Kronecker Delta Rule for Long Context Linear Attention

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.

Computer Science Machine Learning Submitted on 19 Oct 2026 Title:Kronecker Delta Rule for Long Context Linear Attention View PDF https://arxiv.org/pdf/2610.26834 HTML experimental https://arxiv.org/html/2610.26834v1 Abstract: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. Submission history From: Anamaria-Roberta Hartl view email https://arxiv.org/show-email/4f3da3db/2610.26834 v1 Mon, 19 Oct 2026 17:56:52 UTC 267 KB Additional Features References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer What is the Explorer? https://info.arxiv.org/labs/showcase.html arxiv-bibliographic-explorer Connected Papers What is Connected Papers? https://www.connectedpapers.com/about Litmaps What is Litmaps? https://www.litmaps.co/ scite Smart Citations What are Smart Citations? https://www.scite.ai/ Code, Data and Media Associated with this Article alphaXiv What is alphaXiv? https://alphaxiv.org/ CatalyzeX Code Finder for Papers What is CatalyzeX? https://www.catalyzex.com DagsHub What is DagsHub? https://dagshub.com/ Gotit.pub What is GotitPub? http://gotit.pub/faq Hugging Face What is Huggingface? https://huggingface.co/huggingface ScienceCast What is ScienceCast? https://sciencecast.org/welcome Demos Recommenders and Search Tools Influence Flower What are Influence Flowers? https://influencemap.cmlab.dev/ CORE Recommender What is CORE? https://core.ac.uk/services/recommender IArxiv Recommender What is IArxiv? https://iarxiv.org/about 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 https://info.arxiv.org/labs/index.html .