{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2ILTPYNY3GF4AEIXSM4TKFTQSF","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":"01fa3e710027d99292265ea490b5aa0a8f39a9c14d26064bd256ea2eddfe12da","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-11T08:57:08Z","title_canon_sha256":"662069aabdd2022a038230cc9e7156bf6491755db596da1dacc9a44e4dfd0a34"},"schema_version":"1.0","source":{"id":"1802.03713","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03713","created_at":"2026-07-05T02:25:15Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03713v8","created_at":"2026-07-05T02:25:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03713","created_at":"2026-07-05T02:25:15Z"},{"alias_kind":"pith_short_12","alias_value":"2ILTPYNY3GF4","created_at":"2026-07-05T02:25:15Z"},{"alias_kind":"pith_short_16","alias_value":"2ILTPYNY3GF4AEIX","created_at":"2026-07-05T02:25:15Z"},{"alias_kind":"pith_short_8","alias_value":"2ILTPYNY","created_at":"2026-07-05T02:25:15Z"}],"graph_snapshots":[{"event_id":"sha256:e83952542e217333d98558c71e2535fba4d63fe4f61dd3c24364e47628d52fe2","target":"graph","created_at":"2026-07-05T02:25:15Z","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/1802.03713/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well known that neural networks with rectified linear units (ReLU) activation functions are positively scale-invariant. Conventional algorithms like stochastic gradient descent optimize the neural networks in the vector space of weights, which is, however, not positively scale-invariant. This mismatch may lead to problems during the optimization process. Then, a natural question is: \\emph{can we construct a new vector space that is positively scale-invariant and sufficient to represent ReLU neural networks so as to better facilitate the optimization process }? In this paper, we provide o","authors_text":"Huishuai Zhang, Qi Meng, Shuxin Zheng, Tie-Yan Liu, Wei Chen, Zhi-Ming Ma","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-11T08:57:08Z","title":"$\\mathcal{G}$-SGD: Optimizing ReLU Neural Networks in its Positively Scale-Invariant Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03713","kind":"arxiv","version":8},"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:c8cf64ada78f1cc493eb485b74366bc8a0b66336eff043411727e75419e4cabc","target":"record","created_at":"2026-07-05T02:25:15Z","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":"01fa3e710027d99292265ea490b5aa0a8f39a9c14d26064bd256ea2eddfe12da","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2018-02-11T08:57:08Z","title_canon_sha256":"662069aabdd2022a038230cc9e7156bf6491755db596da1dacc9a44e4dfd0a34"},"schema_version":"1.0","source":{"id":"1802.03713","kind":"arxiv","version":8}},"canonical_sha256":"d21737e1b8d98bc011179339351670914f7b98eeae66c2e60ee511549c273f4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d21737e1b8d98bc011179339351670914f7b98eeae66c2e60ee511549c273f4e","first_computed_at":"2026-07-05T02:25:15.033975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:25:15.033975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aUnYv+NFStL1whHwowZKxA19i2lKTV2QmIK2JP00AquQgBKKseLrgygKHaqhVI+nLb6zAbqtPTHBI25kDcxsDg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:25:15.034448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03713","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8cf64ada78f1cc493eb485b74366bc8a0b66336eff043411727e75419e4cabc","sha256:e83952542e217333d98558c71e2535fba4d63fe4f61dd3c24364e47628d52fe2"],"state_sha256":"ec9e7c5567dbcf434cbe742e14f560cd40c9fea9f1f58868daa852ff5ff7e579"}