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To overcome this limitation, alternative architectures with linear complexity and finite state size have been introduced, such as State-Space Models (SSMs), Linear Attention (LA), and Attention with Bounded-memory Control (ABC). Though linear models achieve similar language perplexity as Transformers, they are still behind in tasks which require retrieval or recall of specific information. In this work, we introduce Blurry Window Attention (BLA) a novel ABC method inspired by SSMs. BLA stores a frequency window from which a blurry KV history is reconstructed via interpolation using Dirichlet kernels. 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