{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BRMBWHUXXUTPLZRAHKELKTGJF5","short_pith_number":"pith:BRMBWHUX","canonical_record":{"source":{"id":"1705.08664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-24T09:02:52Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"187db8fe5c6cdb203cc234450fd81990080ff2b3065cd00fa94f9111f2bc77b0","abstract_canon_sha256":"b1480c3a7d8dbf9be72bf514682a1749b87d8b680f8344a0f6f7dbce59e451b8"},"schema_version":"1.0"},"canonical_sha256":"0c581b1e97bd26f5e6203a88b54cc92f57cc584f3fa3dab125d7132d2a153838","source":{"kind":"arxiv","id":"1705.08664","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08664","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08664v1","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08664","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"BRMBWHUXXUTP","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BRMBWHUXXUTPLZRA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BRMBWHUX","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BRMBWHUXXUTPLZRAHKELKTGJF5","target":"record","payload":{"canonical_record":{"source":{"id":"1705.08664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-24T09:02:52Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"187db8fe5c6cdb203cc234450fd81990080ff2b3065cd00fa94f9111f2bc77b0","abstract_canon_sha256":"b1480c3a7d8dbf9be72bf514682a1749b87d8b680f8344a0f6f7dbce59e451b8"},"schema_version":"1.0"},"canonical_sha256":"0c581b1e97bd26f5e6203a88b54cc92f57cc584f3fa3dab125d7132d2a153838","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:44.641921Z","signature_b64":"Rk0fVEPOWSqhMKkEypEZDgFV/5o1h6MK/3PCpWUVg8W+h/CQ/0kjx9Mw6yZXyzLn1ehEza+PnGS7JN7lDBjbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c581b1e97bd26f5e6203a88b54cc92f57cc584f3fa3dab125d7132d2a153838","last_reissued_at":"2026-05-18T00:43:44.641311Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:44.641311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.08664","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":"2026-05-18T00:43:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WYIq0rZGGhtFNpt1IlODab1cnad/oTuyBJ2k/48v5/J0HPfzHJDdtfSB4cancRR7vJN2txjgj4tDWrAkTjHPDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:12:56.374625Z"},"content_sha256":"1e38c894470244005266eb53ed10b27183301d509a308608c5474cfe84d2d35a","schema_version":"1.0","event_id":"sha256:1e38c894470244005266eb53ed10b27183301d509a308608c5474cfe84d2d35a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BRMBWHUXXUTPLZRAHKELKTGJF5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Towards Understanding the Invertibility of Convolutional Neural Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"stat.ML","authors_text":"Anna C. Gilbert, Honglak Lee, Kibok Lee, Yi Zhang, Yuting Zhang","submitted_at":"2017-05-24T09:02:52Z","abstract_excerpt":"Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is consistent with CNNs with random weights. We give an exact connection to a particular model of model-based compressive sensing (and its recovery algorithms) and random-weight CNNs. We show empirically that several learned networks are consistent with our mathematical analysis and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08664","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":"2026-05-18T00:43:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFgIAgcqqgJADnW52JhpgB1ahzfklbu2SJQ2HnQG6hwzj8Wk3vQiEczsoqYe660LSfbaNMo2eZOSfW/PJmpYCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:12:56.375441Z"},"content_sha256":"45bda8e84a48e64d658d7f0ac77c0d2167e0db0f4b3a74c137091b7d9204a707","schema_version":"1.0","event_id":"sha256:45bda8e84a48e64d658d7f0ac77c0d2167e0db0f4b3a74c137091b7d9204a707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BRMBWHUXXUTPLZRAHKELKTGJF5/bundle.json","state_url":"https://pith.science/pith/BRMBWHUXXUTPLZRAHKELKTGJF5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BRMBWHUXXUTPLZRAHKELKTGJF5/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":"2026-06-08T16:12:56Z","links":{"resolver":"https://pith.science/pith/BRMBWHUXXUTPLZRAHKELKTGJF5","bundle":"https://pith.science/pith/BRMBWHUXXUTPLZRAHKELKTGJF5/bundle.json","state":"https://pith.science/pith/BRMBWHUXXUTPLZRAHKELKTGJF5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BRMBWHUXXUTPLZRAHKELKTGJF5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BRMBWHUXXUTPLZRAHKELKTGJF5","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":"b1480c3a7d8dbf9be72bf514682a1749b87d8b680f8344a0f6f7dbce59e451b8","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-24T09:02:52Z","title_canon_sha256":"187db8fe5c6cdb203cc234450fd81990080ff2b3065cd00fa94f9111f2bc77b0"},"schema_version":"1.0","source":{"id":"1705.08664","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.08664","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"arxiv_version","alias_value":"1705.08664v1","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08664","created_at":"2026-05-18T00:43:44Z"},{"alias_kind":"pith_short_12","alias_value":"BRMBWHUXXUTP","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BRMBWHUXXUTPLZRA","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BRMBWHUX","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:45bda8e84a48e64d658d7f0ac77c0d2167e0db0f4b3a74c137091b7d9204a707","target":"graph","created_at":"2026-05-18T00:43:44Z","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":"Several recent works have empirically observed that Convolutional Neural Nets (CNNs) are (approximately) invertible. To understand this approximate invertibility phenomenon and how to leverage it more effectively, we focus on a theoretical explanation and develop a mathematical model of sparse signal recovery that is consistent with CNNs with random weights. We give an exact connection to a particular model of model-based compressive sensing (and its recovery algorithms) and random-weight CNNs. We show empirically that several learned networks are consistent with our mathematical analysis and ","authors_text":"Anna C. Gilbert, Honglak Lee, Kibok Lee, Yi Zhang, Yuting Zhang","cross_cats":["cs.LG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-24T09:02:52Z","title":"Towards Understanding the Invertibility of Convolutional Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08664","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":"sha256:1e38c894470244005266eb53ed10b27183301d509a308608c5474cfe84d2d35a","target":"record","created_at":"2026-05-18T00:43:44Z","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":"b1480c3a7d8dbf9be72bf514682a1749b87d8b680f8344a0f6f7dbce59e451b8","cross_cats_sorted":["cs.LG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2017-05-24T09:02:52Z","title_canon_sha256":"187db8fe5c6cdb203cc234450fd81990080ff2b3065cd00fa94f9111f2bc77b0"},"schema_version":"1.0","source":{"id":"1705.08664","kind":"arxiv","version":1}},"canonical_sha256":"0c581b1e97bd26f5e6203a88b54cc92f57cc584f3fa3dab125d7132d2a153838","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c581b1e97bd26f5e6203a88b54cc92f57cc584f3fa3dab125d7132d2a153838","first_computed_at":"2026-05-18T00:43:44.641311Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:44.641311Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rk0fVEPOWSqhMKkEypEZDgFV/5o1h6MK/3PCpWUVg8W+h/CQ/0kjx9Mw6yZXyzLn1ehEza+PnGS7JN7lDBjbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:44.641921Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.08664","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e38c894470244005266eb53ed10b27183301d509a308608c5474cfe84d2d35a","sha256:45bda8e84a48e64d658d7f0ac77c0d2167e0db0f4b3a74c137091b7d9204a707"],"state_sha256":"691a3aa2ff2b781172fa99f825206d2522f5863313e9545e58d24df72a24f2a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FO56nu9f5hVg+5aVHLsvVdozkDdpWSP3jmo4Ih7dTRNEEpmklAbIyFcBZeUiYXJv8z5OesRPwGr+LlX5/QlnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:12:56.378469Z","bundle_sha256":"693baffa2d8bfa54e846d9a71f94da260ce2a6de072b13a5f02a8c931b5a4e78"}}