{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BJ7KXYJ4K53LNYVHKTMFTC65T4","short_pith_number":"pith:BJ7KXYJ4","canonical_record":{"source":{"id":"1807.07998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-20T18:45:09Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bda87737f8217aa4a670a573559479fdddde4f3a27075ba01be78f951178f08c","abstract_canon_sha256":"a7932e4f017b5e154ae8337c189cc524b14aa5acff862264e40f0b3443486199"},"schema_version":"1.0"},"canonical_sha256":"0a7eabe13c5776b6e2a754d8598bdd9f290dd7a3599f3d9f0869102c52f72d1d","source":{"kind":"arxiv","id":"1807.07998","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07998","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07998v2","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07998","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"BJ7KXYJ4K53L","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BJ7KXYJ4K53LNYVH","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BJ7KXYJ4","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BJ7KXYJ4K53LNYVHKTMFTC65T4","target":"record","payload":{"canonical_record":{"source":{"id":"1807.07998","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-20T18:45:09Z","cross_cats_sorted":["stat.ML"],"title_canon_sha256":"bda87737f8217aa4a670a573559479fdddde4f3a27075ba01be78f951178f08c","abstract_canon_sha256":"a7932e4f017b5e154ae8337c189cc524b14aa5acff862264e40f0b3443486199"},"schema_version":"1.0"},"canonical_sha256":"0a7eabe13c5776b6e2a754d8598bdd9f290dd7a3599f3d9f0869102c52f72d1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:19.278813Z","signature_b64":"hhyr/VPPOd96qlnS7zfuH3LHMxxIlbFshN4bXCg7oI1C8Isa1VMmy0amCMIDlL1mmvLaHSptOT+DPpahYCB+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a7eabe13c5776b6e2a754d8598bdd9f290dd7a3599f3d9f0869102c52f72d1d","last_reissued_at":"2026-05-18T00:02:19.278306Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:19.278306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.07998","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":"2026-05-18T00:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HzWAqEik267OCfL81W9L5A2kY+170uyOh7f4pYxdRjoh4O32o+JfHfinPGbwHaMhLF3laDqKKznNt7LHBKM+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:20:33.506491Z"},"content_sha256":"e780b77be09e18943459b63534ee3496e355775846e690a7189597cb66b440de","schema_version":"1.0","event_id":"sha256:e780b77be09e18943459b63534ee3496e355775846e690a7189597cb66b440de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BJ7KXYJ4K53LNYVHKTMFTC65T4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convolutional Neural Networks Analyzed via Inverse Problem Theory and Sparse Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ML"],"primary_cat":"cs.LG","authors_text":"Cem Tarhan, Gozde Bozdagi Akar","submitted_at":"2018-07-20T18:45:09Z","abstract_excerpt":"Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their indisputable success, CNNs are not mathematically validated as to how and what they learn. In this paper, we prove that during training, CNN elements solve for inverse problems which are optimum solutions stored as CNN neuron filters. We discuss the necessity of mutual coherence between CNN layer elements in order for a network to converge to the optimum so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07998","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":""},"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":"2026-05-18T00:02:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3sRCbGjLvJgsImHe/t/yfv5+nVYHFaUxFyLKfMfmtrI0J8aX89iswToT5wZjOWfKBq/aPVDPItbEPjN7p09MAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T06:20:33.507180Z"},"content_sha256":"1a0290d9fea9c8d6cf1188c7fad90eaedecd9113264db1af163365a005d90a11","schema_version":"1.0","event_id":"sha256:1a0290d9fea9c8d6cf1188c7fad90eaedecd9113264db1af163365a005d90a11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4/bundle.json","state_url":"https://pith.science/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4/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":"2026-05-26T06:20:33Z","links":{"resolver":"https://pith.science/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4","bundle":"https://pith.science/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4/bundle.json","state":"https://pith.science/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJ7KXYJ4K53LNYVHKTMFTC65T4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BJ7KXYJ4K53LNYVHKTMFTC65T4","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":"a7932e4f017b5e154ae8337c189cc524b14aa5acff862264e40f0b3443486199","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-20T18:45:09Z","title_canon_sha256":"bda87737f8217aa4a670a573559479fdddde4f3a27075ba01be78f951178f08c"},"schema_version":"1.0","source":{"id":"1807.07998","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.07998","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"arxiv_version","alias_value":"1807.07998v2","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.07998","created_at":"2026-05-18T00:02:19Z"},{"alias_kind":"pith_short_12","alias_value":"BJ7KXYJ4K53L","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BJ7KXYJ4K53LNYVH","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BJ7KXYJ4","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:1a0290d9fea9c8d6cf1188c7fad90eaedecd9113264db1af163365a005d90a11","target":"graph","created_at":"2026-05-18T00:02:19Z","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":"Inverse problems in imaging such as denoising, deblurring, superresolution (SR) have been addressed for many decades. In recent years, convolutional neural networks (CNNs) have been widely used for many inverse problem areas. Although their indisputable success, CNNs are not mathematically validated as to how and what they learn. In this paper, we prove that during training, CNN elements solve for inverse problems which are optimum solutions stored as CNN neuron filters. We discuss the necessity of mutual coherence between CNN layer elements in order for a network to converge to the optimum so","authors_text":"Cem Tarhan, Gozde Bozdagi Akar","cross_cats":["stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-20T18:45:09Z","title":"Convolutional Neural Networks Analyzed via Inverse Problem Theory and Sparse Representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.07998","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:e780b77be09e18943459b63534ee3496e355775846e690a7189597cb66b440de","target":"record","created_at":"2026-05-18T00:02:19Z","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":"a7932e4f017b5e154ae8337c189cc524b14aa5acff862264e40f0b3443486199","cross_cats_sorted":["stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2018-07-20T18:45:09Z","title_canon_sha256":"bda87737f8217aa4a670a573559479fdddde4f3a27075ba01be78f951178f08c"},"schema_version":"1.0","source":{"id":"1807.07998","kind":"arxiv","version":2}},"canonical_sha256":"0a7eabe13c5776b6e2a754d8598bdd9f290dd7a3599f3d9f0869102c52f72d1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a7eabe13c5776b6e2a754d8598bdd9f290dd7a3599f3d9f0869102c52f72d1d","first_computed_at":"2026-05-18T00:02:19.278306Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:19.278306Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hhyr/VPPOd96qlnS7zfuH3LHMxxIlbFshN4bXCg7oI1C8Isa1VMmy0amCMIDlL1mmvLaHSptOT+DPpahYCB+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:19.278813Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.07998","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e780b77be09e18943459b63534ee3496e355775846e690a7189597cb66b440de","sha256:1a0290d9fea9c8d6cf1188c7fad90eaedecd9113264db1af163365a005d90a11"],"state_sha256":"ba9f6d4cd93d199d51edcee9e51f4f79a3ebce48b0e80bf70752ec38692bbb89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NYJbzXPgxuDfiQGrBgBTZb+XVMgzCtx6Ge26j0UCcTr2zqwdij7SSz+PYuCdg13Wmewc603nPLISKbFV1Qz/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T06:20:33.510449Z","bundle_sha256":"6d422b4b769f34e7032d4a59148e74b13217af0fd934d64fba383ef1c09827a3"}}