{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W72WX337OEEERRVFNPPBAKWYRX","short_pith_number":"pith:W72WX337","canonical_record":{"source":{"id":"1310.7991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-10-30T01:12:03Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"779ee96b57b5a911fc85ea8773f63dcee1a8a2a3948d74012de2138004041c04","abstract_canon_sha256":"5719187c9d589dc5c1ab4b9393d7bb9074faa9780b99e7d60d60ae2426840e35"},"schema_version":"1.0"},"canonical_sha256":"b7f56bef7f710848c6a56bde102ad88dd9d4d0e8b376a9b50ba2bcdbe23ad273","source":{"kind":"arxiv","id":"1310.7991","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7991","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7991v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7991","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"W72WX337OEEE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W72WX337OEEERRVF","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W72WX337","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W72WX337OEEERRVFNPPBAKWYRX","target":"record","payload":{"canonical_record":{"source":{"id":"1310.7991","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-10-30T01:12:03Z","cross_cats_sorted":["math.OC","stat.ML"],"title_canon_sha256":"779ee96b57b5a911fc85ea8773f63dcee1a8a2a3948d74012de2138004041c04","abstract_canon_sha256":"5719187c9d589dc5c1ab4b9393d7bb9074faa9780b99e7d60d60ae2426840e35"},"schema_version":"1.0"},"canonical_sha256":"b7f56bef7f710848c6a56bde102ad88dd9d4d0e8b376a9b50ba2bcdbe23ad273","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:22.716887Z","signature_b64":"ssVyQ5BxjXivsWaSSXwmiwP9pa9BRjp7tK9hUJr4Sf9jfaiM0rWxeh+gZG4lVSUVWjpE44qnUiQkmZevOpNaBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7f56bef7f710848c6a56bde102ad88dd9d4d0e8b376a9b50ba2bcdbe23ad273","last_reissued_at":"2026-05-18T02:46:22.716465Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:22.716465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.7991","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":"2026-05-18T02:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rtdul3gdDoyaUI6FRv2Uw0lbLCJmhIUWtBggfyIVc1huRQBHtc7CXsivoq6WnRg0vQxiphd5drmZcMMR84mvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:05:11.843438Z"},"content_sha256":"62ba802c272169b5d4a149494f198449a94cebd4a24b25d03f73a044e1b60f12","schema_version":"1.0","event_id":"sha256:62ba802c272169b5d4a149494f198449a94cebd4a24b25d03f73a044e1b60f12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W72WX337OEEERRVFNPPBAKWYRX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC","stat.ML"],"primary_cat":"cs.LG","authors_text":"Alekh Agarwal, Animashree Anandkumar, Praneeth Netrapalli, Prateek Jain","submitted_at":"2013-10-30T01:12:03Z","abstract_excerpt":"We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via $\\ell_1$ minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7991","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":"2026-05-18T02:46:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4PkAz0TD+Sh0BlsMT8PK/5jpf7TzIciYyd0SxJYBgO797hxOeCvzG0jHRsu4aASJAMJQrANT5kydlVMJwSHDCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:05:11.843958Z"},"content_sha256":"f40ab32f24278735adf8951cc7da318fb0f1036b92151ba3d1abd7fa589084da","schema_version":"1.0","event_id":"sha256:f40ab32f24278735adf8951cc7da318fb0f1036b92151ba3d1abd7fa589084da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W72WX337OEEERRVFNPPBAKWYRX/bundle.json","state_url":"https://pith.science/pith/W72WX337OEEERRVFNPPBAKWYRX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W72WX337OEEERRVFNPPBAKWYRX/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":"2026-05-26T07:05:11Z","links":{"resolver":"https://pith.science/pith/W72WX337OEEERRVFNPPBAKWYRX","bundle":"https://pith.science/pith/W72WX337OEEERRVFNPPBAKWYRX/bundle.json","state":"https://pith.science/pith/W72WX337OEEERRVFNPPBAKWYRX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W72WX337OEEERRVFNPPBAKWYRX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W72WX337OEEERRVFNPPBAKWYRX","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":"5719187c9d589dc5c1ab4b9393d7bb9074faa9780b99e7d60d60ae2426840e35","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-10-30T01:12:03Z","title_canon_sha256":"779ee96b57b5a911fc85ea8773f63dcee1a8a2a3948d74012de2138004041c04"},"schema_version":"1.0","source":{"id":"1310.7991","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.7991","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"arxiv_version","alias_value":"1310.7991v2","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.7991","created_at":"2026-05-18T02:46:22Z"},{"alias_kind":"pith_short_12","alias_value":"W72WX337OEEE","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W72WX337OEEERRVF","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W72WX337","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:f40ab32f24278735adf8951cc7da318fb0f1036b92151ba3d1abd7fa589084da","target":"graph","created_at":"2026-05-18T02:46:22Z","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 consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is a popular heuristic for sparse coding, where the dictionary and the coefficients are estimated in alternate steps, keeping the other fixed. Typically, the coefficients are estimated via $\\ell_1$ minimization, keeping the dictionary fixed, and the dictionary is estimated through least squares, keeping the coefficients fixed. In this paper, we establish local","authors_text":"Alekh Agarwal, Animashree Anandkumar, Praneeth Netrapalli, Prateek Jain","cross_cats":["math.OC","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-10-30T01:12:03Z","title":"Learning Sparsely Used Overcomplete Dictionaries via Alternating Minimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.7991","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":"sha256:62ba802c272169b5d4a149494f198449a94cebd4a24b25d03f73a044e1b60f12","target":"record","created_at":"2026-05-18T02:46:22Z","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":"5719187c9d589dc5c1ab4b9393d7bb9074faa9780b99e7d60d60ae2426840e35","cross_cats_sorted":["math.OC","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2013-10-30T01:12:03Z","title_canon_sha256":"779ee96b57b5a911fc85ea8773f63dcee1a8a2a3948d74012de2138004041c04"},"schema_version":"1.0","source":{"id":"1310.7991","kind":"arxiv","version":2}},"canonical_sha256":"b7f56bef7f710848c6a56bde102ad88dd9d4d0e8b376a9b50ba2bcdbe23ad273","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7f56bef7f710848c6a56bde102ad88dd9d4d0e8b376a9b50ba2bcdbe23ad273","first_computed_at":"2026-05-18T02:46:22.716465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:22.716465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ssVyQ5BxjXivsWaSSXwmiwP9pa9BRjp7tK9hUJr4Sf9jfaiM0rWxeh+gZG4lVSUVWjpE44qnUiQkmZevOpNaBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:22.716887Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.7991","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62ba802c272169b5d4a149494f198449a94cebd4a24b25d03f73a044e1b60f12","sha256:f40ab32f24278735adf8951cc7da318fb0f1036b92151ba3d1abd7fa589084da"],"state_sha256":"159eeba20370899e1c7e86b71cd83a7508380b5f3cb077e306e6d70a3b31159f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wrkxi0o1COv5lPLKvtHnkR9IPBnkXXndryvyTq4XRFk1Ir83T+n78IHQLIIYj81xoVMCu75etyRhHQkTusYRCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:05:11.847329Z","bundle_sha256":"b6d38186777e1cdabb551f30f079d942399b6f9a2e82a373715324bc86a80361"}}