{"paper":{"title":"Radial Isotropic Position via an Implicit Newton's Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Arun Jambulapati, Jonathan Li, Kevin Tian","submitted_at":"2025-04-08T05:00:28Z","abstract_excerpt":"Placing a dataset $A = \\{\\mathbf{a}_i\\}_{i \\in [n]} \\subset \\mathbb{R}^d$ in radial isotropic position, i.e., finding an invertible $\\mathbf{R} \\in \\mathbb{R}^{d \\times d}$ such that the unit vectors $\\{(\\mathbf{R} \\mathbf{a}_i) \\|\\mathbf{R} \\mathbf{a}_i\\|_2^{-1}\\}_{i \\in [n]}$ are in isotropic position, is a powerful tool with applications in functional analysis, communication complexity, coding theory, and the design of learning algorithms. When the transformed dataset has a second moment matrix within a $\\exp(\\pm \\epsilon)$ factor of a multiple of $\\mathbf{I}_d$, we call $\\mathbf{R}$ an $\\e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.05687","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/2504.05687/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"}