{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:BNRQCBNDFE2F4UFNXNNNKRSB6K","short_pith_number":"pith:BNRQCBND","canonical_record":{"source":{"id":"2205.01940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-05-04T08:23:04Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"697b489489e9a5f99cf9155856652b54c44e3c25d9dbfc48a9219b1fc152cf50","abstract_canon_sha256":"bfdb3e48ed9b4207dd42da108723b574efaa65a9850f830b567f7e1a510a4d8e"},"schema_version":"1.0"},"canonical_sha256":"0b630105a329345e50adbb5ad54641f296c1100d0d4cd73de11cb1a6881bd6dd","source":{"kind":"arxiv","id":"2205.01940","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01940","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01940v2","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01940","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"BNRQCBNDFE2F","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"pith_short_16","alias_value":"BNRQCBNDFE2F4UFN","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"pith_short_8","alias_value":"BNRQCBND","created_at":"2026-07-05T04:43:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:BNRQCBNDFE2F4UFNXNNNKRSB6K","target":"record","payload":{"canonical_record":{"source":{"id":"2205.01940","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-05-04T08:23:04Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"697b489489e9a5f99cf9155856652b54c44e3c25d9dbfc48a9219b1fc152cf50","abstract_canon_sha256":"bfdb3e48ed9b4207dd42da108723b574efaa65a9850f830b567f7e1a510a4d8e"},"schema_version":"1.0"},"canonical_sha256":"0b630105a329345e50adbb5ad54641f296c1100d0d4cd73de11cb1a6881bd6dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:01.596139Z","signature_b64":"XSfkqNZkS1Y/vQ08R634QAwl+rPn3sUCdoAcGzWcg5aelIFP6ODEBlW9K2SdQyGl4+ZXgmeEbczD0FVNsKGeAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b630105a329345e50adbb5ad54641f296c1100d0d4cd73de11cb1a6881bd6dd","last_reissued_at":"2026-07-05T04:43:01.595731Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:01.595731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2205.01940","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:43:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9r2O0KqqA2tykZMVfmrc6r75YnH2TBbLuIrjR68vpLmzlUNJuc1MnP5E8eQgE5Odgbq2s7iN9EcvvXFOGWuyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:10:57.445557Z"},"content_sha256":"8c07a6cd388430e2ee8581ac71e6cf3340f0fdd8ff2a88aecd5d16d392bd25d3","schema_version":"1.0","event_id":"sha256:8c07a6cd388430e2ee8581ac71e6cf3340f0fdd8ff2a88aecd5d16d392bd25d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:BNRQCBNDFE2F4UFNXNNNKRSB6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Theoretical Analysis of Transformation Complexity of ReLU DNNs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Jie Ren, Meng Zhou, Mingjie Li, Quanshi Zhang, Shih-Han Chan","submitted_at":"2022-05-04T08:23:04Z","abstract_excerpt":"This paper aims to theoretically analyze the complexity of feature transformations encoded in piecewise linear DNNs with ReLU layers. We propose metrics to measure three types of complexities of transformations based on the information theory. We further discover and prove the strong correlation between the complexity and the disentanglement of transformations. Based on the proposed metrics, we analyze two typical phenomena of the change of the transformation complexity during the training process, and explore the ceiling of a DNN's complexity. The proposed metrics can also be used as a loss t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01940","kind":"arxiv","version":2},"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/2205.01940/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":"2026-07-05T04:43:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KR+wmaF7GvZtAlhZZj35k0URXIKlwaAPBg0HqSXsRdQdkIHYHTmQxDkFVyKaiCfT2lSsGwf9nUkS7oFUwEyDCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:10:57.446590Z"},"content_sha256":"5e198cb0b64b4cae50041b841ee3d48c41ac3bec99698b67b684f7e975107936","schema_version":"1.0","event_id":"sha256:5e198cb0b64b4cae50041b841ee3d48c41ac3bec99698b67b684f7e975107936"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K/bundle.json","state_url":"https://pith.science/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K/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":"2026-08-19T21:10:57Z","links":{"resolver":"https://pith.science/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K","bundle":"https://pith.science/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K/bundle.json","state":"https://pith.science/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BNRQCBNDFE2F4UFNXNNNKRSB6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BNRQCBNDFE2F4UFNXNNNKRSB6K","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":"bfdb3e48ed9b4207dd42da108723b574efaa65a9850f830b567f7e1a510a4d8e","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-05-04T08:23:04Z","title_canon_sha256":"697b489489e9a5f99cf9155856652b54c44e3c25d9dbfc48a9219b1fc152cf50"},"schema_version":"1.0","source":{"id":"2205.01940","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2205.01940","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"arxiv_version","alias_value":"2205.01940v2","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2205.01940","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"pith_short_12","alias_value":"BNRQCBNDFE2F","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"pith_short_16","alias_value":"BNRQCBNDFE2F4UFN","created_at":"2026-07-05T04:43:01Z"},{"alias_kind":"pith_short_8","alias_value":"BNRQCBND","created_at":"2026-07-05T04:43:01Z"}],"graph_snapshots":[{"event_id":"sha256:5e198cb0b64b4cae50041b841ee3d48c41ac3bec99698b67b684f7e975107936","target":"graph","created_at":"2026-07-05T04:43:01Z","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/2205.01940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper aims to theoretically analyze the complexity of feature transformations encoded in piecewise linear DNNs with ReLU layers. We propose metrics to measure three types of complexities of transformations based on the information theory. We further discover and prove the strong correlation between the complexity and the disentanglement of transformations. Based on the proposed metrics, we analyze two typical phenomena of the change of the transformation complexity during the training process, and explore the ceiling of a DNN's complexity. The proposed metrics can also be used as a loss t","authors_text":"Jie Ren, Meng Zhou, Mingjie Li, Quanshi Zhang, Shih-Han Chan","cross_cats":["cs.AI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-05-04T08:23:04Z","title":"Towards Theoretical Analysis of Transformation Complexity of ReLU DNNs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.01940","kind":"arxiv","version":2},"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":"sha256:8c07a6cd388430e2ee8581ac71e6cf3340f0fdd8ff2a88aecd5d16d392bd25d3","target":"record","created_at":"2026-07-05T04:43:01Z","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":"bfdb3e48ed9b4207dd42da108723b574efaa65a9850f830b567f7e1a510a4d8e","cross_cats_sorted":["cs.AI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2022-05-04T08:23:04Z","title_canon_sha256":"697b489489e9a5f99cf9155856652b54c44e3c25d9dbfc48a9219b1fc152cf50"},"schema_version":"1.0","source":{"id":"2205.01940","kind":"arxiv","version":2}},"canonical_sha256":"0b630105a329345e50adbb5ad54641f296c1100d0d4cd73de11cb1a6881bd6dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b630105a329345e50adbb5ad54641f296c1100d0d4cd73de11cb1a6881bd6dd","first_computed_at":"2026-07-05T04:43:01.595731Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:43:01.595731Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XSfkqNZkS1Y/vQ08R634QAwl+rPn3sUCdoAcGzWcg5aelIFP6ODEBlW9K2SdQyGl4+ZXgmeEbczD0FVNsKGeAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:43:01.596139Z","signed_message":"canonical_sha256_bytes"},"source_id":"2205.01940","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c07a6cd388430e2ee8581ac71e6cf3340f0fdd8ff2a88aecd5d16d392bd25d3","sha256:5e198cb0b64b4cae50041b841ee3d48c41ac3bec99698b67b684f7e975107936"],"state_sha256":"a3c3a18b2fd9d4b81f4e3921640b7bbbae32f9eaed29ef281292ca67eb4f0406"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ak8K3edwbyWcSjkUeojj401TRN1j7DNVYGNk+NhWXyl/WgBuSeLMESIsWHTU6TWx3H2jZeqaCBj6DT3HonaYBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T21:10:57.454001Z","bundle_sha256":"d183c43c1efbae7959df1457f76b29eef43b69a13c3c164fb237edb62659f954"}}