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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

Chinese

我们建议KronLSTM,基于KroneckerDeltaRule的线性注意架构,是相关矩阵记忆的新更新规则。KronLSTM扩展了XLSTM家族,用一个记忆修订机制来纠正目标关联,同时在矩阵空间中仅在一个方向上修改记忆。这种最小程度的侵入性记忆修订减少了与以前存储的信息的干扰,而不是整个入口序列的更新,因此KronLSTM特别适合长期背景语言建模。由此产生的记忆动态可以数学上描述为一个马尔科夫链,它汇聚到稳定的状态分布中,而记忆矩阵的预期准则在整个输入序列中保持一致限制。因此,KronLSTM确保了稳定的记忆动态,而

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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