{"paper":{"title":"On the Injective Norm of Sums of Random Tensors and the Moments of Gaussian Chaoses","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Ishaq Aden-Ali","submitted_at":"2025-03-13T17:31:51Z","abstract_excerpt":"We prove an upper bound on the expected $\\ell_p$ injective norm of sums of subgaussian random tensors. Our proof is simple and does not rely on any explicit geometric or chaining arguments. Instead, it follows from a simple application of the PAC-Bayesian lemma, a tool that has proven effective at controlling the suprema of certain ``smooth'' empirical processes in recent years. Our bound strictly improves a very recent result of Bandeira, Gopi, Jiang, Lucca, and Rothvoss. In the Euclidean case ($p=2$), our bound sharpens a result of Lata{\\l}a that was central to proving his estimates on the m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.10580","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/2503.10580/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"}