{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O6N4HYW64P5RCWLBWCMPPN3I32","short_pith_number":"pith:O6N4HYW6","schema_version":"1.0","canonical_sha256":"779bc3e2dee3fb115961b098f7b768deadaea9d790fe3366d2c2a3e73f687cff","source":{"kind":"arxiv","id":"2509.01198","version":1},"attestation_state":"computed","paper":{"title":"Preserving Vector Space Properties in Dimensionality Reduction: A Relationship Preserving Loss Framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Alexander Kovalenko, Eddi Weinwurm","submitted_at":"2025-09-01T07:31:11Z","abstract_excerpt":"Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving Loss (RPL), a loss function that preserves these properties by minimizing discrepancies between relationship matrices (e.g., Gram or cosine) of high-dimensional data and their low-dimensional embeddings. RPL trains neural networks for non-linear projections and is supported by error bounds derived from matrix perturbation theory. Initial experiments suggest t"},"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":"2509.01198","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-09-01T07:31:11Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"89bf2c4531a848bad8be153e57ba0c2de039e8bcd0218de14fa982162222385e","abstract_canon_sha256":"7aea2d096b902d6f49aefd112464afc017b2d75e4ba7f8f4d18d89688d5f1bda"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:55.900170Z","signature_b64":"7crRUnHviH82JQmElXtS2nHm0ureXNQrquboRo8Vef2zidf9O24wk+ikcn0xdjrDCa1OuNMxLnoEortko0eTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"779bc3e2dee3fb115961b098f7b768deadaea9d790fe3366d2c2a3e73f687cff","last_reissued_at":"2026-07-05T12:02:55.899405Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:55.899405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Preserving Vector Space Properties in Dimensionality Reduction: A Relationship Preserving Loss Framework","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"cs.LG","authors_text":"Alexander Kovalenko, Eddi Weinwurm","submitted_at":"2025-09-01T07:31:11Z","abstract_excerpt":"Dimensionality reduction can distort vector space properties such as orthogonality and linear independence, which are critical for tasks including cross-modal retrieval, clustering, and classification. We propose a Relationship Preserving Loss (RPL), a loss function that preserves these properties by minimizing discrepancies between relationship matrices (e.g., Gram or cosine) of high-dimensional data and their low-dimensional embeddings. RPL trains neural networks for non-linear projections and is supported by error bounds derived from matrix perturbation theory. Initial experiments suggest t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01198","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/2509.01198/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":"2509.01198","created_at":"2026-07-05T12:02:55.899700+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.01198v1","created_at":"2026-07-05T12:02:55.899700+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01198","created_at":"2026-07-05T12:02:55.899700+00:00"},{"alias_kind":"pith_short_12","alias_value":"O6N4HYW64P5R","created_at":"2026-07-05T12:02:55.899700+00:00"},{"alias_kind":"pith_short_16","alias_value":"O6N4HYW64P5RCWLB","created_at":"2026-07-05T12:02:55.899700+00:00"},{"alias_kind":"pith_short_8","alias_value":"O6N4HYW6","created_at":"2026-07-05T12:02:55.899700+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32","json":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32.json","graph_json":"https://pith.science/api/pith-number/O6N4HYW64P5RCWLBWCMPPN3I32/graph.json","events_json":"https://pith.science/api/pith-number/O6N4HYW64P5RCWLBWCMPPN3I32/events.json","paper":"https://pith.science/paper/O6N4HYW6"},"agent_actions":{"view_html":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32","download_json":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32.json","view_paper":"https://pith.science/paper/O6N4HYW6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.01198&json=true","fetch_graph":"https://pith.science/api/pith-number/O6N4HYW64P5RCWLBWCMPPN3I32/graph.json","fetch_events":"https://pith.science/api/pith-number/O6N4HYW64P5RCWLBWCMPPN3I32/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32/action/storage_attestation","attest_author":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32/action/author_attestation","sign_citation":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32/action/citation_signature","submit_replication":"https://pith.science/pith/O6N4HYW64P5RCWLBWCMPPN3I32/action/replication_record"}},"created_at":"2026-07-05T12:02:55.899700+00:00","updated_at":"2026-07-05T12:02:55.899700+00:00"}