{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:DJWNGFR37ZPYMHJPJPVMDIP34T","short_pith_number":"pith:DJWNGFR3","canonical_record":{"source":{"id":"2009.12078","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-09-25T08:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"c8787f78832d6b47e1261a32d4a0dfa974ab7b4dd5e5dcb4443e23e1cae40326","abstract_canon_sha256":"27fb12aaae8f1df2e6f4eb004d99d04c6860b315bfc6448c80476a69d857830c"},"schema_version":"1.0"},"canonical_sha256":"1a6cd3163bfe5f861d2f4beac1a1fbe4c0f6a2bbd68a7944c3b7ad08b361af55","source":{"kind":"arxiv","id":"2009.12078","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.12078","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"2009.12078v3","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.12078","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"DJWNGFR37ZPY","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"pith_short_16","alias_value":"DJWNGFR37ZPYMHJP","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"pith_short_8","alias_value":"DJWNGFR3","created_at":"2026-07-05T02:14:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:DJWNGFR37ZPYMHJPJPVMDIP34T","target":"record","payload":{"canonical_record":{"source":{"id":"2009.12078","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-09-25T08:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"c8787f78832d6b47e1261a32d4a0dfa974ab7b4dd5e5dcb4443e23e1cae40326","abstract_canon_sha256":"27fb12aaae8f1df2e6f4eb004d99d04c6860b315bfc6448c80476a69d857830c"},"schema_version":"1.0"},"canonical_sha256":"1a6cd3163bfe5f861d2f4beac1a1fbe4c0f6a2bbd68a7944c3b7ad08b361af55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:14:55.104971Z","signature_b64":"zCpv5lPK9a4VSaPGVc3A2Er9BuyqXEm0ctNYuAY0j9lX1tcb3JXRvTzBiGBFD/RGRdJuihbfqNDPK8mAQ4TSDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a6cd3163bfe5f861d2f4beac1a1fbe4c0f6a2bbd68a7944c3b7ad08b361af55","last_reissued_at":"2026-07-05T02:14:55.104434Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:14:55.104434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.12078","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WdeNmzcPWWZBQ/y8+lYRTJbqY4Q86l4bXtvrls7pRdYlC0/8IUCScxxxP4uy4rq6HAjQ2EzLw/ejYG0irfOIAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T18:40:15.802804Z"},"content_sha256":"3d0defd6631d4d533e2cb0c0d99fae0db140ac6d3b03de9757ddc1b664291b13","schema_version":"1.0","event_id":"sha256:3d0defd6631d4d533e2cb0c0d99fae0db140ac6d3b03de9757ddc1b664291b13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:DJWNGFR37ZPYMHJPJPVMDIP34T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Half-Space Proximal Stochastic Gradient Method for Group-Sparsity Regularized Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Ji, Guanyi Wang, Sheng Yi, Tianyi Chen, Tianyu Ding, Zhihui Zhu","submitted_at":"2020-09-25T08:00:07Z","abstract_excerpt":"Optimizing with group sparsity is significant in enhancing model interpretability in machining learning applications, e.g., feature selection, compressed sensing and model compression. However, for large-scale stochastic training problems, effective group sparsity exploration are typically hard to achieve. Particularly, the state-of-the-art stochastic optimization algorithms usually generate merely dense solutions. To overcome this shortage, we propose a stochastic method -- Half-space Stochastic Projected Gradient (HSPG) method to search solutions of high group sparsity while maintain the con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.12078","kind":"arxiv","version":3},"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/2009.12078/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":"2026-07-05T02:14:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r3wwphZifkpwvO8zVZzA9QMmlGM7AdT3wwowm7gw2B2gZHBtxgeDNFNevxRoexGrE4AeAz/JaSBwh9GOKPqaAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T18:40:15.803173Z"},"content_sha256":"d09675c080a44d6f45538fa1865d88a705689345c54b28f083903ba9ebf30584","schema_version":"1.0","event_id":"sha256:d09675c080a44d6f45538fa1865d88a705689345c54b28f083903ba9ebf30584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DJWNGFR37ZPYMHJPJPVMDIP34T/bundle.json","state_url":"https://pith.science/pith/DJWNGFR37ZPYMHJPJPVMDIP34T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DJWNGFR37ZPYMHJPJPVMDIP34T/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":"2026-07-12T18:40:15Z","links":{"resolver":"https://pith.science/pith/DJWNGFR37ZPYMHJPJPVMDIP34T","bundle":"https://pith.science/pith/DJWNGFR37ZPYMHJPJPVMDIP34T/bundle.json","state":"https://pith.science/pith/DJWNGFR37ZPYMHJPJPVMDIP34T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DJWNGFR37ZPYMHJPJPVMDIP34T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DJWNGFR37ZPYMHJPJPVMDIP34T","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":"27fb12aaae8f1df2e6f4eb004d99d04c6860b315bfc6448c80476a69d857830c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-09-25T08:00:07Z","title_canon_sha256":"c8787f78832d6b47e1261a32d4a0dfa974ab7b4dd5e5dcb4443e23e1cae40326"},"schema_version":"1.0","source":{"id":"2009.12078","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.12078","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"2009.12078v3","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.12078","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"DJWNGFR37ZPY","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"pith_short_16","alias_value":"DJWNGFR37ZPYMHJP","created_at":"2026-07-05T02:14:55Z"},{"alias_kind":"pith_short_8","alias_value":"DJWNGFR3","created_at":"2026-07-05T02:14:55Z"}],"graph_snapshots":[{"event_id":"sha256:d09675c080a44d6f45538fa1865d88a705689345c54b28f083903ba9ebf30584","target":"graph","created_at":"2026-07-05T02:14:55Z","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/2009.12078/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Optimizing with group sparsity is significant in enhancing model interpretability in machining learning applications, e.g., feature selection, compressed sensing and model compression. However, for large-scale stochastic training problems, effective group sparsity exploration are typically hard to achieve. Particularly, the state-of-the-art stochastic optimization algorithms usually generate merely dense solutions. To overcome this shortage, we propose a stochastic method -- Half-space Stochastic Projected Gradient (HSPG) method to search solutions of high group sparsity while maintain the con","authors_text":"Bo Ji, Guanyi Wang, Sheng Yi, Tianyi Chen, Tianyu Ding, Zhihui Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-09-25T08:00:07Z","title":"Half-Space Proximal Stochastic Gradient Method for Group-Sparsity Regularized Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.12078","kind":"arxiv","version":3},"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":"sha256:3d0defd6631d4d533e2cb0c0d99fae0db140ac6d3b03de9757ddc1b664291b13","target":"record","created_at":"2026-07-05T02:14:55Z","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":"27fb12aaae8f1df2e6f4eb004d99d04c6860b315bfc6448c80476a69d857830c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-09-25T08:00:07Z","title_canon_sha256":"c8787f78832d6b47e1261a32d4a0dfa974ab7b4dd5e5dcb4443e23e1cae40326"},"schema_version":"1.0","source":{"id":"2009.12078","kind":"arxiv","version":3}},"canonical_sha256":"1a6cd3163bfe5f861d2f4beac1a1fbe4c0f6a2bbd68a7944c3b7ad08b361af55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1a6cd3163bfe5f861d2f4beac1a1fbe4c0f6a2bbd68a7944c3b7ad08b361af55","first_computed_at":"2026-07-05T02:14:55.104434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:14:55.104434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zCpv5lPK9a4VSaPGVc3A2Er9BuyqXEm0ctNYuAY0j9lX1tcb3JXRvTzBiGBFD/RGRdJuihbfqNDPK8mAQ4TSDA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:14:55.104971Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.12078","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d0defd6631d4d533e2cb0c0d99fae0db140ac6d3b03de9757ddc1b664291b13","sha256:d09675c080a44d6f45538fa1865d88a705689345c54b28f083903ba9ebf30584"],"state_sha256":"a746ba6238dc144fc72cbda4725a8e2ba790863c2a8dbb32f6abf4be748a11b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0AroOrSeOAkBCO5GSmeUc0Lo8iWpcByX7dzhw33JEBDv+Tun4M1ZBW7VXERFKlJni84rbSJmNCue0tkU+7TYBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T18:40:15.805238Z","bundle_sha256":"6fa65d613d7f0b8a7299fa82fec6499e8dee3e758df31eaff71742ae1f15a5ba"}}