{"slug": "kronecker-delta-rule-for-long-context-linear-attention", "title": "Kronecker Delta Rule for Long Context Linear Attention", "summary": "Researchers submitted a paper to arXiv on 19 October 2026 proposing KronLSTM, a linear attention architecture built on a new update rule called the Kronecker Delta Rule for associative matrix memories. KronLSTM extends the xLSTM family with a memory-revision mechanism that corrects targeted associations along a single direction in matrix space, which the authors say reduces interference with stored information and keeps the expected norm of the memory matrix uniformly bounded without extra normalization. The authors report KronLSTM is competitive with and often outperforms existing linear attention architectures including the (Gated) DeltaNet family, with particularly strong results on long-context benchmarks, and released code on GitHub and models on Hugging Face as open source.", "body_md": "# Computer Science > Machine Learning\n\n  [Submitted on 19 Oct 2026]\n\n# Title:Kronecker Delta Rule for Long Context Linear Attention\n\n[View PDF](https://arxiv.org/pdf/2610.26834)\n\n[HTML (experimental)](https://arxiv.org/html/2610.26834v1)\n\nAbstract:We propose KronLSTM, a linear attention architecture based on the Kronecker Delta Rule, a novel update rule for associative matrix memories. KronLSTM extends the xLSTM family with a memory-revision mechanism that corrects targeted associations while modifying the memory only along a single direction in matrix space. This minimally invasive memory revision reduces interference with previously stored information compared with delta-rule updates, making it particularly well suited for long-context language modeling. The resulting memory dynamics can be mathematically described as a Markov chain that converges to a steady-state distribution, while the expected norm of the memory matrix remains uniformly bounded throughout the entire input sequence. Hence, KronLSTM ensures stable memory dynamics without requiring additional normalization and stabilization mechanisms for the memory state. Experiments show that KronLSTM is competitive with, and often outperforms, existing linear attention architectures, including models of the (Gated) DeltaNet family, with particularly strong performance on long context benchmarks. These results establish the Kronecker Delta Rule as an effective and analytically tractable foundation for stable associative memory in recurrent linear attention architectures. Our code ([this https URL](https://github.com/NX-AI/KronLSTM)) and models ([this https URL](https://huggingface.co/collections/NX-AI/kronlstm)) are open-source.\n    \n\n## Submission history\n\nFrom: Anamaria-Roberta Hartl [\n[view email](https://arxiv.org/show-email/4f3da3db/2610.26834)]\n\n**[v1]** Mon, 19 Oct 2026 17:56:52 UTC (267 KB)\n\n### Additional Features\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))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))\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/kronecker-delta-rule-for-long-context-linear-attention", "canonical_source": "https://arxiv.org/abs/2610.26834", "published_at": "2026-10-20 13:06:20+00:00", "updated_at": "2026-10-20 13:17:36.762394+00:00", "lang": "en", "topics": ["machine-learning", "large-language-models", "ai-research", "natural-language-processing"], "entities": ["KronLSTM", "Kronecker Delta Rule", "xLSTM", "DeltaNet", "arXiv", "Anamaria-Roberta Hartl", "NX-AI", "Hugging Face"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/kronecker-delta-rule-for-long-context-linear-attention", "markdown": "https://wpnews.pro/news/kronecker-delta-rule-for-long-context-linear-attention.md", "text": "https://wpnews.pro/news/kronecker-delta-rule-for-long-context-linear-attention.txt", "jsonld": "https://wpnews.pro/news/kronecker-delta-rule-for-long-context-linear-attention.jsonld"}}