{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7U7QK6W54TRCOWK23OXEMZJF24","short_pith_number":"pith:7U7QK6W5","canonical_record":{"source":{"id":"2401.15482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-27T19:07:49Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"07ec825cce43258deda32abe18c0ac349f56c4a3695b7c9100183998ad470315","abstract_canon_sha256":"14d009abcf42f5c4af95ba7e4243c29f181a71a0c2e315c1fe8e8ecf11705e8e"},"schema_version":"1.0"},"canonical_sha256":"fd3f057adde4e227595adbae466525d7246bd6e6ba72ea07b521ffd3d5599ce1","source":{"kind":"arxiv","id":"2401.15482","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.15482","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"2401.15482v2","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.15482","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"7U7QK6W54TRC","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"pith_short_16","alias_value":"7U7QK6W54TRCOWK2","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"pith_short_8","alias_value":"7U7QK6W5","created_at":"2026-07-05T08:11:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7U7QK6W54TRCOWK23OXEMZJF24","target":"record","payload":{"canonical_record":{"source":{"id":"2401.15482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-27T19:07:49Z","cross_cats_sorted":["cs.GT","math.OC"],"title_canon_sha256":"07ec825cce43258deda32abe18c0ac349f56c4a3695b7c9100183998ad470315","abstract_canon_sha256":"14d009abcf42f5c4af95ba7e4243c29f181a71a0c2e315c1fe8e8ecf11705e8e"},"schema_version":"1.0"},"canonical_sha256":"fd3f057adde4e227595adbae466525d7246bd6e6ba72ea07b521ffd3d5599ce1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:11:23.032808Z","signature_b64":"Lc8+Vwcv5a98JSVUl2YlWfsRtPSpV4ExbrGiRgUzn7oHOxlRtUTQr3YTGSdQ5cC8tviL63RD87bWKdhAZOBzAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd3f057adde4e227595adbae466525d7246bd6e6ba72ea07b521ffd3d5599ce1","last_reissued_at":"2026-07-05T08:11:23.032346Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:11:23.032346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.15482","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5hgHCm4Cx7NE6nbK5unKvX6Roo94HkHfEkvdnZ4jrjySajl8DJxuWmFaWBdCtK6KaPiqvv4iVUXxtBg63xFPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:56:11.332723Z"},"content_sha256":"6d289b7138972426d8bb80b0801454d570b02860e05b527e7c7a96f338ad6694","schema_version":"1.0","event_id":"sha256:6d289b7138972426d8bb80b0801454d570b02860e05b527e7c7a96f338ad6694"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7U7QK6W54TRCOWK23OXEMZJF24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.GT","math.OC"],"primary_cat":"cs.LG","authors_text":"Han Huang, Rongjie Lai","submitted_at":"2024-01-27T19:07:49Z","abstract_excerpt":"Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance MFG and demands extensive computational time per instance, limiting practicality. To overcome this, we develop a novel framework to learn the MFG solution operator. Our model takes a MFG instances as input and output their solutions with one forward pass. To ensure the proposed parametrization is well-suited for operator learning, we introduce and prove the notion of sampling in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.15482","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/2401.15482/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":"2026-07-05T08:11:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3o7RGoRG/0FTWmUvJWfSp+6+Ti0h9tKMAi9BRh1H6dgz6lYkHAsH0dLgDOzTUVazbbxoOFzkG6B1RHl2ho/kBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:56:11.333204Z"},"content_sha256":"aab83b2b1db8a5887fe209db0fa43524602e0b516911fa62bad7dd4a44245ee6","schema_version":"1.0","event_id":"sha256:aab83b2b1db8a5887fe209db0fa43524602e0b516911fa62bad7dd4a44245ee6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7U7QK6W54TRCOWK23OXEMZJF24/bundle.json","state_url":"https://pith.science/pith/7U7QK6W54TRCOWK23OXEMZJF24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7U7QK6W54TRCOWK23OXEMZJF24/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":"2026-08-09T23:56:11Z","links":{"resolver":"https://pith.science/pith/7U7QK6W54TRCOWK23OXEMZJF24","bundle":"https://pith.science/pith/7U7QK6W54TRCOWK23OXEMZJF24/bundle.json","state":"https://pith.science/pith/7U7QK6W54TRCOWK23OXEMZJF24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7U7QK6W54TRCOWK23OXEMZJF24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7U7QK6W54TRCOWK23OXEMZJF24","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":"14d009abcf42f5c4af95ba7e4243c29f181a71a0c2e315c1fe8e8ecf11705e8e","cross_cats_sorted":["cs.GT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-27T19:07:49Z","title_canon_sha256":"07ec825cce43258deda32abe18c0ac349f56c4a3695b7c9100183998ad470315"},"schema_version":"1.0","source":{"id":"2401.15482","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.15482","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"arxiv_version","alias_value":"2401.15482v2","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.15482","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"pith_short_12","alias_value":"7U7QK6W54TRC","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"pith_short_16","alias_value":"7U7QK6W54TRCOWK2","created_at":"2026-07-05T08:11:23Z"},{"alias_kind":"pith_short_8","alias_value":"7U7QK6W5","created_at":"2026-07-05T08:11:23Z"}],"graph_snapshots":[{"event_id":"sha256:aab83b2b1db8a5887fe209db0fa43524602e0b516911fa62bad7dd4a44245ee6","target":"graph","created_at":"2026-07-05T08:11:23Z","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/2401.15482/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Recent advances in deep learning has witnessed many innovative frameworks that solve high dimensional mean-field games (MFG) accurately and efficiently. These methods, however, are restricted to solving single-instance MFG and demands extensive computational time per instance, limiting practicality. To overcome this, we develop a novel framework to learn the MFG solution operator. Our model takes a MFG instances as input and output their solutions with one forward pass. To ensure the proposed parametrization is well-suited for operator learning, we introduce and prove the notion of sampling in","authors_text":"Han Huang, Rongjie Lai","cross_cats":["cs.GT","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-27T19:07:49Z","title":"Unsupervised Solution Operator Learning for Mean-Field Games via Sampling-Invariant Parametrizations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.15482","kind":"arxiv","version":2},"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":"sha256:6d289b7138972426d8bb80b0801454d570b02860e05b527e7c7a96f338ad6694","target":"record","created_at":"2026-07-05T08:11:23Z","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":"14d009abcf42f5c4af95ba7e4243c29f181a71a0c2e315c1fe8e8ecf11705e8e","cross_cats_sorted":["cs.GT","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-01-27T19:07:49Z","title_canon_sha256":"07ec825cce43258deda32abe18c0ac349f56c4a3695b7c9100183998ad470315"},"schema_version":"1.0","source":{"id":"2401.15482","kind":"arxiv","version":2}},"canonical_sha256":"fd3f057adde4e227595adbae466525d7246bd6e6ba72ea07b521ffd3d5599ce1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd3f057adde4e227595adbae466525d7246bd6e6ba72ea07b521ffd3d5599ce1","first_computed_at":"2026-07-05T08:11:23.032346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:11:23.032346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Lc8+Vwcv5a98JSVUl2YlWfsRtPSpV4ExbrGiRgUzn7oHOxlRtUTQr3YTGSdQ5cC8tviL63RD87bWKdhAZOBzAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:11:23.032808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.15482","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d289b7138972426d8bb80b0801454d570b02860e05b527e7c7a96f338ad6694","sha256:aab83b2b1db8a5887fe209db0fa43524602e0b516911fa62bad7dd4a44245ee6"],"state_sha256":"574dad88e905157282b25f1bb2f0015e463fd76a4b8e3765150373a89aabe52d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ADklx+3bfOs8SdSLzTvxzX+/e5SQ59XRpAR+qYvZuzE0tXm/dhCB5O7VjonJpfqlHErkyn3shcjLmoTcMSwkDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T23:56:11.336660Z","bundle_sha256":"297cc7ceca8f5878cbad5f998757b356e0597ccdd1902553f39c0dcac37cff50"}}