{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:54XX2UYVT6672QLES64LDI3ZTT","short_pith_number":"pith:54XX2UYV","canonical_record":{"source":{"id":"2406.09694","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2024-06-14T03:38:40Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5501a57809e6a328a512395520a77342363f57be33a5409d7643a1a9ac3b47ec","abstract_canon_sha256":"b76aaa2f2bad765c9cda57a56b51e0ba548b1f4375ae7800e7b7ab160e8bdb5d"},"schema_version":"1.0"},"canonical_sha256":"ef2f7d53159fbdfd416497b8b1a3799ce3aa5e08117ac5f96cf67ecd325ee1c6","source":{"kind":"arxiv","id":"2406.09694","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09694","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09694v2","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09694","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"54XX2UYVT667","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"54XX2UYVT6672QLE","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"54XX2UYV","created_at":"2026-07-05T09:06:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:54XX2UYVT6672QLES64LDI3ZTT","target":"record","payload":{"canonical_record":{"source":{"id":"2406.09694","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2024-06-14T03:38:40Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"5501a57809e6a328a512395520a77342363f57be33a5409d7643a1a9ac3b47ec","abstract_canon_sha256":"b76aaa2f2bad765c9cda57a56b51e0ba548b1f4375ae7800e7b7ab160e8bdb5d"},"schema_version":"1.0"},"canonical_sha256":"ef2f7d53159fbdfd416497b8b1a3799ce3aa5e08117ac5f96cf67ecd325ee1c6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:06:27.201953Z","signature_b64":"81zWhd7erFrr3Wa8aT5ODoRCgPm90euk0xnOsLWt16aPBuV0we+zoj+EdKvgz2371xnzodwoi/d75L8oQeziBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef2f7d53159fbdfd416497b8b1a3799ce3aa5e08117ac5f96cf67ecd325ee1c6","last_reissued_at":"2026-07-05T09:06:27.201423Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:06:27.201423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.09694","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":"2026-07-05T09:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iAJueQjvnNQVXPRqV/oFJkcRxxC887TLK1+nZkbvs3tPq6b/IdFgr8dbxn+W/HLeHosAS0dXxGLj3rO1liLlCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:48:16.279280Z"},"content_sha256":"271a86438e55218464e4c1c0b5b2f2cc5494b5cd4de26f56f69502b99388bd95","schema_version":"1.0","event_id":"sha256:271a86438e55218464e4c1c0b5b2f2cc5494b5cd4de26f56f69502b99388bd95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:54XX2UYVT6672QLES64LDI3ZTT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Efficient Approach to Regression Problems with Tensor Neural Networks","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Hehu Xie, Yifan Wang, Yongxin Li, Zhongshuo Lin","submitted_at":"2024-06-14T03:38:40Z","abstract_excerpt":"This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex, high-dimensional functions. The TNN demonstrates superior performance compared to conventional Feed-Forward Networks (FFN) and Radial Basis Function Networks (RBN) in terms of both approximation accuracy and generalization capacity, even with a comparable number of parameters. A significant innovation in our approach is the integration of statistical regression and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09694","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/2406.09694/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":"2026-07-05T09:06:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1OUy+zGt0eJyTm2WPPwJKkjMlOHrFmbHGhcLISsNbD3dHU0P4XYa31pYk6P/sRFQYJM7pNNVSdYW+cmbKrrlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T13:48:16.279671Z"},"content_sha256":"3cf1514fb40c3cb2d48e6f828a69446e63b56d36df41c9974a44cf7349c90307","schema_version":"1.0","event_id":"sha256:3cf1514fb40c3cb2d48e6f828a69446e63b56d36df41c9974a44cf7349c90307"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/54XX2UYVT6672QLES64LDI3ZTT/bundle.json","state_url":"https://pith.science/pith/54XX2UYVT6672QLES64LDI3ZTT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/54XX2UYVT6672QLES64LDI3ZTT/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":"2026-07-06T13:48:16Z","links":{"resolver":"https://pith.science/pith/54XX2UYVT6672QLES64LDI3ZTT","bundle":"https://pith.science/pith/54XX2UYVT6672QLES64LDI3ZTT/bundle.json","state":"https://pith.science/pith/54XX2UYVT6672QLES64LDI3ZTT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/54XX2UYVT6672QLES64LDI3ZTT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:54XX2UYVT6672QLES64LDI3ZTT","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":"b76aaa2f2bad765c9cda57a56b51e0ba548b1f4375ae7800e7b7ab160e8bdb5d","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2024-06-14T03:38:40Z","title_canon_sha256":"5501a57809e6a328a512395520a77342363f57be33a5409d7643a1a9ac3b47ec"},"schema_version":"1.0","source":{"id":"2406.09694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.09694","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"2406.09694v2","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.09694","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"54XX2UYVT667","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"pith_short_16","alias_value":"54XX2UYVT6672QLE","created_at":"2026-07-05T09:06:27Z"},{"alias_kind":"pith_short_8","alias_value":"54XX2UYV","created_at":"2026-07-05T09:06:27Z"}],"graph_snapshots":[{"event_id":"sha256:3cf1514fb40c3cb2d48e6f828a69446e63b56d36df41c9974a44cf7349c90307","target":"graph","created_at":"2026-07-05T09:06:27Z","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/2406.09694/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex, high-dimensional functions. The TNN demonstrates superior performance compared to conventional Feed-Forward Networks (FFN) and Radial Basis Function Networks (RBN) in terms of both approximation accuracy and generalization capacity, even with a comparable number of parameters. A significant innovation in our approach is the integration of statistical regression and ","authors_text":"Hehu Xie, Yifan Wang, Yongxin Li, Zhongshuo Lin","cross_cats":["cs.LG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2024-06-14T03:38:40Z","title":"An Efficient Approach to Regression Problems with Tensor Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.09694","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":"sha256:271a86438e55218464e4c1c0b5b2f2cc5494b5cd4de26f56f69502b99388bd95","target":"record","created_at":"2026-07-05T09:06:27Z","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":"b76aaa2f2bad765c9cda57a56b51e0ba548b1f4375ae7800e7b7ab160e8bdb5d","cross_cats_sorted":["cs.LG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"stat.ML","submitted_at":"2024-06-14T03:38:40Z","title_canon_sha256":"5501a57809e6a328a512395520a77342363f57be33a5409d7643a1a9ac3b47ec"},"schema_version":"1.0","source":{"id":"2406.09694","kind":"arxiv","version":2}},"canonical_sha256":"ef2f7d53159fbdfd416497b8b1a3799ce3aa5e08117ac5f96cf67ecd325ee1c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef2f7d53159fbdfd416497b8b1a3799ce3aa5e08117ac5f96cf67ecd325ee1c6","first_computed_at":"2026-07-05T09:06:27.201423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:06:27.201423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81zWhd7erFrr3Wa8aT5ODoRCgPm90euk0xnOsLWt16aPBuV0we+zoj+EdKvgz2371xnzodwoi/d75L8oQeziBw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:06:27.201953Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.09694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:271a86438e55218464e4c1c0b5b2f2cc5494b5cd4de26f56f69502b99388bd95","sha256:3cf1514fb40c3cb2d48e6f828a69446e63b56d36df41c9974a44cf7349c90307"],"state_sha256":"7714e795e2205c36df7f1c9771a4f4463ca53c2502bd96dd3ee0a62ca1d7ef40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItzbQnaK/tuvV7FL7urMS3SsHIrnVjs5ZEoXumirSzJDXa7GqgQFCv+j3CJQIbiR+kl+Q5/BtrkOaDGjGTvnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T13:48:16.281576Z","bundle_sha256":"c9543ab540be087a18a9ff19ff1339cab5b0d8de601c87efb3f3df9cc30e0556"}}