{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:4QWCO3SLL7IDPNHNY4DR2GFHHP","short_pith_number":"pith:4QWCO3SL","schema_version":"1.0","canonical_sha256":"e42c276e4b5fd037b4edc7071d18a73bd9475fd6fe56d32fa263080f6e9103f7","source":{"kind":"arxiv","id":"2210.08339","version":4},"attestation_state":"computed","paper":{"title":"Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.RO","cs.SY","eess.SY"],"primary_cat":"cs.LG","authors_text":"Joseph A. Vincent, Mac Schwager","submitted_at":"2022-10-15T17:15:53Z","abstract_excerpt":"Neural networks are increasingly used in robotics as policies, state transition models, state estimation models, or all of the above. With these components being learned from data, it is important to be able to analyze what behaviors were learned and how this affects closed-loop performance. In this paper we take steps toward this goal by developing methods for computing control invariant sets and regions of attraction (ROAs) of dynamical systems represented as neural networks. We focus our attention on feedforward neural networks with the rectified linear unit (ReLU) activation, which are kno"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2210.08339","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-10-15T17:15:53Z","cross_cats_sorted":["cs.AI","cs.RO","cs.SY","eess.SY"],"title_canon_sha256":"4134be49a6868bf9d2e51ecb43fa30e233a387b3fd0450c6d9811bb48a26e1c6","abstract_canon_sha256":"68ff1ef5a8ed1835e16fe3c9141a557724f49435f2de7ccb8979623752a55ac1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:09.308122Z","signature_b64":"YE0IjUBXnbvu+AEvXDmVdHHkq+e24NIAZCHYysZ5fd6XFqjk65PL15Lw1tLAaul/LNgWRMZi7f7gHBMAN82yDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e42c276e4b5fd037b4edc7071d18a73bd9475fd6fe56d32fa263080f6e9103f7","last_reissued_at":"2026-07-05T10:41:09.307722Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:09.307722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI","cs.RO","cs.SY","eess.SY"],"primary_cat":"cs.LG","authors_text":"Joseph A. Vincent, Mac Schwager","submitted_at":"2022-10-15T17:15:53Z","abstract_excerpt":"Neural networks are increasingly used in robotics as policies, state transition models, state estimation models, or all of the above. With these components being learned from data, it is important to be able to analyze what behaviors were learned and how this affects closed-loop performance. In this paper we take steps toward this goal by developing methods for computing control invariant sets and regions of attraction (ROAs) of dynamical systems represented as neural networks. We focus our attention on feedforward neural networks with the rectified linear unit (ReLU) activation, which are kno"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2210.08339","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2210.08339/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2210.08339","created_at":"2026-07-05T10:41:09.307777+00:00"},{"alias_kind":"arxiv_version","alias_value":"2210.08339v4","created_at":"2026-07-05T10:41:09.307777+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2210.08339","created_at":"2026-07-05T10:41:09.307777+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QWCO3SLL7ID","created_at":"2026-07-05T10:41:09.307777+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QWCO3SLL7IDPNHN","created_at":"2026-07-05T10:41:09.307777+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QWCO3SL","created_at":"2026-07-05T10:41:09.307777+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP","json":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP.json","graph_json":"https://pith.science/api/pith-number/4QWCO3SLL7IDPNHNY4DR2GFHHP/graph.json","events_json":"https://pith.science/api/pith-number/4QWCO3SLL7IDPNHNY4DR2GFHHP/events.json","paper":"https://pith.science/paper/4QWCO3SL"},"agent_actions":{"view_html":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP","download_json":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP.json","view_paper":"https://pith.science/paper/4QWCO3SL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2210.08339&json=true","fetch_graph":"https://pith.science/api/pith-number/4QWCO3SLL7IDPNHNY4DR2GFHHP/graph.json","fetch_events":"https://pith.science/api/pith-number/4QWCO3SLL7IDPNHNY4DR2GFHHP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP/action/storage_attestation","attest_author":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP/action/author_attestation","sign_citation":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP/action/citation_signature","submit_replication":"https://pith.science/pith/4QWCO3SLL7IDPNHNY4DR2GFHHP/action/replication_record"}},"created_at":"2026-07-05T10:41:09.307777+00:00","updated_at":"2026-07-05T10:41:09.307777+00:00"}