{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P6T6BC6HLEKMLEE7IAIPPAWTCV","short_pith_number":"pith:P6T6BC6H","canonical_record":{"source":{"id":"1508.06095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2015-08-25T10:09:31Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"a7a01213de6c5e9444794b76ea5373df14d26f6ea2f2cee5c19059e82ada967f","abstract_canon_sha256":"94fdf409cf9a7e2ae215bb0dcee787007d10b0bf2df632604b1214c824b6a23c"},"schema_version":"1.0"},"canonical_sha256":"7fa7e08bc75914c5909f4010f782d31564632f60adc5697fd836653fbe110e53","source":{"kind":"arxiv","id":"1508.06095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06095","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06095v1","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06095","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"P6T6BC6HLEKM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P6T6BC6HLEKMLEE7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P6T6BC6H","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P6T6BC6HLEKMLEE7IAIPPAWTCV","target":"record","payload":{"canonical_record":{"source":{"id":"1508.06095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2015-08-25T10:09:31Z","cross_cats_sorted":["cs.LG","stat.ML"],"title_canon_sha256":"a7a01213de6c5e9444794b76ea5373df14d26f6ea2f2cee5c19059e82ada967f","abstract_canon_sha256":"94fdf409cf9a7e2ae215bb0dcee787007d10b0bf2df632604b1214c824b6a23c"},"schema_version":"1.0"},"canonical_sha256":"7fa7e08bc75914c5909f4010f782d31564632f60adc5697fd836653fbe110e53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:46.875288Z","signature_b64":"cGhYK/7posuZUj2yAJK2eIMCd75j7R1lxFhBvCpXyxZ/KTFjMXv1C3lXpsyyyt0wFePKl+cVWO/aGjXB4joBCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fa7e08bc75914c5909f4010f782d31564632f60adc5697fd836653fbe110e53","last_reissued_at":"2026-05-18T01:34:46.874651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:46.874651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.06095","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":"2026-05-18T01:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7J+UQa+RgRfvxawh49Q9hdsYUn2n7tcT3JBc5laRKG6hRWTF84iQaUXcfDS0PWW7nlAjD7mta3kswN7vgao0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:58:22.287843Z"},"content_sha256":"593a8339c11624fa8e3ff60c70b5643f19bbfdb7dfb9f33dee6f0fe0bbd8045e","schema_version":"1.0","event_id":"sha256:593a8339c11624fa8e3ff60c70b5643f19bbfdb7dfb9f33dee6f0fe0bbd8045e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P6T6BC6HLEKMLEE7IAIPPAWTCV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.NE","authors_text":"Luca Rubini, Mario Gai, Patrick Gallinari, Rossella Cancelliere","submitted_at":"2015-08-25T10:09:31Z","abstract_excerpt":"In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06095","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":""},"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":"2026-05-18T01:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gs0+MKxxwRvP92vCeeOuFY8SgEbu75smYZcHXhf0dPIrlfcnctGMPcV3jA9mA6bw4YUIf2a/MlhR5xjFIY5LBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:58:22.288194Z"},"content_sha256":"9a5acebb45fc9fd54401126e26b5527188bb061ed540f5e28a7dfdccd9e9a9e0","schema_version":"1.0","event_id":"sha256:9a5acebb45fc9fd54401126e26b5527188bb061ed540f5e28a7dfdccd9e9a9e0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV/bundle.json","state_url":"https://pith.science/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV/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":"2026-05-28T03:58:22Z","links":{"resolver":"https://pith.science/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV","bundle":"https://pith.science/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV/bundle.json","state":"https://pith.science/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6T6BC6HLEKMLEE7IAIPPAWTCV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P6T6BC6HLEKMLEE7IAIPPAWTCV","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":"94fdf409cf9a7e2ae215bb0dcee787007d10b0bf2df632604b1214c824b6a23c","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2015-08-25T10:09:31Z","title_canon_sha256":"a7a01213de6c5e9444794b76ea5373df14d26f6ea2f2cee5c19059e82ada967f"},"schema_version":"1.0","source":{"id":"1508.06095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.06095","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"1508.06095v1","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06095","created_at":"2026-05-18T01:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"P6T6BC6HLEKM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P6T6BC6HLEKMLEE7","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P6T6BC6H","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:9a5acebb45fc9fd54401126e26b5527188bb061ed540f5e28a7dfdccd9e9a9e0","target":"graph","created_at":"2026-05-18T01:34:46Z","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":"In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such cases, so that we introduce, in the framework of Tikhonov regularization, a matricial reformulation of the problem which allows us to use the condition number as a diagnostic tool for identification of instability. By imposing well-conditioning requirements on the relevant matrices, our theoretical analysis allows the identification of an optimal value for the r","authors_text":"Luca Rubini, Mario Gai, Patrick Gallinari, Rossella Cancelliere","cross_cats":["cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2015-08-25T10:09:31Z","title":"OCReP: An Optimally Conditioned Regularization for Pseudoinversion Based Neural Training"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06095","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":"sha256:593a8339c11624fa8e3ff60c70b5643f19bbfdb7dfb9f33dee6f0fe0bbd8045e","target":"record","created_at":"2026-05-18T01:34:46Z","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":"94fdf409cf9a7e2ae215bb0dcee787007d10b0bf2df632604b1214c824b6a23c","cross_cats_sorted":["cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.NE","submitted_at":"2015-08-25T10:09:31Z","title_canon_sha256":"a7a01213de6c5e9444794b76ea5373df14d26f6ea2f2cee5c19059e82ada967f"},"schema_version":"1.0","source":{"id":"1508.06095","kind":"arxiv","version":1}},"canonical_sha256":"7fa7e08bc75914c5909f4010f782d31564632f60adc5697fd836653fbe110e53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fa7e08bc75914c5909f4010f782d31564632f60adc5697fd836653fbe110e53","first_computed_at":"2026-05-18T01:34:46.874651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:46.874651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGhYK/7posuZUj2yAJK2eIMCd75j7R1lxFhBvCpXyxZ/KTFjMXv1C3lXpsyyyt0wFePKl+cVWO/aGjXB4joBCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:46.875288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.06095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:593a8339c11624fa8e3ff60c70b5643f19bbfdb7dfb9f33dee6f0fe0bbd8045e","sha256:9a5acebb45fc9fd54401126e26b5527188bb061ed540f5e28a7dfdccd9e9a9e0"],"state_sha256":"a1daad48f35183851c0691caa8437f79193d92af58bd2c47e8f9d649dc9520ea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gT8F/4bYhTNbRT0Tje1cGB65x17WEx4Ls4aIhGT7WfC70O+mhkp9OOpWsqOu0VWmK3dCHNQKW1FONzvDQxCOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:58:22.290191Z","bundle_sha256":"59e06b56e1e1ee88279a1cd9abfd7d8c58651340e607e1d9b8bd7d7c8af9a13a"}}