{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:2RJHDDFAOMDI4GGATVBRPGRRCN","short_pith_number":"pith:2RJHDDFA","schema_version":"1.0","canonical_sha256":"d452718ca073068e18c09d43179a311356a45efbd8f44d9195dc6156b3c73030","source":{"kind":"arxiv","id":"2501.18812","version":2},"attestation_state":"computed","paper":{"title":"Estimating the Probability of Sampling a Trained Neural Network at Random","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Adam Scherlis, Nora Belrose","submitted_at":"2025-01-31T00:16:06Z","abstract_excerpt":"We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the \"local volume\" of the anchor. We adapt an existing basin-volume estimator, which is very fast but in many cases only provides a lower bound. We show that this lower bound can be improved with an importance-sampling method using gradient information that is already provided by popular optimizers. The negative logarithm of local volume can also be interpreted as a measu"},"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":"2501.18812","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-01-31T00:16:06Z","cross_cats_sorted":[],"title_canon_sha256":"aae08cf638fd01b5c6c69654eb254658cd2a973162d72681d1636867e6948e6d","abstract_canon_sha256":"a37c4238ecc494fcdc67e69dfc2461c8950c9c1e5cff66a04a6333468a5e70b6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:45:59.761739Z","signature_b64":"7jfL78x1MmFsf3Zv8QpXkmAVK/hWFdw1K1JLC//PviLLYNWKKUpMuZIrwRO6EWIzZVH346hjePkj2k6CA37gAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d452718ca073068e18c09d43179a311356a45efbd8f44d9195dc6156b3c73030","last_reissued_at":"2026-07-05T10:45:59.761158Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:45:59.761158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimating the Probability of Sampling a Trained Neural Network at Random","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Adam Scherlis, Nora Belrose","submitted_at":"2025-01-31T00:16:06Z","abstract_excerpt":"We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the \"local volume\" of the anchor. We adapt an existing basin-volume estimator, which is very fast but in many cases only provides a lower bound. We show that this lower bound can be improved with an importance-sampling method using gradient information that is already provided by popular optimizers. The negative logarithm of local volume can also be interpreted as a measu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.18812","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/2501.18812/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":"2501.18812","created_at":"2026-07-05T10:45:59.761233+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.18812v2","created_at":"2026-07-05T10:45:59.761233+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.18812","created_at":"2026-07-05T10:45:59.761233+00:00"},{"alias_kind":"pith_short_12","alias_value":"2RJHDDFAOMDI","created_at":"2026-07-05T10:45:59.761233+00:00"},{"alias_kind":"pith_short_16","alias_value":"2RJHDDFAOMDI4GGA","created_at":"2026-07-05T10:45:59.761233+00:00"},{"alias_kind":"pith_short_8","alias_value":"2RJHDDFA","created_at":"2026-07-05T10:45:59.761233+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.31282","citing_title":"Revisiting the Volume Hypothesis","ref_index":300,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN","json":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN.json","graph_json":"https://pith.science/api/pith-number/2RJHDDFAOMDI4GGATVBRPGRRCN/graph.json","events_json":"https://pith.science/api/pith-number/2RJHDDFAOMDI4GGATVBRPGRRCN/events.json","paper":"https://pith.science/paper/2RJHDDFA"},"agent_actions":{"view_html":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN","download_json":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN.json","view_paper":"https://pith.science/paper/2RJHDDFA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.18812&json=true","fetch_graph":"https://pith.science/api/pith-number/2RJHDDFAOMDI4GGATVBRPGRRCN/graph.json","fetch_events":"https://pith.science/api/pith-number/2RJHDDFAOMDI4GGATVBRPGRRCN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN/action/storage_attestation","attest_author":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN/action/author_attestation","sign_citation":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN/action/citation_signature","submit_replication":"https://pith.science/pith/2RJHDDFAOMDI4GGATVBRPGRRCN/action/replication_record"}},"created_at":"2026-07-05T10:45:59.761233+00:00","updated_at":"2026-07-05T10:45:59.761233+00:00"}