{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:XTLDZVL72BWEJNQSGCMCOP3OPM","short_pith_number":"pith:XTLDZVL7","schema_version":"1.0","canonical_sha256":"bcd63cd57fd06c44b6123098273f6e7b1bf6a203e1d3faf12c0f9facae9692bd","source":{"kind":"arxiv","id":"2305.15835","version":2},"attestation_state":"computed","paper":{"title":"PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Bingbing Xu, Bo Lin, Fei Sun, Huawei Shen, Liang Hou, Xueqi Cheng, Yige Yuan","submitted_at":"2023-05-25T08:23:26Z","abstract_excerpt":"The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as data augmentation, adversarial training, and noise injection, may encounter limited generalization due to model non-smoothness. In this paper, we propose to investigate generalization from a Partial Differential Equation (PDE) perspective, aiming to enhance it directly through the underlying function of neural networks, rather than focusing on adjusting input "},"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":"2305.15835","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2023-05-25T08:23:26Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"f970214cd0f9363cb29c89c393169412210c87f3e4bd80261cde110a28126ea9","abstract_canon_sha256":"9136406812377e22f1e48f85913ef1d57233678cfa99c0ecb5c45a2f9ecc438b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:24:19.257270Z","signature_b64":"YUvjo5XxGiKRqGeKTRvrhdXTC4drfruTUN3PuW+Dqz92hxhhQpBnLQwWVaTImy4zjx/RBffAz4A6H+1HliIXBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bcd63cd57fd06c44b6123098273f6e7b1bf6a203e1d3faf12c0f9facae9692bd","last_reissued_at":"2026-07-05T07:24:19.256770Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:24:19.256770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PDE+: Enhancing Generalization via PDE with Adaptive Distributional Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Bingbing Xu, Bo Lin, Fei Sun, Huawei Shen, Liang Hou, Xueqi Cheng, Yige Yuan","submitted_at":"2023-05-25T08:23:26Z","abstract_excerpt":"The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as data augmentation, adversarial training, and noise injection, may encounter limited generalization due to model non-smoothness. In this paper, we propose to investigate generalization from a Partial Differential Equation (PDE) perspective, aiming to enhance it directly through the underlying function of neural networks, rather than focusing on adjusting input "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.15835","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/2305.15835/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":"2305.15835","created_at":"2026-07-05T07:24:19.256827+00:00"},{"alias_kind":"arxiv_version","alias_value":"2305.15835v2","created_at":"2026-07-05T07:24:19.256827+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.15835","created_at":"2026-07-05T07:24:19.256827+00:00"},{"alias_kind":"pith_short_12","alias_value":"XTLDZVL72BWE","created_at":"2026-07-05T07:24:19.256827+00:00"},{"alias_kind":"pith_short_16","alias_value":"XTLDZVL72BWEJNQS","created_at":"2026-07-05T07:24:19.256827+00:00"},{"alias_kind":"pith_short_8","alias_value":"XTLDZVL7","created_at":"2026-07-05T07:24:19.256827+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/XTLDZVL72BWEJNQSGCMCOP3OPM","json":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM.json","graph_json":"https://pith.science/api/pith-number/XTLDZVL72BWEJNQSGCMCOP3OPM/graph.json","events_json":"https://pith.science/api/pith-number/XTLDZVL72BWEJNQSGCMCOP3OPM/events.json","paper":"https://pith.science/paper/XTLDZVL7"},"agent_actions":{"view_html":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM","download_json":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM.json","view_paper":"https://pith.science/paper/XTLDZVL7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2305.15835&json=true","fetch_graph":"https://pith.science/api/pith-number/XTLDZVL72BWEJNQSGCMCOP3OPM/graph.json","fetch_events":"https://pith.science/api/pith-number/XTLDZVL72BWEJNQSGCMCOP3OPM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM/action/storage_attestation","attest_author":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM/action/author_attestation","sign_citation":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM/action/citation_signature","submit_replication":"https://pith.science/pith/XTLDZVL72BWEJNQSGCMCOP3OPM/action/replication_record"}},"created_at":"2026-07-05T07:24:19.256827+00:00","updated_at":"2026-07-05T07:24:19.256827+00:00"}