{"paper":{"title":"Between-User Collapse Under Popularity-Biased Feedback: A Centered-Covariance Theorem and Computable Phase Boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.IR","authors_text":"Sahil Medepalli","submitted_at":"2026-08-03T17:33:25Z","abstract_excerpt":"We study how popularity-biased BPR training reshapes the between-user geometry of collaborative-filtering embeddings. We work with the mean-centered user covariance $C=\\tfrac1n U^\\top H U$, the object that measures how distinguishable users are from one another, as opposed to the uncentered second moment used in prior work. We prove that under popularity-biased feedback with stationary items, $C$ converges to a steady state proportional to the item-noise covariance $Q$. Thus between-user spread collapses toward a noise floor. We derive a closed-form, computable phase boundary in the training h"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.02548","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/2608.02548/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"}