{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:623LAYE56IRN6UKWBOZPTHHBPF","short_pith_number":"pith:623LAYE5","canonical_record":{"source":{"id":"1107.5988","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-29T15:00:47Z","cross_cats_sorted":[],"title_canon_sha256":"44e27af7c36f149ef7338623581911b38274cd464dae78da819ed56eb08b045d","abstract_canon_sha256":"f9dd26477286ff336fb8d426ca84d68773d3e3c5861f8ed3623d99e819415b43"},"schema_version":"1.0"},"canonical_sha256":"f6b6b0609df222df51560bb2f99ce1794f624fd1933f47f3d06ddcd060282c95","source":{"kind":"arxiv","id":"1107.5988","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5988","created_at":"2026-05-18T02:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5988v6","created_at":"2026-05-18T02:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5988","created_at":"2026-05-18T02:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"623LAYE56IRN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"623LAYE56IRN6UKW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"623LAYE5","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:623LAYE56IRN6UKWBOZPTHHBPF","target":"record","payload":{"canonical_record":{"source":{"id":"1107.5988","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-29T15:00:47Z","cross_cats_sorted":[],"title_canon_sha256":"44e27af7c36f149ef7338623581911b38274cd464dae78da819ed56eb08b045d","abstract_canon_sha256":"f9dd26477286ff336fb8d426ca84d68773d3e3c5861f8ed3623d99e819415b43"},"schema_version":"1.0"},"canonical_sha256":"f6b6b0609df222df51560bb2f99ce1794f624fd1933f47f3d06ddcd060282c95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:21:42.569512Z","signature_b64":"T4ghkzxtwGQgVd0l3m/96Ua1CKSrqncamlL5M3TZABBdRM+eaf5yrzfU6Y/Uj26+bJfYjt8d3qNMRwBC3IXmCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6b6b0609df222df51560bb2f99ce1794f624fd1933f47f3d06ddcd060282c95","last_reissued_at":"2026-05-18T02:21:42.568860Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:21:42.568860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.5988","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8N+LKjsdEKtxP2BVK3y3/9O6X7MKFRbS//EUCnK9CCLHIzbjyUcNiZh4gjp95IO7qffqrXis84cgxUiL1GEUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:23:51.729443Z"},"content_sha256":"9d1ab0f363fdd1e1278f4362350e4608babc9be574af35cbc54444607f3242f4","schema_version":"1.0","event_id":"sha256:9d1ab0f363fdd1e1278f4362350e4608babc9be574af35cbc54444607f3242f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:623LAYE56IRN6UKWBOZPTHHBPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence and Rate Analysis of Neural Networks for Sparse Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Aur\\`ele Balavoine, Christopher J. Rozell, Justin Romberg","submitted_at":"2011-07-29T15:00:47Z","abstract_excerpt":"We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal processing. However, the LCA lacks analysis of its convergence properties and previous results on neural networks for nonsmooth optimization do not apply to the specifics of the LCA architecture. We show that the LCA has desirable convergence proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5988","kind":"arxiv","version":6},"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":"2026-05-18T02:21:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oic09SZpqvnSBzRQG08v6i0+LxtA20wy3OI84KocOdWzdr3HOT1m612rxmwL9QsuwdcPQaWovdNGjFXk33qcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:23:51.730015Z"},"content_sha256":"1ed215b1bb49f54882eb202b6cd99fc185e8a209c75e1cb7a2207be0a57b8974","schema_version":"1.0","event_id":"sha256:1ed215b1bb49f54882eb202b6cd99fc185e8a209c75e1cb7a2207be0a57b8974"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/623LAYE56IRN6UKWBOZPTHHBPF/bundle.json","state_url":"https://pith.science/pith/623LAYE56IRN6UKWBOZPTHHBPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/623LAYE56IRN6UKWBOZPTHHBPF/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":"2026-05-27T09:23:51Z","links":{"resolver":"https://pith.science/pith/623LAYE56IRN6UKWBOZPTHHBPF","bundle":"https://pith.science/pith/623LAYE56IRN6UKWBOZPTHHBPF/bundle.json","state":"https://pith.science/pith/623LAYE56IRN6UKWBOZPTHHBPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/623LAYE56IRN6UKWBOZPTHHBPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:623LAYE56IRN6UKWBOZPTHHBPF","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":"f9dd26477286ff336fb8d426ca84d68773d3e3c5861f8ed3623d99e819415b43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-29T15:00:47Z","title_canon_sha256":"44e27af7c36f149ef7338623581911b38274cd464dae78da819ed56eb08b045d"},"schema_version":"1.0","source":{"id":"1107.5988","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5988","created_at":"2026-05-18T02:21:42Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5988v6","created_at":"2026-05-18T02:21:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5988","created_at":"2026-05-18T02:21:42Z"},{"alias_kind":"pith_short_12","alias_value":"623LAYE56IRN","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"623LAYE56IRN6UKW","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"623LAYE5","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:1ed215b1bb49f54882eb202b6cd99fc185e8a209c75e1cb7a2207be0a57b8974","target":"graph","created_at":"2026-05-18T02:21:42Z","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":"We present an analysis of the Locally Competitive Algorithm (LCA), a Hopfield-style neural network that efficiently solves sparse approximation problems (e.g., approximating a vector from a dictionary using just a few non-zero coefficients). This class of problems plays a significant role in both theories of neural coding and applications in signal processing. However, the LCA lacks analysis of its convergence properties and previous results on neural networks for nonsmooth optimization do not apply to the specifics of the LCA architecture. We show that the LCA has desirable convergence proper","authors_text":"Aur\\`ele Balavoine, Christopher J. Rozell, Justin Romberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-29T15:00:47Z","title":"Convergence and Rate Analysis of Neural Networks for Sparse Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5988","kind":"arxiv","version":6},"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":"sha256:9d1ab0f363fdd1e1278f4362350e4608babc9be574af35cbc54444607f3242f4","target":"record","created_at":"2026-05-18T02:21:42Z","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":"f9dd26477286ff336fb8d426ca84d68773d3e3c5861f8ed3623d99e819415b43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-07-29T15:00:47Z","title_canon_sha256":"44e27af7c36f149ef7338623581911b38274cd464dae78da819ed56eb08b045d"},"schema_version":"1.0","source":{"id":"1107.5988","kind":"arxiv","version":6}},"canonical_sha256":"f6b6b0609df222df51560bb2f99ce1794f624fd1933f47f3d06ddcd060282c95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6b6b0609df222df51560bb2f99ce1794f624fd1933f47f3d06ddcd060282c95","first_computed_at":"2026-05-18T02:21:42.568860Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:21:42.568860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T4ghkzxtwGQgVd0l3m/96Ua1CKSrqncamlL5M3TZABBdRM+eaf5yrzfU6Y/Uj26+bJfYjt8d3qNMRwBC3IXmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:21:42.569512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5988","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d1ab0f363fdd1e1278f4362350e4608babc9be574af35cbc54444607f3242f4","sha256:1ed215b1bb49f54882eb202b6cd99fc185e8a209c75e1cb7a2207be0a57b8974"],"state_sha256":"09338a99c66e155683c2a3fefc91693da77797ff885e9036b0094ab82b1d5f58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YpnlF4Q23yTQ6hb//U01h3fPlk/8nr5WoplNPw3vtnmAuR6Be1e1bTLrvlBIemzHNd290utyDefzjUzf6FIpCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:23:51.733149Z","bundle_sha256":"2a0b511f567ab3057a1a39b3f50e3c1a870dc13ff1fc7bc2b980358b1f217250"}}