{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UT6KSVKG74T64BQJ7HNDQDXA3P","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":"3479732b95112a0e4dacf62b8b848f9a6c401a8d9cb13b5ec4fa4e2a8068d6e7","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-12T15:17:14Z","title_canon_sha256":"ecd3f92cca537ebc891ed33af1c426b2ffa845bfa571da3023d2d18b79995dbc"},"schema_version":"1.0","source":{"id":"1803.04304","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.04304","created_at":"2026-05-18T00:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1803.04304v1","created_at":"2026-05-18T00:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.04304","created_at":"2026-05-18T00:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"UT6KSVKG74T6","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UT6KSVKG74T64BQJ","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UT6KSVKG","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:64b732ddc83dab93a28aead0a11a3e3ac88b839ef8614219fdc1388a04d3fb33","target":"graph","created_at":"2026-05-18T00:21:32Z","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"},"paper":{"abstract_excerpt":"Rectified linear units, or ReLUs, have become the preferred activation function for artificial neural networks. In this paper we consider two basic learning problems assuming that the underlying data follow a generative model based on a ReLU-network -- a neural network with ReLU activations. As a primarily theoretical study, we limit ourselves to a single-layer network. The first problem we study corresponds to dictionary-learning in the presence of nonlinearity (modeled by the ReLU functions). Given a set of observation vectors $\\mathbf{y}^i \\in \\mathbb{R}^d, i =1, 2, \\dots , n$, we aim to re","authors_text":"Ankit Singh Rawat, Arya Mazumdar","cross_cats":["cs.IT","cs.LG","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-12T15:17:14Z","title":"Representation Learning and Recovery in the ReLU Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.04304","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:d50794bff2996e60e57a662c0fb87ee3af79e021298a4877cea59b586dec5069","target":"record","created_at":"2026-05-18T00:21:32Z","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":"3479732b95112a0e4dacf62b8b848f9a6c401a8d9cb13b5ec4fa4e2a8068d6e7","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-03-12T15:17:14Z","title_canon_sha256":"ecd3f92cca537ebc891ed33af1c426b2ffa845bfa571da3023d2d18b79995dbc"},"schema_version":"1.0","source":{"id":"1803.04304","kind":"arxiv","version":1}},"canonical_sha256":"a4fca95546ff27ee0609f9da380ee0dbca8e44ab19befc666b095dbca9773ef1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a4fca95546ff27ee0609f9da380ee0dbca8e44ab19befc666b095dbca9773ef1","first_computed_at":"2026-05-18T00:21:32.030001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:21:32.030001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6xOX57tz9axxRs3wwYUn6xg13nf+KWC98yDsr/w2/U3X5lpf+pY8AQ9jIkDBM3ghHoovRQJvaxIDXjxP22hgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:21:32.030536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.04304","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d50794bff2996e60e57a662c0fb87ee3af79e021298a4877cea59b586dec5069","sha256:64b732ddc83dab93a28aead0a11a3e3ac88b839ef8614219fdc1388a04d3fb33"],"state_sha256":"dc76bb8597e299832697f2a257d1a92040e30428be436add2ba69a6730bdbddd"}