{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:BYKUX7DBMH4UD2VGSVR76I5D4T","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":"5ae8bf64c92caa49b63b0d4af8a061251134354ad232cf9824dacfc353a515d7","cross_cats_sorted":["cs.CC","math.PR","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-20T20:03:52Z","title_canon_sha256":"90208347d5563d856d6f1c9ab47a48ba17704eeddd0c885d91fd9ace9d4394ab"},"schema_version":"1.0","source":{"id":"2106.10744","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.10744","created_at":"2026-07-05T03:14:56Z"},{"alias_kind":"arxiv_version","alias_value":"2106.10744v2","created_at":"2026-07-05T03:14:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.10744","created_at":"2026-07-05T03:14:56Z"},{"alias_kind":"pith_short_12","alias_value":"BYKUX7DBMH4U","created_at":"2026-07-05T03:14:56Z"},{"alias_kind":"pith_short_16","alias_value":"BYKUX7DBMH4UD2VG","created_at":"2026-07-05T03:14:56Z"},{"alias_kind":"pith_short_8","alias_value":"BYKUX7DB","created_at":"2026-07-05T03:14:56Z"}],"graph_snapshots":[{"event_id":"sha256:e2639ea41866cd3cac7137a91d0685ad99e9621ad78a52c1be63b4c2ca02897a","target":"graph","created_at":"2026-07-05T03:14:56Z","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/2106.10744/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show a simple reduction which demonstrates the cryptographic hardness of learning a single periodic neuron over isotropic Gaussian distributions in the presence of noise. More precisely, our reduction shows that any polynomial-time algorithm (not necessarily gradient-based) for learning such functions under small noise implies a polynomial-time quantum algorithm for solving worst-case lattice problems, whose hardness form the foundation of lattice-based cryptography. Our core hard family of functions, which are well-approximated by one-layer neural networks, take the general form of a univa","authors_text":"Ilias Zadik, Joan Bruna, Min Jae Song","cross_cats":["cs.CC","math.PR","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-20T20:03:52Z","title":"On the Cryptographic Hardness of Learning Single Periodic Neurons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.10744","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":"sha256:8f4304ddbbb6a3572f1ded51de6630749bf1bf8e82f3a689adfcb2d91b718d96","target":"record","created_at":"2026-07-05T03:14:56Z","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":"5ae8bf64c92caa49b63b0d4af8a061251134354ad232cf9824dacfc353a515d7","cross_cats_sorted":["cs.CC","math.PR","math.ST","stat.ML","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-06-20T20:03:52Z","title_canon_sha256":"90208347d5563d856d6f1c9ab47a48ba17704eeddd0c885d91fd9ace9d4394ab"},"schema_version":"1.0","source":{"id":"2106.10744","kind":"arxiv","version":2}},"canonical_sha256":"0e154bfc6161f941eaa69563ff23a3e4c7e31b5614260223fd15db28f133b3ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e154bfc6161f941eaa69563ff23a3e4c7e31b5614260223fd15db28f133b3ce","first_computed_at":"2026-07-05T03:14:56.103343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:14:56.103343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hl44DtCcPkRCmBFIl3uOCahka3sJOSSn+WT7zVEKVke3XL9cswZYyg0qumENhZJn2OoD2SSaQqzKhZvs4PAkCg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:14:56.103689Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.10744","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f4304ddbbb6a3572f1ded51de6630749bf1bf8e82f3a689adfcb2d91b718d96","sha256:e2639ea41866cd3cac7137a91d0685ad99e9621ad78a52c1be63b4c2ca02897a"],"state_sha256":"750740253b4d54e4f65589d0d4def5cfb21a613a3a3a7e8d9a47a47b3fc24fae"}