d9b0cb499"},"schema_version":"1.0","source":{"id":"2410.08633","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.08633","created_at":"2026-07-05T10:28:24Z"},{"alias_kind":"arxiv_version","alias_value":"2410.08633v3","created_at":"2026-07-05T10:28:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.08633","created_at":"2026-07-05T10:28:24Z"},{"alias_kind":"pith_short_12","alias_value":"JOVJU5JALXNB","created_at":"2026-07-05T10:28:24Z"},{"alias_kind":"pith_short_16","alias_value":"JOVJU5JALXNBHUW4","created_at":"2026-07-05T10:28:24Z"},{"alias_kind":"pith_short_8","alias_value":"JOVJU5JA","created_at":"2026-07-05T10:28:24Z"}],"graph_snapshots":[{"event_id":"sha256:4440a4cc0f5359efeff8d8b194ba13a8fe6c194c896fc4a88034c59b73ba0759","target":"graph","created_at":"2026-07-05T10:28:24Z","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/2410.08633/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work provides the first theoretical analysis of training transformers to solve complex problems by recursively generating intermediate states, analogous to fine-tuning for chain-of-thought (CoT) reasoning. We consider training a one-layer transformer to solve the fundamental $k$-parity problem, extending the work on RNNs by Wies et al. (2023). We establish three key results: (1) any finite-precision gradient-based algorithm, without intermediate supervision, requires substantial iterations to solve parity with finite samples. (2) In contrast, when intermediate parities are incorporated in","authors_text":"Juno Kim, Taiji Suzuki","cross_cats":["stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-11T08:55:17Z","title":"Transformers Provably Solve Parity Efficiently with Chain of Thought"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.08633","kind":"arxiv","version":3},"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:b5f16df8fa4f8ee2ca8c6cefd1eab148daed65f73377ec93865f5176d4b5bcfc","target":"record","created_at":"2026-07-05T10:28:24Z","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":"cdeb8d84d67909fa4d7ca2b803cc79e098ffbf8b1ea90b19e09ba4b6ccac8c32","cross_cats_sorted":["stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-10-11T08:55:17Z","title_canon_sha256":"448b0bd0febfb18dfc84fa556aa49fdca8806ea8007219392fc5d14d9b0cb499"},"schema_version":"1.0","source":{"id":"2410.08633","kind":"arxiv","version":3}},"canonical_sha256":"4baa9a75205dda13d2dc81b446cf12bd3c376a66a094e594c3fbf283ffed3732","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4baa9a75205dda13d2dc81b446cf12bd3c376a66a094e594c3fbf283ffed3732","first_computed_at":"2026-07-05T10:28:24.149030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:28:24.149030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ivLVZ54aHtPAvncmp8m1qT+/5HIQ4xZcDghCBdEcsYTM4VuX3SrLXRDwt9vH5B+tudhy/cN+IVWQ9pW0DKbAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:28:24.149967Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.08633","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5f16df8fa4f8ee2ca8c6cefd1eab148daed65f73377ec93865f5176d4b5bcfc","sha256:4440a4cc0f5359efeff8d8b194ba13a8fe6c194c896fc4a88034c59b73ba0759"],"state_sha256":"1eeaedbeb91216e0f7d92cbd983d9213c450513998b56a39ad2a9e9f25722b9f"}