{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NC4OV3NTTKMZRQGLS2QYROX5RZ","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":"a77be9dd8ab54cf9ed123c595ee4318c33c684758460d3c845b736c129a42111","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-08-17T00:42:34Z","title_canon_sha256":"3b2bae0489505a0e0ed3417054f20f0b6ef719233650198806a380f36c643c9d"},"schema_version":"1.0","source":{"id":"1908.06214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.06214","created_at":"2026-07-05T00:24:17Z"},{"alias_kind":"arxiv_version","alias_value":"1908.06214v2","created_at":"2026-07-05T00:24:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.06214","created_at":"2026-07-05T00:24:17Z"},{"alias_kind":"pith_short_12","alias_value":"NC4OV3NTTKMZ","created_at":"2026-07-05T00:24:17Z"},{"alias_kind":"pith_short_16","alias_value":"NC4OV3NTTKMZRQGL","created_at":"2026-07-05T00:24:17Z"},{"alias_kind":"pith_short_8","alias_value":"NC4OV3NT","created_at":"2026-07-05T00:24:17Z"}],"graph_snapshots":[{"event_id":"sha256:f1cf0d122b6c7931e7ceb406992917093d980dfda0079d3a79ef11ebc7390a94","target":"graph","created_at":"2026-07-05T00:24:17Z","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/1908.06214/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A linear restriction of a function is the same function with its domain restricted to points on a given line. This paper addresses the problem of computing a succinct representation for a linear restriction of a piecewise-linear neural network. This primitive, which we call ExactLine, allows us to exactly characterize the result of applying the network to all of the infinitely many points on a line. In particular, ExactLine computes a partitioning of the given input line segment such that the network is affine on each partition. We present an efficient algorithm for computing ExactLine for net","authors_text":"Aditya V. Thakur, Matthew Sotoudeh","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-08-17T00:42:34Z","title":"Computing Linear Restrictions of Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06214","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":"sha256:4983308d7e60ef8503a4e025011a0c25bbf0a4c33fb05f1aced79ce94e752c1b","target":"record","created_at":"2026-07-05T00:24:17Z","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":"a77be9dd8ab54cf9ed123c595ee4318c33c684758460d3c845b736c129a42111","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-08-17T00:42:34Z","title_canon_sha256":"3b2bae0489505a0e0ed3417054f20f0b6ef719233650198806a380f36c643c9d"},"schema_version":"1.0","source":{"id":"1908.06214","kind":"arxiv","version":2}},"canonical_sha256":"68b8eaedb39a9998c0cb96a188bafd8e533d220b724e3d441ea52106f5caa61a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68b8eaedb39a9998c0cb96a188bafd8e533d220b724e3d441ea52106f5caa61a","first_computed_at":"2026-07-05T00:24:17.957690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:24:17.957690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zVZ6knQkGUMXjIU7OXWGk32R5WwIQipMGkKHNXWby7Iccc0bGpm/c3ZNaLk02QnPhmJ2GtL4ArIEV4AoXVkGAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:24:17.958121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.06214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4983308d7e60ef8503a4e025011a0c25bbf0a4c33fb05f1aced79ce94e752c1b","sha256:f1cf0d122b6c7931e7ceb406992917093d980dfda0079d3a79ef11ebc7390a94"],"state_sha256":"e4f24aeb96c31ddf8705463983ec9f9624e91a0bae083d6c056b6ffc6a00646d"}