{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:LJHX7ZQ4DRQJ6GL53CD7YV6TUV","short_pith_number":"pith:LJHX7ZQ4","schema_version":"1.0","canonical_sha256":"5a4f7fe61c1c609f197dd887fc57d3a5638f1755f2b70136f3ebe04f4981662b","source":{"kind":"arxiv","id":"2401.07993","version":2},"attestation_state":"computed","paper":{"title":"Carrying over algorithm in transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jorrit Kruthoff","submitted_at":"2024-01-15T22:36:11Z","abstract_excerpt":"Addition is perhaps one of the simplest arithmetic tasks one can think of and is usually performed using the carrying over algorithm. This algorithm consists of two tasks: adding digits in the same position and carrying over a one whenever necessary. We study how transformer models implement this algorithm and how the two aforementioned tasks are allocated to different parts of the network. We first focus on two-layer encoder-only models and show that the carrying over algorithm is implemented in a modular fashion. The first layer is mostly responsible for adding digits in the same position. T"},"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":"2401.07993","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-15T22:36:11Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"cee88beddab2ff6cfde109cf2cb56039b76f0f0adef7a5edd23d35674b3df299","abstract_canon_sha256":"5a851f1859e76cbba4297d5c8003795ef3296af33d71b1fbcbc9fe8cfa75b141"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:34:37.483198Z","signature_b64":"cCMzDtdrU6mUR6GBEA2iJo87KCE7EK3824LHpw3jYXsfz8OQoG9OWqaszy3reE3IWcoICposEBSsXnGSy0AJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a4f7fe61c1c609f197dd887fc57d3a5638f1755f2b70136f3ebe04f4981662b","last_reissued_at":"2026-07-05T07:34:37.482742Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:34:37.482742Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Carrying over algorithm in transformers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jorrit Kruthoff","submitted_at":"2024-01-15T22:36:11Z","abstract_excerpt":"Addition is perhaps one of the simplest arithmetic tasks one can think of and is usually performed using the carrying over algorithm. This algorithm consists of two tasks: adding digits in the same position and carrying over a one whenever necessary. We study how transformer models implement this algorithm and how the two aforementioned tasks are allocated to different parts of the network. We first focus on two-layer encoder-only models and show that the carrying over algorithm is implemented in a modular fashion. The first layer is mostly responsible for adding digits in the same position. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.07993","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/2401.07993/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":"2401.07993","created_at":"2026-07-05T07:34:37.482795+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.07993v2","created_at":"2026-07-05T07:34:37.482795+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.07993","created_at":"2026-07-05T07:34:37.482795+00:00"},{"alias_kind":"pith_short_12","alias_value":"LJHX7ZQ4DRQJ","created_at":"2026-07-05T07:34:37.482795+00:00"},{"alias_kind":"pith_short_16","alias_value":"LJHX7ZQ4DRQJ6GL5","created_at":"2026-07-05T07:34:37.482795+00:00"},{"alias_kind":"pith_short_8","alias_value":"LJHX7ZQ4","created_at":"2026-07-05T07:34:37.482795+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.07824","citing_title":"Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV","json":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV.json","graph_json":"https://pith.science/api/pith-number/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/graph.json","events_json":"https://pith.science/api/pith-number/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/events.json","paper":"https://pith.science/paper/LJHX7ZQ4"},"agent_actions":{"view_html":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV","download_json":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV.json","view_paper":"https://pith.science/paper/LJHX7ZQ4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.07993&json=true","fetch_graph":"https://pith.science/api/pith-number/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/graph.json","fetch_events":"https://pith.science/api/pith-number/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/action/storage_attestation","attest_author":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/action/author_attestation","sign_citation":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/action/citation_signature","submit_replication":"https://pith.science/pith/LJHX7ZQ4DRQJ6GL53CD7YV6TUV/action/replication_record"}},"created_at":"2026-07-05T07:34:37.482795+00:00","updated_at":"2026-07-05T07:34:37.482795+00:00"}