{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:2BL5XNLHSENUNDGK46LXJTG7W7","short_pith_number":"pith:2BL5XNLH","schema_version":"1.0","canonical_sha256":"d057dbb567911b468ccae79774ccdfb7c2ff0c4f4faf8c4cd076ec2ae01cb888","source":{"kind":"arxiv","id":"2401.17675","version":1},"attestation_state":"computed","paper":{"title":"Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"stat.ML","authors_text":"Hau-Tieng Wu, Seonghyeon Jeong","submitted_at":"2024-01-31T08:52:45Z","abstract_excerpt":"We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely resemble the original data points in a high-dimensional space, minimizing KL divergence. Investigating t-SNE properties such as perplexity and affinity under a weak convergence assumption on the sampled dataset, we examine the behavior of points generated by t-SNE under continuous gradient flow. Demonstrating that points generated by t-SNE remain bounded, we"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2401.17675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2024-01-31T08:52:45Z","cross_cats_sorted":["cs.DS","cs.LG"],"title_canon_sha256":"e32eec5032e1a4eb35f832ba6d8c14f7742a159b9f9faba9d423de6036e84eb9","abstract_canon_sha256":"4e9acde55d3b8f0a2f67534687b7e78030054b8e270f2a819b4406047180e82e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:39:40.420884Z","signature_b64":"nSxFqFOUnB+soaKORqpzFsvDlaKPmqE200hAm4zcDn5AqxHpeomPPF8In2Q1Yap5RSrv5qKIcs6XqTzp5QGJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d057dbb567911b468ccae79774ccdfb7c2ff0c4f4faf8c4cd076ec2ae01cb888","last_reissued_at":"2026-07-05T07:39:40.420432Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:39:40.420432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG"],"primary_cat":"stat.ML","authors_text":"Hau-Tieng Wu, Seonghyeon Jeong","submitted_at":"2024-01-31T08:52:45Z","abstract_excerpt":"We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely resemble the original data points in a high-dimensional space, minimizing KL divergence. Investigating t-SNE properties such as perplexity and affinity under a weak convergence assumption on the sampled dataset, we examine the behavior of points generated by t-SNE under continuous gradient flow. Demonstrating that points generated by t-SNE remain bounded, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.17675","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/2401.17675/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2401.17675","created_at":"2026-07-05T07:39:40.420488+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.17675v1","created_at":"2026-07-05T07:39:40.420488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.17675","created_at":"2026-07-05T07:39:40.420488+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BL5XNLHSENU","created_at":"2026-07-05T07:39:40.420488+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BL5XNLHSENUNDGK","created_at":"2026-07-05T07:39:40.420488+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BL5XNLH","created_at":"2026-07-05T07:39:40.420488+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.12041","citing_title":"On the continuum limit of t-SNE for data visualization","ref_index":25,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7","json":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7.json","graph_json":"https://pith.science/api/pith-number/2BL5XNLHSENUNDGK46LXJTG7W7/graph.json","events_json":"https://pith.science/api/pith-number/2BL5XNLHSENUNDGK46LXJTG7W7/events.json","paper":"https://pith.science/paper/2BL5XNLH"},"agent_actions":{"view_html":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7","download_json":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7.json","view_paper":"https://pith.science/paper/2BL5XNLH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.17675&json=true","fetch_graph":"https://pith.science/api/pith-number/2BL5XNLHSENUNDGK46LXJTG7W7/graph.json","fetch_events":"https://pith.science/api/pith-number/2BL5XNLHSENUNDGK46LXJTG7W7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7/action/storage_attestation","attest_author":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7/action/author_attestation","sign_citation":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7/action/citation_signature","submit_replication":"https://pith.science/pith/2BL5XNLHSENUNDGK46LXJTG7W7/action/replication_record"}},"created_at":"2026-07-05T07:39:40.420488+00:00","updated_at":"2026-07-05T07:39:40.420488+00:00"}