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[Submitted on 18 Oct 2026] Title:Transformers Learn Two Competing Sorting Algorithms, and Only One Length-Generalizes View a PDF of the paper titled Transformers Learn Two Competing Sorting Algorithms, and Only One Length-Generalizes, by Khashayar Gatmiry and 7 other authors View PDF HTML (experimental) Abstract:We show that two-layer transformers trained to near-zero loss on a sorting task converge to one of two mechanistically distinct solution classes depending on their initialization. One solution class consists of solutions that do not use the second attention layer to sort, but also fail to length-generalize. The other, which uses both attention layers, length-generalizes perfectly, despite only being trained to sort sequences of a fixed length. By carefully choosing the weight initialization, we demonstrate that we can steer the model toward learning one solution or the other. We identify input types that are rare at the training length but increasingly common at longer sequence lengths as a source of this disparity in length-generalization, and find that layer-wise specialization of the second class of solutions allows them to handle these rare sequences more accurately. In the second class, we discover a mechanism by which the second layer attention can use the contextual information gathered by the first layer attention to reduce its search space. On the related task of finding the minimum of a sequence, we find a similar two solution-type phenomenon, but with the opposite generalization pattern, where a different form of layer-wise specialization causes the two-layer solution to length-generalize worse than the single-attention solution. Subjects: Machine Learning (cs.LG); Computation and Language (cs.CL) Cite as: arXiv:2610.26974 [cs.LG] (or arXiv:2610.26974v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2610.26974 arXiv-issued DOI via DataCite Submission history From: Huangyuan Su [view email] [v1] Sun, 18 Oct 2026 20:21:16 UTC (21,550 KB) Full-text links: Access Paper: View a PDF of the paper titled Transformers Learn Two Competing Sorting Algorithms, and Only One Length-Generalizes, by Khashayar Gatmiry and 7 other authors View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.LG new | recent | 2026-10 Change to browse by: cs cs.CL References & Citations SciX 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?)