{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YTWVYVGTWTVXBC2PRDO74FDQS7","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":"d72539a0712e0cf27d9ddee5ed147a533c85e173ec2b9650874888cd73f56ab6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-18T06:58:36Z","title_canon_sha256":"09b8f0e9029741ffa2aad3b27af3c2a3319454e8a707593c28093ea804470bb7"},"schema_version":"1.0","source":{"id":"1907.07904","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07904","created_at":"2026-05-17T23:40:15Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07904v1","created_at":"2026-05-17T23:40:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07904","created_at":"2026-05-17T23:40:15Z"},{"alias_kind":"pith_short_12","alias_value":"YTWVYVGTWTVX","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YTWVYVGTWTVXBC2P","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YTWVYVGT","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:237ed3b24423718c31ac06773f20c2d0f08c6897186762c205c5f437ea0076af","target":"graph","created_at":"2026-05-17T23:40:15Z","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"},"paper":{"abstract_excerpt":"Deep learning has been shown to achieve impressive results in several domains like computer vision and natural language processing. A key element of this success has been the development of new loss functions, like the popular cross-entropy loss, which has been shown to provide faster convergence and to reduce the vanishing gradient problem in very deep structures. While the cross-entropy loss is usually justified from a probabilistic perspective, this paper shows an alternative and more direct interpretation of this loss in terms of t-norms and their associated generator functions, and derive","authors_text":"Francesco Giannini, Giuseppe Marra, Marco Gori, Marco Maggini, Michelangelo Diligenti","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-18T06:58:36Z","title":"On the relation between Loss Functions and T-Norms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07904","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":"sha256:053ff0c239da126f4e95ea55b1bd2f59d51a8027db0ccf5b45aec9f8d2bb35f9","target":"record","created_at":"2026-05-17T23:40:15Z","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":"d72539a0712e0cf27d9ddee5ed147a533c85e173ec2b9650874888cd73f56ab6","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2019-07-18T06:58:36Z","title_canon_sha256":"09b8f0e9029741ffa2aad3b27af3c2a3319454e8a707593c28093ea804470bb7"},"schema_version":"1.0","source":{"id":"1907.07904","kind":"arxiv","version":1}},"canonical_sha256":"c4ed5c54d3b4eb708b4f88ddfe147097d616d936231dace864faf37724be4746","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4ed5c54d3b4eb708b4f88ddfe147097d616d936231dace864faf37724be4746","first_computed_at":"2026-05-17T23:40:15.750549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:15.750549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wodpQKy+GOKwPqXEKI86JttxwP4C98ezXpXqnOOvG0TnPFkgXPW3VD+oQ2jg57Pzi+Su789HxKW1/xB6XHzvDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:15.751362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07904","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:053ff0c239da126f4e95ea55b1bd2f59d51a8027db0ccf5b45aec9f8d2bb35f9","sha256:237ed3b24423718c31ac06773f20c2d0f08c6897186762c205c5f437ea0076af"],"state_sha256":"ece41dd399ad04bb0f3b1100bd6930f291920568574ec3c77e582a44f0655e5a"}