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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

Hindi

हम KronLSTM, एक लाइनर ध्यान आर्किटेक्चर के आधार पर Kronecker डेल्टा नियम, एसोसिएटिव मैट्रिक्स मेमोरी के लिए एक नए अद्यतन नियम की सिफारिश करते हैं. KronLSTM एक मेमोरी-रेडिशन तंत्र के साथ xLSTM परिवार का विस्तार करता है जो लक्षित संबंधों को सही करता है जबकि मैट्रिक्स अंतरिक्ष में केवल एक दिशा में मेमोरी को संशोधित करता है. यह न्यूनतम आक्रामक मेमोरी संशोधन पहले संग्रहीत जानकारी के साथ हस्तक्षेप को डेल्टा-रेडिक्स अद्यतन की तुलना में कम करता है, जिससे यह विशेष रूप से लंबी संदर्भ भाषा मॉडलिंग के लिए उपयुक्त है. परिणामस्वरूप मेमोरी गतिशीलता गणितीय रूप से एक

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.

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

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