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[Submitted on 12 Aug 2026] Title:Diagnosing Faults in Reinforcement Learning Simulators and World Models with Canonical Polynomial Invariants View a PDF of the paper titled Diagnosing Faults in Reinforcement Learning Simulators and World Models with Canonical Polynomial Invariants, by Tesfay Zemuy Gebrekidan and 1 other authors View PDF HTML (experimental) Abstract:A large literature builds physical structure into learned dynamics on the premise that models respecting the underlying physics predict better. We test that premise using exact polynomial invariants recovered from trajectories and canonicalised as reduced Gröbner bases over $\mathbb{Q}$. On Acrobot, exactness provides little benefit for prediction: a consistency regulariser reduces algebraic residual while leaving rollout fidelity essentially unchanged, and a shaping potential recovered from a system with a 100% mass error accelerates learning as effectively as the correct potential. Exact canonical invariants instead prove valuable for diagnosis. We develop two procedures: screening, which identifies the violated physical constraint, and attribution, which recovers the faulty invariant and identifies the responsible physical parameter. To enable this, we introduce normal-form deflation and quotient-space recovery. Across fifteen injected faults, screening localises every broken constraint with no false alarms, whereas observation-space baselines do not localise any; attribution recovers the responsible parameter on all seven parameter faults. Paired difference tests detect all faults, showing that the advantage is localisation rather than detection. Perturbing reference generators by $10^{-4}$ preserves 14--15/15 localisations, showing that screening does not require exactness, whereas ideal-equality decisions distinguish perturbations of only $10^{-12}$, showing that exactness is required for algebraic comparison. Applied to 350 release pairs across eleven RL environments, the diagnostic finds no evidence of changed simulator dynamics, instead revealing properties of the benchmark implementations themselves. Comments: 9 pages with 4 figures, 2 tables and supplementary file Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI) Cite as: arXiv:2609.13194 [cs.LG] (or arXiv:2609.13194v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2609.13194 arXiv-issued DOI via DataCite Submission history From: Hadush Hailu Gebrerufael Mr. [view email] [v1] Wed, 12 Aug 2026 15:28:11 UTC (330 KB) Full-text links: Access Paper: View a PDF of the paper titled Diagnosing Faults in Reinforcement Learning Simulators and World Models with Canonical Polynomial Invariants, by Tesfay Zemuy Gebrekidan and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG new | recent | 2026-09 Change to browse by: cs cs.AI 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?)