{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:4VVQOJIIKCROUX4GAQLXGZ2BGV","short_pith_number":"pith:4VVQOJII","canonical_record":{"source":{"id":"2408.02801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-08-05T19:38:45Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"b11f65122ff5b3b500791b57b02e01247ef0d0682385b1da0fb4525af2a983f4","abstract_canon_sha256":"064c2065a3f183ac4cfb10b3e88516cc2020e8d6a9ed7cf2d38d8ec8445a9c22"},"schema_version":"1.0"},"canonical_sha256":"e56b07250850a2ea5f860417736741355398dffd3b2fc6b43356177d3734a1fd","source":{"kind":"arxiv","id":"2408.02801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.02801","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"2408.02801v1","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.02801","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"4VVQOJIIKCRO","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"pith_short_16","alias_value":"4VVQOJIIKCROUX4G","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"pith_short_8","alias_value":"4VVQOJII","created_at":"2026-07-05T08:52:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:4VVQOJIIKCROUX4GAQLXGZ2BGV","target":"record","payload":{"canonical_record":{"source":{"id":"2408.02801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-08-05T19:38:45Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"b11f65122ff5b3b500791b57b02e01247ef0d0682385b1da0fb4525af2a983f4","abstract_canon_sha256":"064c2065a3f183ac4cfb10b3e88516cc2020e8d6a9ed7cf2d38d8ec8445a9c22"},"schema_version":"1.0"},"canonical_sha256":"e56b07250850a2ea5f860417736741355398dffd3b2fc6b43356177d3734a1fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:52:40.430776Z","signature_b64":"17VsmUZeT5RA/xJC4B4od9vB8QUsDbn9lprEH6jz2/2M3RtFUNmA80DKAi5RSXoZ3yTreDOHnGMMc8PRNJxMBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e56b07250850a2ea5f860417736741355398dffd3b2fc6b43356177d3734a1fd","last_reissued_at":"2026-07-05T08:52:40.430205Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:52:40.430205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.02801","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYYAb2n7/T32Oj0AcRA+bEeOt1bMBg09LPMAo+/3trKdpJqQP+SDVrTCQgcBVq9NZ7I8hYcIFDmO/dw4MZHMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:09:17.099837Z"},"content_sha256":"bf6923b57cf57b0fe733e3ab4c25285c0337ff5c7ffdbbbeceb2dff2839bcf61","schema_version":"1.0","event_id":"sha256:bf6923b57cf57b0fe733e3ab4c25285c0337ff5c7ffdbbbeceb2dff2839bcf61"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:4VVQOJIIKCROUX4GAQLXGZ2BGV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sparse Deep Learning Models with the $\\ell_1$ Regularization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Lixin Shen, Mingsong Yan, Rui Wang, Yuesheng Xu","submitted_at":"2024-08-05T19:38:45Z","abstract_excerpt":"Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the sparsity level of learned neural networks. We first derive the $\\ell_1$-norm sparsity-promoting deep learning models including single and multiple regularization parameters models, from a statistical viewpoint. We then characterize the sparsity level of a regularized neural network in terms of the choice of the regularization parameters. Based on the characterizations, we develop iterative algorithms for selecting reg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02801","kind":"arxiv","version":1},"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/2408.02801/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":"2026-07-05T08:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xyUusmox/dLfMsIf3eYt6OhahoCWtOBZZIZI53zaw0aVCMui77JAR203qL4Mt+dp75nx6Ts0vlSJLjGUmhyODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:09:17.100206Z"},"content_sha256":"0196666db5a45f9750db315e8306cddb1a33386769e6921fc4c8247855654425","schema_version":"1.0","event_id":"sha256:0196666db5a45f9750db315e8306cddb1a33386769e6921fc4c8247855654425"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV/bundle.json","state_url":"https://pith.science/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV/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":"2026-07-07T08:09:17Z","links":{"resolver":"https://pith.science/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV","bundle":"https://pith.science/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV/bundle.json","state":"https://pith.science/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VVQOJIIKCROUX4GAQLXGZ2BGV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:4VVQOJIIKCROUX4GAQLXGZ2BGV","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":"064c2065a3f183ac4cfb10b3e88516cc2020e8d6a9ed7cf2d38d8ec8445a9c22","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-08-05T19:38:45Z","title_canon_sha256":"b11f65122ff5b3b500791b57b02e01247ef0d0682385b1da0fb4525af2a983f4"},"schema_version":"1.0","source":{"id":"2408.02801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.02801","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"2408.02801v1","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.02801","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"4VVQOJIIKCRO","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"pith_short_16","alias_value":"4VVQOJIIKCROUX4G","created_at":"2026-07-05T08:52:40Z"},{"alias_kind":"pith_short_8","alias_value":"4VVQOJII","created_at":"2026-07-05T08:52:40Z"}],"graph_snapshots":[{"event_id":"sha256:0196666db5a45f9750db315e8306cddb1a33386769e6921fc4c8247855654425","target":"graph","created_at":"2026-07-05T08:52:40Z","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/2408.02801/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Sparse neural networks are highly desirable in deep learning in reducing its complexity. The goal of this paper is to study how choices of regularization parameters influence the sparsity level of learned neural networks. We first derive the $\\ell_1$-norm sparsity-promoting deep learning models including single and multiple regularization parameters models, from a statistical viewpoint. We then characterize the sparsity level of a regularized neural network in terms of the choice of the regularization parameters. Based on the characterizations, we develop iterative algorithms for selecting reg","authors_text":"Lixin Shen, Mingsong Yan, Rui Wang, Yuesheng Xu","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-08-05T19:38:45Z","title":"Sparse Deep Learning Models with the $\\ell_1$ Regularization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.02801","kind":"arxiv","version":1},"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:bf6923b57cf57b0fe733e3ab4c25285c0337ff5c7ffdbbbeceb2dff2839bcf61","target":"record","created_at":"2026-07-05T08:52:40Z","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":"064c2065a3f183ac4cfb10b3e88516cc2020e8d6a9ed7cf2d38d8ec8445a9c22","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-08-05T19:38:45Z","title_canon_sha256":"b11f65122ff5b3b500791b57b02e01247ef0d0682385b1da0fb4525af2a983f4"},"schema_version":"1.0","source":{"id":"2408.02801","kind":"arxiv","version":1}},"canonical_sha256":"e56b07250850a2ea5f860417736741355398dffd3b2fc6b43356177d3734a1fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e56b07250850a2ea5f860417736741355398dffd3b2fc6b43356177d3734a1fd","first_computed_at":"2026-07-05T08:52:40.430205Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:52:40.430205Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"17VsmUZeT5RA/xJC4B4od9vB8QUsDbn9lprEH6jz2/2M3RtFUNmA80DKAi5RSXoZ3yTreDOHnGMMc8PRNJxMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:52:40.430776Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.02801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf6923b57cf57b0fe733e3ab4c25285c0337ff5c7ffdbbbeceb2dff2839bcf61","sha256:0196666db5a45f9750db315e8306cddb1a33386769e6921fc4c8247855654425"],"state_sha256":"1fc73031536d8da7a570ebfa88703c8278ee73ba7d64cecf16f380c6467f26e9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WrYAfgCnC9uOQjUC3ICT7xjkkTyMbUW0DX0Xrq90Q63zxpUbOqZ3neJMWKHuPZb4xwaJ4x6AGd+bzFQHi5rMCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:09:17.102263Z","bundle_sha256":"d0bcefc1c1ca808fa575828e4d3daa0dfcc86aefb2e3851d46fe4eb733d72083"}}