这篇论文指出了线性注意力在图去噪上的根本局限，并提出 GCA 来补上短板。在 DiGress 上效果持平标准 Transformer 还省了结构特征计算，挺实用的。
本文提出 Graph Convolutional Attention (GCA)，一种利用输入图谱实现谱去噪的注意力机制。理论证明线性注意力在去噪任务中只能学习平均谱滤波器，而 GCA 通过图滤波查询和键可自适应处理谱多样性。在随机块模型上，GCA 与理想化的 Spectral Attention 机制性能匹配。在 DiGress 模型中，GCA 无需计算昂贵的结构特征即可达到标准图 Transformer 的效果，结合 PEARL 位置编码还能避免显式特征分解，加速推理。实验表明 GCA 在合成和真实数据集上持续提升去噪与扩散性能，增益与谱多样性正相关。
Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion
Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att