{"slug": "the-output-space-hypothesis-enumerative-equivalence-checking-for-tensor-programs", "title": "The Output-Space Hypothesis:Enumerative Equivalence Checking for Tensor Programs", "summary": "A September 17, 2026 arXiv paper proposes the Output-Space Hypothesis, an enumerative equivalence-checking approach implemented in a system called Dirigo that flips the standard quantifier order to check a single output tensor location across all inputs via symbolic execution. Tested on a public dataset of 6,988 AI-written CUDA kernels all marked correct by differential testing, Dirigo identified 600 kernels that are actually buggy, finding 97.3% of those bugs within two minutes. The result matters because differential testing on random tensor inputs can miss subtle optimization bugs that require extremely low-likelihood input relationships.", "body_md": "# Computer Science > Programming Languages\n\n  [Submitted on 17 Sep 2026]\n\n# Title:The Output-Space Hypothesis: Enumerative Equivalence Checking for Tensor Programs\n\n[View PDF](https://arxiv.org/pdf/2609.19611)\n\n[HTML (experimental)](https://arxiv.org/html/2609.19611v1)\n\nAbstract:Tensor programs, as used in deep learning models, are a prime target for optimization, as small performance improvements can have a large impact across training or inference workloads. However, such optimizations are complicated and can produce subtle bugs. Traditionally, correctness is assumed when differential testing against a reference on random inputs fails to reveal bugs. However, the inputs to these programs are massive tensors, and finding bugs can require generating extremely low likelihood inputs with precise relationships among their values.\n\nWe propose a novel way to find bugs more consistently by flipping the quantifiers. Rather than generating a single input and checking all output tensor locations for equivalence, what if you could check a single output tensor location's equivalence for all inputs? We implement this idea in a system, \\dirigo, by using a novel symbolic execution strategy. We demonstrate that \\dirigo can find bugs effectively in a public dataset of 6,988 AI-written CUDA kernels that are all marked correct by differential testing. Of these, \\dirigo finds 600 kernels that are actually buggy, and finds 97.3\\% of those bugs within two minutes.\n\n### Current browse context:\n\ncs.PL\n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer \n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers \n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps \n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations \n\n*(*[What are Smart Citations?](https://www.scite.ai/))\n# Code, Data and Media Associated with this Article\n\nalphaXiv \n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers \n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub \n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub \n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face \n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast \n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))\n# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower \n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender \n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\n# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth 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.\n\nHave an idea for a project that will add value for arXiv's community? [**Learn more about arXivLabs**](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/the-output-space-hypothesis-enumerative-equivalence-checking-for-tensor-programs", "canonical_source": "https://arxiv.org/abs/2609.19611", "published_at": "2026-10-05 23:28:14+00:00", "updated_at": "2026-10-05 23:48:51.052575+00:00", "lang": "en", "topics": ["ai-research", "machine-learning", "artificial-intelligence", "developer-tools"], "entities": ["Dirigo", "arXiv", "CUDA"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/the-output-space-hypothesis-enumerative-equivalence-checking-for-tensor-programs", "markdown": "https://wpnews.pro/news/the-output-space-hypothesis-enumerative-equivalence-checking-for-tensor-programs.md", "text": "https://wpnews.pro/news/the-output-space-hypothesis-enumerative-equivalence-checking-for-tensor-programs.txt", "jsonld": "https://wpnews.pro/news/the-output-space-hypothesis-enumerative-equivalence-checking-for-tensor-programs.jsonld"}}