{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2GCDGRS4DE66FX25YYTNXZTLTC","short_pith_number":"pith:2GCDGRS4","schema_version":"1.0","canonical_sha256":"d18433465c193de2df5dc626dbe66b988f82e0f19816a72f8e4fcbf56800a0b0","source":{"kind":"arxiv","id":"2605.14277","version":1},"attestation_state":"computed","paper":{"title":"Parallelizing Counterfactual Regret Minimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Counterfactual regret minimization can be reframed as linear algebra operations to run up to four orders of magnitude faster on GPUs.","cross_cats":["cs.GT"],"primary_cat":"cs.AI","authors_text":"Juho Kim, Tuomas Sandholm","submitted_at":"2026-05-14T02:22:27Z","abstract_excerpt":"Parallelization has played an instrumental role in the field of artificial intelligence (AI), drastically reducing the time taken to train and evaluate large AI models. In contrast to its impact in the broader field of AI, applying parallelization to computational game solving is relatively unexplored, despite its great potential. In this paper, we parallelize the family of counterfactual regret minimization (CFR) algorithms, which were central to important breakthroughs for solving large imperfect-information games. We present a generalized parallelization framework, reframing CFR as a series"},"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":true,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.14277","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.AI","submitted_at":"2026-05-14T02:22:27Z","cross_cats_sorted":["cs.GT"],"title_canon_sha256":"06dc76c3524195e86b9d7082d0afd1bed7dd246c2148d53d14663494659907dd","abstract_canon_sha256":"cd93e7940ddcd3129242c938329234a37819e400343a83a442a85a4cf1e8ba00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:10.327136Z","signature_b64":"TQqmrjgR1c+Vr8zpLCTlEbaGYUVv8b1noiAnD5pEGbXkPp4fY0xCzdeOjOSae54SC9i8an8gWtGmXdzPFJOHBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d18433465c193de2df5dc626dbe66b988f82e0f19816a72f8e4fcbf56800a0b0","last_reissued_at":"2026-05-17T23:39:10.326403Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:10.326403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parallelizing Counterfactual Regret Minimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Counterfactual regret minimization can be reframed as linear algebra operations to run up to four orders of magnitude faster on GPUs.","cross_cats":["cs.GT"],"primary_cat":"cs.AI","authors_text":"Juho Kim, Tuomas Sandholm","submitted_at":"2026-05-14T02:22:27Z","abstract_excerpt":"Parallelization has played an instrumental role in the field of artificial intelligence (AI), drastically reducing the time taken to train and evaluate large AI models. In contrast to its impact in the broader field of AI, applying parallelization to computational game solving is relatively unexplored, despite its great potential. In this paper, we parallelize the family of counterfactual regret minimization (CFR) algorithms, which were central to important breakthroughs for solving large imperfect-information games. We present a generalized parallelization framework, reframing CFR as a series"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present a generalized parallelization framework, reframing CFR as a series of linear algebra operations. ... our CFR implementation on a GPU is up to four orders of magnitude faster than Google DeepMind OpenSpiel's CFR implementations on a CPU.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the linear-algebra reformulation of CFR exactly preserves the original regret bounds and convergence properties without introducing floating-point or parallelism-induced errors.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Reframing CFR as linear algebra operations enables GPU parallelization with up to 10,000x speedup over standard CPU implementations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Counterfactual regret minimization can be reframed as linear algebra operations to run up to four orders of magnitude faster on GPUs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"39a4fd2aed4b2291ed27bd286a82299a586b6bcc211813eca9f14f2d027b6edb"},"source":{"id":"2605.14277","kind":"arxiv","version":1},"verdict":{"id":"e8ab605e-9bd9-40e4-aa38-1f1fefe5bcad","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:35:14.273833Z","strongest_claim":"We present a generalized parallelization framework, reframing CFR as a series of linear algebra operations. ... our CFR implementation on a GPU is up to four orders of magnitude faster than Google DeepMind OpenSpiel's CFR implementations on a CPU.","one_line_summary":"Reframing CFR as linear algebra operations enables GPU parallelization with up to 10,000x speedup over standard CPU implementations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the linear-algebra reformulation of CFR exactly preserves the original regret bounds and convergence properties without introducing floating-point or parallelism-induced errors.","pith_extraction_headline":"Counterfactual regret minimization can be reframed as linear algebra operations to run up to four orders of magnitude faster on GPUs."},"references":{"count":37,"sample":[{"doi":"","year":1996,"title":"G. E. Blelloch. Programming parallel algorithms.Commun. ACM, 39(3):85–97, 1996","work_id":"a00a7f95-dc58-4cd7-9f81-422fb0760f8a","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2015,"title":"N. Brown and T. Sandholm. Regret-based pruning in extensive-form games. InProceedings of the Annual Conference on Neural Information Processing Systems (NeurIPS), 2015","work_id":"031822f0-9430-4f1b-87af-e4fffaceefc8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2017,"title":"N. Brown and T. Sandholm. Reduced space and faster convergence in imperfect-information games via pruning. InProceedings of the International Conference on Machine Learning (ICML), 2017","work_id":"19a9bbc7-290a-4cbf-b72e-47f92db508b6","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2018,"title":"N. Brown and T. Sandholm. Superhuman AI for heads-up no-limit poker: Libratus beats top professionals.Science, 359(6374):418–424, 2018","work_id":"ef7b56a3-56e6-44b7-91f5-2599930721da","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"N. Brown and T. Sandholm. Superhuman AI for multiplayer poker.Science, 365(6456):885–890, 2019","work_id":"deee810e-0e04-44e2-a5ee-100c7117dc2d","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":37,"snapshot_sha256":"ef62d8edbb1d9cfc03f09378f8b59359f5c55dc96cd38e898790ee10b3e5d42c","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":"2605.14277","created_at":"2026-05-17T23:39:10.326513+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.14277v1","created_at":"2026-05-17T23:39:10.326513+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.14277","created_at":"2026-05-17T23:39:10.326513+00:00"},{"alias_kind":"pith_short_12","alias_value":"2GCDGRS4DE66","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"2GCDGRS4DE66FX25","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"2GCDGRS4","created_at":"2026-05-18T12:33:37.589309+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/2GCDGRS4DE66FX25YYTNXZTLTC","json":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC.json","graph_json":"https://pith.science/api/pith-number/2GCDGRS4DE66FX25YYTNXZTLTC/graph.json","events_json":"https://pith.science/api/pith-number/2GCDGRS4DE66FX25YYTNXZTLTC/events.json","paper":"https://pith.science/paper/2GCDGRS4"},"agent_actions":{"view_html":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC","download_json":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC.json","view_paper":"https://pith.science/paper/2GCDGRS4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.14277&json=true","fetch_graph":"https://pith.science/api/pith-number/2GCDGRS4DE66FX25YYTNXZTLTC/graph.json","fetch_events":"https://pith.science/api/pith-number/2GCDGRS4DE66FX25YYTNXZTLTC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC/action/storage_attestation","attest_author":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC/action/author_attestation","sign_citation":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC/action/citation_signature","submit_replication":"https://pith.science/pith/2GCDGRS4DE66FX25YYTNXZTLTC/action/replication_record"}},"created_at":"2026-05-17T23:39:10.326513+00:00","updated_at":"2026-05-17T23:39:10.326513+00:00"}