SOFT: Softmax-free Transformer with Linear Complexity

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention. Various attempts on approximating the self-attention computation with linear complexity have been made in Natural Language Processing. However, an in-depth analysis in this work shows that they are either theoretically flawed or empirically ineffective for visual recognition. We further identify that their limitations are rooted in keeping the softmax self-attention during approximations. Specifically, conventional self-attention is computed by normalizing the scaled dot-product between token feature vectors.