{"paper":{"title":"Computing k-means in mixed precision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Lloyd's k-means remains stable when distance computations drop to lower precision.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Erin Carson, Xiaobo Liu, Xinye Chen","submitted_at":"2024-07-16T22:48:35Z","abstract_excerpt":"Motivated by the increasing availability of low- and mixed-precision arithmetic on modern hardware, we develop mixed-precision variants of Lloyd's algorithm for k-means clustering. The main ingredient is a family of mixed-precision kernels for Euclidean distance computation. These kernels are guided by rounding-error analysis and use a simple reliability test to decide whether the expanded distance formula can be evaluated safely with low precision or a higher-precision correction by the direct distance formula is required. Thus, most distance computations can be carried out with low precision"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We confirm the stability of the widely used distance computation formula. We propose a mixed-precision framework for k-means computation and investigate the effects of low-precision distance computation within the framework. Through extensive simulations on various data clustering and image segmentation tasks, we verify the applicability and robustness of the mixed precision k-means method.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The simulations on the chosen datasets and tasks are representative of the numerical behavior that will occur in other k-means workloads; the paper does not provide a general proof that low-precision distance computation remains stable for arbitrary data distributions or cluster counts.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Mixed-precision Lloyd's k-means remains stable and effective for normalized data in clustering and image segmentation tasks, with care needed for unnormalized data to avoid overflow.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Lloyd's k-means remains stable when distance computations drop to lower precision.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"8d04226398625274e9377981d426770eb9761ee4ada44c981b8a934f50c5a71c"},"source":{"id":"2407.12208","kind":"arxiv","version":3},"verdict":{"id":"167991de-a756-4ab3-9378-af608c13f217","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T22:31:09.317633Z","strongest_claim":"We confirm the stability of the widely used distance computation formula. We propose a mixed-precision framework for k-means computation and investigate the effects of low-precision distance computation within the framework. Through extensive simulations on various data clustering and image segmentation tasks, we verify the applicability and robustness of the mixed precision k-means method.","one_line_summary":"Mixed-precision Lloyd's k-means remains stable and effective for normalized data in clustering and image segmentation tasks, with care needed for unnormalized data to avoid overflow.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The simulations on the chosen datasets and tasks are representative of the numerical behavior that will occur in other k-means workloads; the paper does not provide a general proof that low-precision distance computation remains stable for arbitrary data distributions or cluster counts.","pith_extraction_headline":"Lloyd's k-means remains stable when distance computations drop to lower precision."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.12208/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"}