Newest papers

Kronecker Delta Rule for Long Context Linear Attention

Anamaria-Roberta Hartl, Levente Zólyomi, Michael List, Gnter Klambauer, Sebastian Böck, Sepp Hochreiter · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26834 · cited by 0 works (OpenAlex) · open-access PDF

Arabic

ونحن نقدم KronLSTM ، وهي فروع الاهتمام الصلب التي تعتمد على قاعدة Kronecker Delta Rule ، وهي قاعدة التحديث الجديد لذكريات القاعدة المشتركة. KronLSTM توسيع الأسرة xLSTM مع ميكانيكية تعديل الذاكرة التي تحقق التعاونات الهدفية مع تعديل الذاكرة فقط في اتجاه واحد في مساحة القاعدة. هذا تعديل الذاكرة الارهابية الحد الأدنى يقلل من التداخلات مع المعلومات المتوفرة سابقا مقارنة مع تحديثات القاعدة القابلة للتعديل ، مما يجعل KronLSTM مثاليًا لتعديل اللغات المشتركة دون الحاجة إلى ميكانيكية الذاكرة المشتركة المرتبطة بالذاكرة. يمكن وصف التعديلات الدماغية المرتبطة

Machine translation (Meta M2M100); the English original follows.

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 (https://github.com/NX-AI/KronLSTM) and models (https://huggingface.co/collections/NX-AI/kronlstm) are open-source.

Read in: English · Spanish · Chinese · Hindi · Arabic · Portuguese · French · German · Japanese · Russian · Korean · Indonesian · Vietnamese

Topics: Markov chain, Computer science, Kronecker product, Associative property, Kronecker delta, Theoretical computer science

Sources: OpenAlex (CC0), arXiv, Crossref. Agent Exchange