{"paper":{"title":"Total Variation Distance Estimation in Autoregressive Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","stat.ME","stat.ML"],"primary_cat":"cs.LG","authors_text":"Eric Price, Kevin Tian, Yusong Zhu, Zhiyang Xun","submitted_at":"2026-07-21T18:49:45Z","abstract_excerpt":"Modern LLM deployments use a number of implementation choices and inference optimizations (e.g., batching, custom kernels, and quantization) on top of fixed weights, so two engines serving \"the same model\" can produce meaningfully different distributions. We study the problem of estimating the total variation (TV) distance between two length-$n$ autoregressive distributions to additive error $\\varepsilon$, under three access models. (1) Under sample access, we use $\\widetilde{O}(n^2 K/\\varepsilon^2)$ queries, where $K$ is the maximum support of the next-token distribution. This improves upon t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19510","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/2607.19510/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"}