{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TRZLVNS3VMNTVJZSMG5LRRLONS","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":"92c6109213d13bed10de9925a9a9c14d0d2e15333ac0607fe3f0806549e46810","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-15T15:39:28Z","title_canon_sha256":"5de56b1bc2bd5535b71a7b4561a20cdd48030686b142c01f80d1accb57b1734e"},"schema_version":"1.0","source":{"id":"2505.10423","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.10423","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"arxiv_version","alias_value":"2505.10423v1","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.10423","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_12","alias_value":"TRZLVNS3VMNT","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_16","alias_value":"TRZLVNS3VMNTVJZS","created_at":"2026-07-05T11:03:38Z"},{"alias_kind":"pith_short_8","alias_value":"TRZLVNS3","created_at":"2026-07-05T11:03:38Z"}],"graph_snapshots":[{"event_id":"sha256:e5b377ba09ecf5aa71ac70324c105e76f928ed44d7585bbdc4ef2896e884b837","target":"graph","created_at":"2026-07-05T11:03:38Z","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/2505.10423/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the relationship between gradient-based optimization of parametric models (e.g., neural networks) and optimization of linear combinations of random features. Our main result shows that if a parametric model can be learned using mini-batch stochastic gradient descent (bSGD) without making assumptions about the data distribution, then with high probability, the target function can also be approximated using a polynomial-sized combination of random features. The size of this combination depends on the number of gradient steps and numerical precision used in the bSGD process. This finding","authors_text":"Ari Karchmer, Eran Malach","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-15T15:39:28Z","title":"The Power of Random Features and the Limits of Distribution-Free Gradient Descent"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.10423","kind":"arxiv","version":1},"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":"sha256:63b0260925dff233148efab2d2064aea4f41f092855ba1060374351b3cd8d46f","target":"record","created_at":"2026-07-05T11:03:38Z","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":"92c6109213d13bed10de9925a9a9c14d0d2e15333ac0607fe3f0806549e46810","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-05-15T15:39:28Z","title_canon_sha256":"5de56b1bc2bd5535b71a7b4561a20cdd48030686b142c01f80d1accb57b1734e"},"schema_version":"1.0","source":{"id":"2505.10423","kind":"arxiv","version":1}},"canonical_sha256":"9c72bab65bab1b3aa73261bab8c56e6ca85f2a34270580f034bd12dbf2628bdb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c72bab65bab1b3aa73261bab8c56e6ca85f2a34270580f034bd12dbf2628bdb","first_computed_at":"2026-07-05T11:03:38.197407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:38.197407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"boG21RPUx0UOy0/YXpDgqxW80IewePrXNhcWXT/VV5IRze4rBy/l//buznjHqjI0VZdHYBALLqfPdk3hi20mAw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:38.197838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.10423","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:63b0260925dff233148efab2d2064aea4f41f092855ba1060374351b3cd8d46f","sha256:e5b377ba09ecf5aa71ac70324c105e76f928ed44d7585bbdc4ef2896e884b837"],"state_sha256":"ceea362764eca4077ae5d92d68e27eabe89c8d99820a9249659c984a81cc9fcb"}