{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:7F6BAO7RWEJZWY4ZEXDWK63ELD","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":"ee0b07591dff24f1afb1535394fc9c564028c4697d575691e8ba1a2cdda89a5b","cross_cats_sorted":["eess.SP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-29T08:12:39Z","title_canon_sha256":"2303c6824c54c310b1f35c075d9a9df4a9b515ed0517dcb7f82ff91faa0c3267"},"schema_version":"1.0","source":{"id":"1903.12384","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12384","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12384v1","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12384","created_at":"2026-05-17T23:49:54Z"},{"alias_kind":"pith_short_12","alias_value":"7F6BAO7RWEJZ","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"7F6BAO7RWEJZWY4Z","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"7F6BAO7R","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:95a75e3a4f5ef0dac59c74903c9a83bb717b1bb92e7149b5aaa6442c038780cc","target":"graph","created_at":"2026-05-17T23:49:54Z","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":"We consider deep feedforward neural networks with rectified linear units from a signal processing perspective. In this view, such representations mark the transition from using a single (data-driven) linear representation to utilizing a large collection of affine linear representations tailored to particular regions of the signal space. This paper provides a precise description of the individual affine linear representations and corresponding domain regions that the (data-driven) neural network associates to each signal of the input space. In particular, we describe atomic decompositions of th","authors_text":"Andreas Heinecke, Wen-Liang Hwang","cross_cats":["eess.SP","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-29T08:12:39Z","title":"Deep Representation with ReLU Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12384","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:fe23841d0b965eec68304aff51a3f44b758e91770dc4d95268bf318d4bc4394a","target":"record","created_at":"2026-05-17T23:49:54Z","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":"ee0b07591dff24f1afb1535394fc9c564028c4697d575691e8ba1a2cdda89a5b","cross_cats_sorted":["eess.SP","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-03-29T08:12:39Z","title_canon_sha256":"2303c6824c54c310b1f35c075d9a9df4a9b515ed0517dcb7f82ff91faa0c3267"},"schema_version":"1.0","source":{"id":"1903.12384","kind":"arxiv","version":1}},"canonical_sha256":"f97c103bf1b1139b639925c7657b6458c142b46d7adab8c8909ed8fa0a479171","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f97c103bf1b1139b639925c7657b6458c142b46d7adab8c8909ed8fa0a479171","first_computed_at":"2026-05-17T23:49:54.199001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:54.199001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hUpSF3XKM74s6U7HewgDtudmJrT/j0wI/jEZWZo+0IvXYs0cNxCkCIyjW1gWktmsHnzZqfiN9pDqX6eTZSD0DA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:54.199464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12384","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe23841d0b965eec68304aff51a3f44b758e91770dc4d95268bf318d4bc4394a","sha256:95a75e3a4f5ef0dac59c74903c9a83bb717b1bb92e7149b5aaa6442c038780cc"],"state_sha256":"946df556477ffcf22d314255db26abc87c5edc9e1f53f00df4bb093d83ed4124"}