In light of the advancements in transformer technology, extant research posits the construction of stereo transformers as a potential solution to the binocular stereo matching challenge. However, constrained by the low-rank bottleneck and quadratic complexity of attention mechanisms, stereo transformers still fail to demonstrate sufficient nonlinear expressiveness within a reasonable inference time. The lack of focus on key homonymous points renders the representations of such methods vulnerable to challenging conditions, including reflections and weak textures. Furthermore, a slow computing speed is not conducive to the application. To overcome these difficulties, we present the \textbf{H}adamard \textbf{A}ttention \textbf{R}ecurrent Stereo \textbf{T}ransformer (HART) that incorporates the following components: 1) For faster inference, we present a Hadamard product paradigm for the attention mechanism, achieving linear computational complexity. 2) We designed a Dense Attention Kernel (DAK) to amplify the differences between relevant and irrelevant feature responses. This allows HART to focus on important details. DAK also converts zero elements to non-zero elements to mitigate the reduced expressiveness caused by the low-rank bottleneck. 3) To compensate for the spatial and channel interaction missing in the Hadamard product, we propose MKOI to capture both global and local information through the interleaving of large and small kernel convolutions. Experimental results demonstrate the effectiveness of our HART. In reflective area, HART ranked \textbf{1st} on the KITTI 2012 benchmark among all published methods at the time of submission. Code is available at \url{https://github.com/ZYangChen/HART}.

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