{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:UKKEEMALMAOX4HUCNFTEIC7LHB","short_pith_number":"pith:UKKEEMAL","canonical_record":{"source":{"id":"2405.16658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T18:29:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"23696c83e20c4c7a9241b6fd444118a097ac46a3466bada39e2e3da1f03ac14f","abstract_canon_sha256":"35b59bceda9bf3aa0e2fb5d17f9f68c9853e0341f73add53105f7cd1d1745449"},"schema_version":"1.0"},"canonical_sha256":"a29442300b601d7e1e826966440beb386e94d96f135d6f4272af5930f5e0ba82","source":{"kind":"arxiv","id":"2405.16658","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16658","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16658v1","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16658","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"UKKEEMALMAOX","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"pith_short_16","alias_value":"UKKEEMALMAOX4HUC","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"pith_short_8","alias_value":"UKKEEMAL","created_at":"2026-07-05T08:23:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:UKKEEMALMAOX4HUCNFTEIC7LHB","target":"record","payload":{"canonical_record":{"source":{"id":"2405.16658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T18:29:24Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"23696c83e20c4c7a9241b6fd444118a097ac46a3466bada39e2e3da1f03ac14f","abstract_canon_sha256":"35b59bceda9bf3aa0e2fb5d17f9f68c9853e0341f73add53105f7cd1d1745449"},"schema_version":"1.0"},"canonical_sha256":"a29442300b601d7e1e826966440beb386e94d96f135d6f4272af5930f5e0ba82","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:23:33.658303Z","signature_b64":"kUdmbCbosfsFIrf0xjOOzrB3qG5Msarjzvk0ozYVYljdm2YfZRNDtmDTbliskeG4nceJ/YRGUph2oOcYaCWtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a29442300b601d7e1e826966440beb386e94d96f135d6f4272af5930f5e0ba82","last_reissued_at":"2026-07-05T08:23:33.657882Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:23:33.657882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.16658","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"opGj3G/Y1Lp9yS/yAjF4Fx4YP0YkWJfL6tifsuHJhguzAR8djmAx4QUj4pJdkaadoM5vMM1uiNnK8wYRP9AzBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:48:27.059038Z"},"content_sha256":"f1c935cb119778b80a53d15175c745e985cf4559a76c5b613559eddbb06f4808","schema_version":"1.0","event_id":"sha256:f1c935cb119778b80a53d15175c745e985cf4559a76c5b613559eddbb06f4808"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:UKKEEMALMAOX4HUCNFTEIC7LHB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Minseok Kim, Yeachan Park, Yeoneung Kim","submitted_at":"2024-05-26T18:29:24Z","abstract_excerpt":"We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\\cite{power2022grokking}. Focusing on the grokking phenomenon that arises in learning arithmetic binary operations via the transformer model, we begin with a discussion on data augmentation in the case of commutative binary operations. To further accelerate, we elucidate arithmetic operations through the lens of the Kolmogorov-Arnold (KA) representation theorem, revealing its correspondence to the transformer archit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16658","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/2405.16658/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lDkLSS5145WMAcp5CnRBVQvdbqoSy/C0DfP5epaBSEpHaKMdn3CH29YmZrjvbaxKx3OewKWyQJbtEDWpKJ/iDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:48:27.059550Z"},"content_sha256":"d28c6aa77dec731289bd6e3189f31110de4a3560ef10a2a1cdb03bda8d9b9589","schema_version":"1.0","event_id":"sha256:d28c6aa77dec731289bd6e3189f31110de4a3560ef10a2a1cdb03bda8d9b9589"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKKEEMALMAOX4HUCNFTEIC7LHB/bundle.json","state_url":"https://pith.science/pith/UKKEEMALMAOX4HUCNFTEIC7LHB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKKEEMALMAOX4HUCNFTEIC7LHB/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":"2026-08-09T04:48:27Z","links":{"resolver":"https://pith.science/pith/UKKEEMALMAOX4HUCNFTEIC7LHB","bundle":"https://pith.science/pith/UKKEEMALMAOX4HUCNFTEIC7LHB/bundle.json","state":"https://pith.science/pith/UKKEEMALMAOX4HUCNFTEIC7LHB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKKEEMALMAOX4HUCNFTEIC7LHB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:UKKEEMALMAOX4HUCNFTEIC7LHB","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":"35b59bceda9bf3aa0e2fb5d17f9f68c9853e0341f73add53105f7cd1d1745449","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T18:29:24Z","title_canon_sha256":"23696c83e20c4c7a9241b6fd444118a097ac46a3466bada39e2e3da1f03ac14f"},"schema_version":"1.0","source":{"id":"2405.16658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16658","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16658v1","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16658","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"UKKEEMALMAOX","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"pith_short_16","alias_value":"UKKEEMALMAOX4HUC","created_at":"2026-07-05T08:23:33Z"},{"alias_kind":"pith_short_8","alias_value":"UKKEEMAL","created_at":"2026-07-05T08:23:33Z"}],"graph_snapshots":[{"event_id":"sha256:d28c6aa77dec731289bd6e3189f31110de4a3560ef10a2a1cdb03bda8d9b9589","target":"graph","created_at":"2026-07-05T08:23:33Z","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/2405.16658/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose novel methodologies aimed at accelerating the grokking phenomenon, which refers to the rapid increment of test accuracy after a long period of overfitting as reported in~\\cite{power2022grokking}. Focusing on the grokking phenomenon that arises in learning arithmetic binary operations via the transformer model, we begin with a discussion on data augmentation in the case of commutative binary operations. To further accelerate, we elucidate arithmetic operations through the lens of the Kolmogorov-Arnold (KA) representation theorem, revealing its correspondence to the transformer archit","authors_text":"Minseok Kim, Yeachan Park, Yeoneung Kim","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T18:29:24Z","title":"Acceleration of Grokking in Learning Arithmetic Operations via Kolmogorov-Arnold Representation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16658","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:f1c935cb119778b80a53d15175c745e985cf4559a76c5b613559eddbb06f4808","target":"record","created_at":"2026-07-05T08:23:33Z","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":"35b59bceda9bf3aa0e2fb5d17f9f68c9853e0341f73add53105f7cd1d1745449","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-05-26T18:29:24Z","title_canon_sha256":"23696c83e20c4c7a9241b6fd444118a097ac46a3466bada39e2e3da1f03ac14f"},"schema_version":"1.0","source":{"id":"2405.16658","kind":"arxiv","version":1}},"canonical_sha256":"a29442300b601d7e1e826966440beb386e94d96f135d6f4272af5930f5e0ba82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a29442300b601d7e1e826966440beb386e94d96f135d6f4272af5930f5e0ba82","first_computed_at":"2026-07-05T08:23:33.657882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:33.657882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kUdmbCbosfsFIrf0xjOOzrB3qG5Msarjzvk0ozYVYljdm2YfZRNDtmDTbliskeG4nceJ/YRGUph2oOcYaCWtAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:33.658303Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.16658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1c935cb119778b80a53d15175c745e985cf4559a76c5b613559eddbb06f4808","sha256:d28c6aa77dec731289bd6e3189f31110de4a3560ef10a2a1cdb03bda8d9b9589"],"state_sha256":"f5fe8b1e50810db66ce2a3b720a5a16786d3a51eaca24c4aeff1b4788f551230"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SEByTMsEvH2tp4UO+taL+BYWpKMlMCaFqHr1ZIrtNOmhSgEt0y6raxZ6f/NkovJ+E7WpgVOwwSmKrKU+Q9yHAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:48:27.063488Z","bundle_sha256":"4aa545b62bdec4d5aaa4b5df3e3a68f54361f5f8a717fdc4ff8b305706309d27"}}