The Mamba layer offers an efficient selective state-space model (SSM) that is highly effective in modeling multiple domains, includingNLP, long-range sequence processing, and computer vision. Selective SSMs are viewed as dual models, in which one trains in parallel on the entire sequence via an IO-aware parallel scan, and deploys in an autoregressive manner. We add a third view and show that such models can be viewed as attention-driven models. This new perspective enables us to empirically and theoretically compare the underlying mechanisms to that of the attention in transformers and allows us to peer inside the inner workings of the Mamba model with explainability methods. Our code is publicly available.

We present a new layer in which dynamic (i.e., input-dependent) Infinite Impulse Response (IIR) filters of order two are used to process the input sequence prior to applying conventional attention. The input is split into chunks, and the coefficients of these filters are determined based on previous chunks to maintain causality. Despite their relatively low order, the causal adaptive filters are shown to focus attention on the relevant sequence elements. The new layer is grounded in control theory, and is shown to generalize diagonal state-space layers. The layer performs on-par with state-of-the-art networks, with a fraction of their parameters and with time complexity that is sub-quadratic with input size. The obtained layer is favorable to layers such as Heyna, GPT2, and Mega, both with respect to the number of parameters and the obtained level of performance on multiple long-range sequence problems.