Softmax-free Linear Transformers

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by stacked self-attention operations. Employing self-attention modules results in a quadratic complexity in both computation and memory usage. Various attempts on approximating the self-attention computation with linear complexity have thus been made in Natural Language Processing. However, an in-depth analysis in this work reveals that they are either theoretically flawed or empirically ineffective for visual recognition. We identify that their limitations are rooted in retaining the softmax self-attention during approximations. Specifically, conventional self-attention is computed by normalizing the scaled dot-product between token feature vectors. Preserving the softmax operation challenges any subsequent linearization efforts. Under this insight, a SOftmax-Free Transformer (abbreviated as SOFT) is proposed for the first time. To eliminate the softmax operator in self-attention, a Gaussian kernel function is adopted to replace the dot-product similarity. This enables a full self-attention matrix to be approximated via a low-rank matrix decomposition. The robustness of our approximation is achieved by calculating its Moore-Penrose inverse using a Newton-Raphson method. Further, an efficient symmetric normalization is introduced on the low-rank self-attention for enhancing model generalizability and transferability. Extensive experiments on ImageNet, COCO and ADE20K show that our SOFT significantly improves the computational efficiency of existing ViT variants. Crucially, with a linear complexity, much longer token sequences are permitted in SOFT, resulting in superior trade-off between accuracy and complexity.