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.

提出 SOftmax-Free Transformer (SOFT)，其采用高斯核函数替代点积相似度，从而能够通过低秩矩阵分解逼近完整的自注意力矩阵，该模型能够明显提高现有 ViT 变体的计算效率，同时具有线性复杂度，且能够容纳更长的令牌序列，优化了准确率和复杂度之间的权衡。

无 Softmax 的线性变换器

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
self-attention. However, the employment of 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 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. Keeping this softmax operation challenges any
subsequent linearization efforts. Based on this insight, for the first time, a
softmax-free transformer or SOFT is proposed. To remove softmax in
self-attention, Gaussian kernel function is used to replace the dot-product
similarity without further normalization. This enables a full self-attention
matrix to be approximated via a low-rank matrix decomposition. The robustness
of the approximation is achieved by calculating its Moore-Penrose inverse using
a Newton-Raphson method. Extensive experiments on ImageNet 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.

提出了一种 softmax-free transformer 或 SOFT 方法，通过使用高斯内核函数替换点积相似性，而不需要标准化以消除 softmax，在计算复杂度上具有线性复杂度，并显著提高了已有 ViT 变种的计算效率。