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[Submitted on 22 Sep 2026] Title:Marginally Correct Tool Caches Can Reverse Group-Normalized Policy Updates View a PDF of the paper titled Marginally Correct Tool Caches Can Reverse Group-Normalized Policy Updates, by Shivam Gupta View PDF HTML (experimental) Abstract:Tool-result caching reduces repeated execution in agent training, but also couples rollout randomness. We study a two-action model in which independent and shared execution preserve every rollout's conditional reward distribution. Despite this marginal agreement, sharing one stochastic result per group can reverse the expected group-normalized policy update. We derive an exact finite-group expression: against a constant alternative, the shared update follows the probability of winning minus the probability of losing, rather than the difference in expected reward. A Bernoulli specialization yields a wrong-direction region and a non-vanishing update-variance floor as group size grows. Centering without group standard-deviation scaling preserves the expected-return direction in this model, using an existing estimator control. Exhaustive finite sums verify 540 configurations and 3,240 estimator evaluations, with a separate ordered-sequence checker. An implementation audit reproduces the sharing path in a pinned, unmodified TVCache stack using 256 scripted rollouts. These results do not measure language-model training performance or refute TVCache's deterministic-output contract. They establish that marginal output validity alone cannot certify a stochastic cache as training-equivalent. Comments: 8 pages, 1 figure, 2 tables. Code and reproducibility materials: this https URL Subjects: Machine Learning (cs.LG) Cite as: arXiv:2609.26866 [cs.LG] (or arXiv:2609.26866v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.26866 arXiv-issued DOI via DataCite Submission history From: Shivam Gupta [view email] [v1] Tue, 22 Sep 2026 16:15:47 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Marginally Correct Tool Caches Can Reverse Group-Normalized Policy Updates, by Shivam Gupta View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) IArxiv recommender toggle IArxiv Recommender (What is IArxiv?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)