{"paper":{"title":"Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Yuto Sugimoto","submitted_at":"2026-02-09T18:34:21Z","abstract_excerpt":"We propose a forward-mode automatic differentiation (AD) framework for tensor renormalization group methods. In this approach, evaluating the derivatives of the partition function up to the order of $k$ increases the matrix-multiplication cost by a factor of $(k+1)(k+2)/2$ compared to computing the free energy alone, and the memory footprint is only $k+1$ times that of the original calculation. In the limit where the derivatives of the singular value decomposition are neglected, we establish a theoretical correspondence between our forward-mode AD and conventional impurity methods. Numerically"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.08987","kind":"arxiv","version":3},"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/2602.08987/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"}