{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:B2RRAZMXBZRMHN2UHGOJ76T5EV","short_pith_number":"pith:B2RRAZMX","canonical_record":{"source":{"id":"2212.03659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-07T14:23:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"517f4a9f6c48b5044aa2c70805fea08c7eaef1daba72adba255b9502111c59af","abstract_canon_sha256":"cafecaf94bf9ada79977de79535b5525bccf11d652aed299d779da49bd8de9f2"},"schema_version":"1.0"},"canonical_sha256":"0ea31065970e62c3b754399c9ffa7d25714160a0926fde64f9eb7f05fe428067","source":{"kind":"arxiv","id":"2212.03659","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.03659","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2212.03659v2","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.03659","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"B2RRAZMXBZRM","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"B2RRAZMXBZRMHN2U","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"B2RRAZMX","created_at":"2026-07-05T09:05:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:B2RRAZMXBZRMHN2UHGOJ76T5EV","target":"record","payload":{"canonical_record":{"source":{"id":"2212.03659","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-07T14:23:43Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"517f4a9f6c48b5044aa2c70805fea08c7eaef1daba72adba255b9502111c59af","abstract_canon_sha256":"cafecaf94bf9ada79977de79535b5525bccf11d652aed299d779da49bd8de9f2"},"schema_version":"1.0"},"canonical_sha256":"0ea31065970e62c3b754399c9ffa7d25714160a0926fde64f9eb7f05fe428067","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:05:29.713124Z","signature_b64":"f/o8+ZFySXpHokT26umKfCPOSbTfML290M+ALwKh/RTAtEru8HJ/UVapAj2Co46jHGsFrfnmQX65bqzGWUjdCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ea31065970e62c3b754399c9ffa7d25714160a0926fde64f9eb7f05fe428067","last_reissued_at":"2026-07-05T09:05:29.712614Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:05:29.712614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2212.03659","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":"2026-07-05T09:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cNDuT+kePAJfxhytV97HzM/IV9H3vb7dSPdY9hw6aUcDWgVJDNujLVmzJE/eVQHp65jaPvjh2gW8vREFqcj/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:44:14.133690Z"},"content_sha256":"ee9e28c710cc087d81c83af97ce3f245128736c389b6d129c55c14bc35a9e11f","schema_version":"1.0","event_id":"sha256:ee9e28c710cc087d81c83af97ce3f245128736c389b6d129c55c14bc35a9e11f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:B2RRAZMXBZRMHN2UHGOJ76T5EV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Objective Linear Ensembles for Robust and Sparse Training of Few-Bit Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Ambrogio Maria Bernardelli, Hoong Chuin LAU, Neil Yorke-Smith, Simone Milanesi, Stefano Gualandi","submitted_at":"2022-12-07T14:23:43Z","abstract_excerpt":"Training neural networks (NNs) using combinatorial optimization solvers has gained attention in recent years. In low-data settings, state-of-the-art mixed integer linear programming solvers can train exactly a NN, avoiding intensive GPU-based training and hyper-parameter tuning and simultaneously training and sparsifying the network. We study the case of few-bit discrete-valued neural networks, both Binarized Neural Networks (BNNs), whose values are restricted to +-1, and Integer Neural Networks (INNs), whose values lie in a range {-P, ..., P}. Few-bit NNs receive increasing recognition due to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.03659","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/2212.03659/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":"2026-07-05T09:05:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RXqK/A+9RAklV1xpaKFmcHYqhuLi1WXMPoXuOLbNpdyKNGOl4Meg8CTP0c9j+7HAQHH1Vxn8MdhdR9EzZfdcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:44:14.134497Z"},"content_sha256":"1f362af4c783efd2ee6eab47e3266387f457d774cffe474a98e3456a781f1931","schema_version":"1.0","event_id":"sha256:1f362af4c783efd2ee6eab47e3266387f457d774cffe474a98e3456a781f1931"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV/bundle.json","state_url":"https://pith.science/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV/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":"2026-08-04T09:44:14Z","links":{"resolver":"https://pith.science/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV","bundle":"https://pith.science/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV/bundle.json","state":"https://pith.science/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2RRAZMXBZRMHN2UHGOJ76T5EV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:B2RRAZMXBZRMHN2UHGOJ76T5EV","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":"cafecaf94bf9ada79977de79535b5525bccf11d652aed299d779da49bd8de9f2","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-07T14:23:43Z","title_canon_sha256":"517f4a9f6c48b5044aa2c70805fea08c7eaef1daba72adba255b9502111c59af"},"schema_version":"1.0","source":{"id":"2212.03659","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2212.03659","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"arxiv_version","alias_value":"2212.03659v2","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2212.03659","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"pith_short_12","alias_value":"B2RRAZMXBZRM","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"pith_short_16","alias_value":"B2RRAZMXBZRMHN2U","created_at":"2026-07-05T09:05:29Z"},{"alias_kind":"pith_short_8","alias_value":"B2RRAZMX","created_at":"2026-07-05T09:05:29Z"}],"graph_snapshots":[{"event_id":"sha256:1f362af4c783efd2ee6eab47e3266387f457d774cffe474a98e3456a781f1931","target":"graph","created_at":"2026-07-05T09:05:29Z","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/2212.03659/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Training neural networks (NNs) using combinatorial optimization solvers has gained attention in recent years. In low-data settings, state-of-the-art mixed integer linear programming solvers can train exactly a NN, avoiding intensive GPU-based training and hyper-parameter tuning and simultaneously training and sparsifying the network. We study the case of few-bit discrete-valued neural networks, both Binarized Neural Networks (BNNs), whose values are restricted to +-1, and Integer Neural Networks (INNs), whose values lie in a range {-P, ..., P}. Few-bit NNs receive increasing recognition due to","authors_text":"Ambrogio Maria Bernardelli, Hoong Chuin LAU, Neil Yorke-Smith, Simone Milanesi, Stefano Gualandi","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-07T14:23:43Z","title":"Multi-Objective Linear Ensembles for Robust and Sparse Training of Few-Bit Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.03659","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:ee9e28c710cc087d81c83af97ce3f245128736c389b6d129c55c14bc35a9e11f","target":"record","created_at":"2026-07-05T09:05:29Z","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":"cafecaf94bf9ada79977de79535b5525bccf11d652aed299d779da49bd8de9f2","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2022-12-07T14:23:43Z","title_canon_sha256":"517f4a9f6c48b5044aa2c70805fea08c7eaef1daba72adba255b9502111c59af"},"schema_version":"1.0","source":{"id":"2212.03659","kind":"arxiv","version":2}},"canonical_sha256":"0ea31065970e62c3b754399c9ffa7d25714160a0926fde64f9eb7f05fe428067","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ea31065970e62c3b754399c9ffa7d25714160a0926fde64f9eb7f05fe428067","first_computed_at":"2026-07-05T09:05:29.712614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:29.712614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f/o8+ZFySXpHokT26umKfCPOSbTfML290M+ALwKh/RTAtEru8HJ/UVapAj2Co46jHGsFrfnmQX65bqzGWUjdCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:29.713124Z","signed_message":"canonical_sha256_bytes"},"source_id":"2212.03659","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee9e28c710cc087d81c83af97ce3f245128736c389b6d129c55c14bc35a9e11f","sha256:1f362af4c783efd2ee6eab47e3266387f457d774cffe474a98e3456a781f1931"],"state_sha256":"34385c7ab67f3045b1e9be91b559395b0224b088b00dab2d3f4b3e8ed99428ba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TDPvD1jzMCMfTFiRJPHxIvSnLSoWlJd7C476v/Ct1upVzsF6CrT8bWimiWtBy4zxdV+3R0T9rVWSSWFTYBY8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:44:14.140217Z","bundle_sha256":"f21d9ff24eb2109f967079ee0ccba1e34431933110b4601d5862519c69b4098e"}}