Title: Transformers with Multiresolution Attention Heads. Abstract: We propose the Transformer with Multiresolution-head Attention (MrsFormer), a class of efficient transformers inspired by the multiresolution approximation (MRA) for approximating a signal f using wavelet bases. MRA decomposes a signal into components that lie on orthogonal subspaces at different scales. Similarly, MrsFormer decomposes the attention heads in the multi-head attention into fine-scale and coarse-scale heads, modeling the attention patterns between tokens and between groups of tokens. Computing the attention heads in MrsFormer requires significantly less computation and memory footprint compared to the standard softmax transformer with multi-head attention. We analyze and validate the advantage of MrsFormer over the standard transformers on a wide range of applications including image and time series classification.