{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:INK3VDHD3XLJENGUPVY66V7UQO","short_pith_number":"pith:INK3VDHD","canonical_record":{"source":{"id":"2404.13785","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-21T21:36:42Z","cross_cats_sorted":[],"title_canon_sha256":"aa20d3ad2ef0dd18c3de5ff4cd25f9bf6e4c3bd6573fe675573767c4ec619bff","abstract_canon_sha256":"d42a19e7accf287663f4a6c7cdd00c8b06b20783a2bfa2cee1b3ddf76739830e"},"schema_version":"1.0"},"canonical_sha256":"4355ba8ce3ddd69234d47d71ef57f483a33a8c9f9822559f1aae3494f9c937d8","source":{"kind":"arxiv","id":"2404.13785","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.13785","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"2404.13785v1","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.13785","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"INK3VDHD3XLJ","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"pith_short_16","alias_value":"INK3VDHD3XLJENGU","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"pith_short_8","alias_value":"INK3VDHD","created_at":"2026-07-05T08:10:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:INK3VDHD3XLJENGUPVY66V7UQO","target":"record","payload":{"canonical_record":{"source":{"id":"2404.13785","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-21T21:36:42Z","cross_cats_sorted":[],"title_canon_sha256":"aa20d3ad2ef0dd18c3de5ff4cd25f9bf6e4c3bd6573fe675573767c4ec619bff","abstract_canon_sha256":"d42a19e7accf287663f4a6c7cdd00c8b06b20783a2bfa2cee1b3ddf76739830e"},"schema_version":"1.0"},"canonical_sha256":"4355ba8ce3ddd69234d47d71ef57f483a33a8c9f9822559f1aae3494f9c937d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:10:37.250506Z","signature_b64":"dv0V+MlNcjNS1XbSnJQFn/EBeFeYMUEcF9m9islaYfyYVQdlXc9rBEbLRgltHvZaoTQCzh7gIfhnU6DgFo0ZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4355ba8ce3ddd69234d47d71ef57f483a33a8c9f9822559f1aae3494f9c937d8","last_reissued_at":"2026-07-05T08:10:37.249994Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:10:37.249994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2404.13785","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":"2026-07-05T08:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mYFwgedkp75EOmRqekTs5upOqJG/XAftVVPCBklxqlJuo2eHfNcgOPlrS1Y6mxJkwX6g0KpwCbpimko9CgqICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:17:35.549580Z"},"content_sha256":"6475405d484627778b595bc278e5a8d1e3e3591a06761e5b9a22572ae14b7fc1","schema_version":"1.0","event_id":"sha256:6475405d484627778b595bc278e5a8d1e3e3591a06761e5b9a22572ae14b7fc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:INK3VDHD3XLJENGUPVY66V7UQO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How to Inverting the Leverage Score Distribution?","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Junze Yin, Weixin Wang, Zhao Song, Zheng Yu, Zhihang Li","submitted_at":"2024-04-21T21:36:42Z","abstract_excerpt":"Leverage score is a fundamental problem in machine learning and theoretical computer science. It has extensive applications in regression analysis, randomized algorithms, and neural network inversion. Despite leverage scores are widely used as a tool, in this paper, we study a novel problem, namely the inverting leverage score problem. We analyze to invert the leverage score distributions back to recover model parameters. Specifically, given a leverage score $\\sigma \\in \\mathbb{R}^n$, the matrix $A \\in \\mathbb{R}^{n \\times d}$, and the vector $b \\in \\mathbb{R}^n$, we analyze the non-convex opt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.13785","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.13785/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":"2026-07-05T08:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7RECBRZBmBdjpmwPqXd7dotAiLQi0b2XWS8C6jNECWefoG6dESmMxOOYBT91OQ0UPL40HWlVB5kECfjqM4+CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T22:17:35.550102Z"},"content_sha256":"98be4e67f47701104583b0e57bd3751fd23de2c9f37b0afcd946ed3c1e6e8c4a","schema_version":"1.0","event_id":"sha256:98be4e67f47701104583b0e57bd3751fd23de2c9f37b0afcd946ed3c1e6e8c4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INK3VDHD3XLJENGUPVY66V7UQO/bundle.json","state_url":"https://pith.science/pith/INK3VDHD3XLJENGUPVY66V7UQO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INK3VDHD3XLJENGUPVY66V7UQO/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":"2026-08-10T22:17:35Z","links":{"resolver":"https://pith.science/pith/INK3VDHD3XLJENGUPVY66V7UQO","bundle":"https://pith.science/pith/INK3VDHD3XLJENGUPVY66V7UQO/bundle.json","state":"https://pith.science/pith/INK3VDHD3XLJENGUPVY66V7UQO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INK3VDHD3XLJENGUPVY66V7UQO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:INK3VDHD3XLJENGUPVY66V7UQO","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":"d42a19e7accf287663f4a6c7cdd00c8b06b20783a2bfa2cee1b3ddf76739830e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-21T21:36:42Z","title_canon_sha256":"aa20d3ad2ef0dd18c3de5ff4cd25f9bf6e4c3bd6573fe675573767c4ec619bff"},"schema_version":"1.0","source":{"id":"2404.13785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2404.13785","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"2404.13785v1","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.13785","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"INK3VDHD3XLJ","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"pith_short_16","alias_value":"INK3VDHD3XLJENGU","created_at":"2026-07-05T08:10:37Z"},{"alias_kind":"pith_short_8","alias_value":"INK3VDHD","created_at":"2026-07-05T08:10:37Z"}],"graph_snapshots":[{"event_id":"sha256:98be4e67f47701104583b0e57bd3751fd23de2c9f37b0afcd946ed3c1e6e8c4a","target":"graph","created_at":"2026-07-05T08:10:37Z","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/2404.13785/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Leverage score is a fundamental problem in machine learning and theoretical computer science. It has extensive applications in regression analysis, randomized algorithms, and neural network inversion. Despite leverage scores are widely used as a tool, in this paper, we study a novel problem, namely the inverting leverage score problem. We analyze to invert the leverage score distributions back to recover model parameters. Specifically, given a leverage score $\\sigma \\in \\mathbb{R}^n$, the matrix $A \\in \\mathbb{R}^{n \\times d}$, and the vector $b \\in \\mathbb{R}^n$, we analyze the non-convex opt","authors_text":"Junze Yin, Weixin Wang, Zhao Song, Zheng Yu, Zhihang Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-21T21:36:42Z","title":"How to Inverting the Leverage Score Distribution?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.13785","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":"sha256:6475405d484627778b595bc278e5a8d1e3e3591a06761e5b9a22572ae14b7fc1","target":"record","created_at":"2026-07-05T08:10:37Z","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":"d42a19e7accf287663f4a6c7cdd00c8b06b20783a2bfa2cee1b3ddf76739830e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.LG","submitted_at":"2024-04-21T21:36:42Z","title_canon_sha256":"aa20d3ad2ef0dd18c3de5ff4cd25f9bf6e4c3bd6573fe675573767c4ec619bff"},"schema_version":"1.0","source":{"id":"2404.13785","kind":"arxiv","version":1}},"canonical_sha256":"4355ba8ce3ddd69234d47d71ef57f483a33a8c9f9822559f1aae3494f9c937d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4355ba8ce3ddd69234d47d71ef57f483a33a8c9f9822559f1aae3494f9c937d8","first_computed_at":"2026-07-05T08:10:37.249994Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:10:37.249994Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dv0V+MlNcjNS1XbSnJQFn/EBeFeYMUEcF9m9islaYfyYVQdlXc9rBEbLRgltHvZaoTQCzh7gIfhnU6DgFo0ZDg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:10:37.250506Z","signed_message":"canonical_sha256_bytes"},"source_id":"2404.13785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6475405d484627778b595bc278e5a8d1e3e3591a06761e5b9a22572ae14b7fc1","sha256:98be4e67f47701104583b0e57bd3751fd23de2c9f37b0afcd946ed3c1e6e8c4a"],"state_sha256":"f95c345e59a4fa06bbc59b654cff5ae3625528f7086948dcfab8273558438ce7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlkk6Z7SJ5vSQs6oo2fg0vMK24wQKL/X8MAZPzDmys0R1xfgv22vvytlxe6fFHrYO8tx16oQ8gE1QR+BHCflDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T22:17:35.554435Z","bundle_sha256":"554b23f77c76607349db547cccb1a2ebbc9832e7a587c4ce12b512311207619a"}}