{"paper":{"title":"Uncertainty Estimation via Hyperspherical Confidence Mapping","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Hyperspherical Confidence Mapping captures uncertainty as the violation of a unit hypersphere constraint on network outputs.","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Eunseo Choi, Heejin Ahn, Ho-Yeon Kim, Jaewon Lee, Myungjun lee, Taeyong jo","submitted_at":"2026-05-07T10:11:01Z","abstract_excerpt":"Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional assumptions, we propose Hyperspherical Confidence Mapping (HCM), a simple yet principled framework for sampling-free and distribution-free uncertainty estimation. HCM decomposes outputs into a magnitude and a normalized direction vector constrained to lie on the unit hypersphere, enabling a novel interpretation of uncertainty as the degree of violation of this"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches, with far lower inference cost and stronger confidence-error alignment.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That uncertainty can be reliably captured by the degree of violation of the unit-hypersphere constraint on the normalized direction vector, without needing distributional assumptions or sampling.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"HCM turns neural outputs into magnitude plus unit hypersphere vector and treats uncertainty as the geometric violation of that unit constraint, yielding deterministic estimates for regression and classification that match ensembles at lower cost.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Hyperspherical Confidence Mapping captures uncertainty as the violation of a unit hypersphere constraint on network outputs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"674d1d4d0de2ad91dc0b3b2a7d536d95a1c1ce829816388b4d6b244ff3091fc7"},"source":{"id":"2605.05964","kind":"arxiv","version":2},"verdict":{"id":"a8a2727e-be81-4290-8623-901c239f570d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-08T14:14:28.259951Z","strongest_claim":"Experiments across diverse benchmarks and real-world industrial tasks demonstrate that HCM matches or surpasses ensemble and evidential approaches, with far lower inference cost and stronger confidence-error alignment.","one_line_summary":"HCM turns neural outputs into magnitude plus unit hypersphere vector and treats uncertainty as the geometric violation of that unit constraint, yielding deterministic estimates for regression and classification that match ensembles at lower cost.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That uncertainty can be reliably captured by the degree of violation of the unit-hypersphere constraint on the normalized direction vector, without needing distributional assumptions or sampling.","pith_extraction_headline":"Hyperspherical Confidence Mapping captures uncertainty as the violation of a unit hypersphere constraint on network outputs."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.05964/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T13:22:04.384304Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-20T08:39:42.708292Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.299986Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T13:06:17.423283Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"1a65f049e5547ba056dc5aea0282aad102f39bdf285869c4098557d0d386a326"},"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"}