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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

Portuguese

Nós propomos KronLSTM, uma arquitetura de atenção linear baseada na Regra do Delta de Kronecker, uma nova regra de atualização para memórias de matriz associativa. KronLSTM estende a família xLSTM com um mecanismo de revisão de memória que corrige associações direcionadas, ao mesmo tempo que modifica a memória apenas em uma direção única no espaço de matriz. Esta revisão de memória minimamente invasiva reduz a interferência com informações previamente armazenadas em comparação com as atualizações de regra do delta, tornando-a particularmente adequada para modelagem de linguagem de longo contexto. A dinâmica de memória resultante pode ser matematicamente descrita como uma cadeia de Markov que converge para uma distribuição de estado estável, enquanto a norma esperada da matriz de memória permanece

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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