{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3UEDUPL3HYMVLSCWU3CRMQ4TEA","short_pith_number":"pith:3UEDUPL3","canonical_record":{"source":{"id":"2312.16699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-27T19:32:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"aada92b50a9377ebad8bd4f51c7199a4cc37dd38af9e873f11aa32358e2dc489","abstract_canon_sha256":"a5ba9ca15a8484df394c855d9e3eb4ee8eec27587dc11fd131aa30bd4a717a47"},"schema_version":"1.0"},"canonical_sha256":"dd083a3d7b3e1955c856a6c516439320165a49894f35850550edba4fc5c757b9","source":{"kind":"arxiv","id":"2312.16699","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.16699","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"2312.16699v2","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.16699","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"3UEDUPL3HYMV","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"pith_short_16","alias_value":"3UEDUPL3HYMVLSCW","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"pith_short_8","alias_value":"3UEDUPL3","created_at":"2026-07-05T07:39:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3UEDUPL3HYMVLSCWU3CRMQ4TEA","target":"record","payload":{"canonical_record":{"source":{"id":"2312.16699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-27T19:32:59Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"aada92b50a9377ebad8bd4f51c7199a4cc37dd38af9e873f11aa32358e2dc489","abstract_canon_sha256":"a5ba9ca15a8484df394c855d9e3eb4ee8eec27587dc11fd131aa30bd4a717a47"},"schema_version":"1.0"},"canonical_sha256":"dd083a3d7b3e1955c856a6c516439320165a49894f35850550edba4fc5c757b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:39:33.225440Z","signature_b64":"W09O8aqjoUSmlCkGrtTLT2UqebsOahFGkILHWKCuXk7bjGIelv7VT80Evx94bnzkdoZAb7cqffgO1B+5rAqcAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd083a3d7b3e1955c856a6c516439320165a49894f35850550edba4fc5c757b9","last_reissued_at":"2026-07-05T07:39:33.224902Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:39:33.224902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2312.16699","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m8M2ZKbDqhvCqLDCx7O6c7mBqNtJOKCS9BF29ifkolJ8uETaoBU5tgzLv+DaC7JlB1FyoSJWgE/uHeqaCtP+Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T15:17:36.413446Z"},"content_sha256":"5d42720b9ca23e6166ad5b804c93ee0f9200cd35b42e32c31fde3abf549f9207","schema_version":"1.0","event_id":"sha256:5d42720b9ca23e6166ad5b804c93ee0f9200cd35b42e32c31fde3abf549f9207"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3UEDUPL3HYMVLSCWU3CRMQ4TEA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Fabian Badilla, Gonzalo Mu\\~noz, Marcos Goycoolea, Thiago Serra","submitted_at":"2023-12-27T19:32:59Z","abstract_excerpt":"The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to test-or stress-their behavior, to adversarially improve their training, and to embed them in optimization models leveraging their predictive power. Many of these MILP models rely on activation bounds. That is, bounds on the input values of each neuron. In this work, we explore the tradeoff between the tightness of these bounds and the computational effort of solv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16699","kind":"arxiv","version":2},"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/2312.16699/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"735GY++pZj4M5zv/yewCNvLueFAmdHsRfrSFZ3nWSADIQf6YrPxzUxq1Q4hOUVzx9EbUYyLlIN3jrZOgTWPgCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T15:17:36.414392Z"},"content_sha256":"628f592e1f216d2559e33009a4383098f767fe140cc433d11f3903bf4d097467","schema_version":"1.0","event_id":"sha256:628f592e1f216d2559e33009a4383098f767fe140cc433d11f3903bf4d097467"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA/bundle.json","state_url":"https://pith.science/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-10T15:17:36Z","links":{"resolver":"https://pith.science/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA","bundle":"https://pith.science/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA/bundle.json","state":"https://pith.science/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3UEDUPL3HYMVLSCWU3CRMQ4TEA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3UEDUPL3HYMVLSCWU3CRMQ4TEA","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":"a5ba9ca15a8484df394c855d9e3eb4ee8eec27587dc11fd131aa30bd4a717a47","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-27T19:32:59Z","title_canon_sha256":"aada92b50a9377ebad8bd4f51c7199a4cc37dd38af9e873f11aa32358e2dc489"},"schema_version":"1.0","source":{"id":"2312.16699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2312.16699","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"2312.16699v2","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2312.16699","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"3UEDUPL3HYMV","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"pith_short_16","alias_value":"3UEDUPL3HYMVLSCW","created_at":"2026-07-05T07:39:33Z"},{"alias_kind":"pith_short_8","alias_value":"3UEDUPL3","created_at":"2026-07-05T07:39:33Z"}],"graph_snapshots":[{"event_id":"sha256:628f592e1f216d2559e33009a4383098f767fe140cc433d11f3903bf4d097467","target":"graph","created_at":"2026-07-05T07:39:33Z","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/2312.16699/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to test-or stress-their behavior, to adversarially improve their training, and to embed them in optimization models leveraging their predictive power. Many of these MILP models rely on activation bounds. That is, bounds on the input values of each neuron. In this work, we explore the tradeoff between the tightness of these bounds and the computational effort of solv","authors_text":"Fabian Badilla, Gonzalo Mu\\~noz, Marcos Goycoolea, Thiago Serra","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-27T19:32:59Z","title":"Computational Tradeoffs of Optimization-Based Bound Tightening in ReLU Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16699","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":"sha256:5d42720b9ca23e6166ad5b804c93ee0f9200cd35b42e32c31fde3abf549f9207","target":"record","created_at":"2026-07-05T07:39:33Z","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":"a5ba9ca15a8484df394c855d9e3eb4ee8eec27587dc11fd131aa30bd4a717a47","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-12-27T19:32:59Z","title_canon_sha256":"aada92b50a9377ebad8bd4f51c7199a4cc37dd38af9e873f11aa32358e2dc489"},"schema_version":"1.0","source":{"id":"2312.16699","kind":"arxiv","version":2}},"canonical_sha256":"dd083a3d7b3e1955c856a6c516439320165a49894f35850550edba4fc5c757b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd083a3d7b3e1955c856a6c516439320165a49894f35850550edba4fc5c757b9","first_computed_at":"2026-07-05T07:39:33.224902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:39:33.224902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W09O8aqjoUSmlCkGrtTLT2UqebsOahFGkILHWKCuXk7bjGIelv7VT80Evx94bnzkdoZAb7cqffgO1B+5rAqcAw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:39:33.225440Z","signed_message":"canonical_sha256_bytes"},"source_id":"2312.16699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d42720b9ca23e6166ad5b804c93ee0f9200cd35b42e32c31fde3abf549f9207","sha256:628f592e1f216d2559e33009a4383098f767fe140cc433d11f3903bf4d097467"],"state_sha256":"a199b74fa138b6479471bb44c8eb8a6193f68896a2c4c6280014630034eb06b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"skwbPoy0MUSX2AN0/bBXKso3RCXWInMsXW30eddhC4OWFwnia0bCwpJKaqtNGgF1MpCy4Ki42k3qDS3LEssjAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T15:17:36.419979Z","bundle_sha256":"1ddfd5e5a6c88700c6836b8da5591f688743c612c7b19bd95abf82eb27fa508b"}}