SymFP：用等变表示的奇异值谱识别结构对称性
Spectral symmetry fingerprints in equivariant representations
几何深度学习论文把等变GNN的秩限制反着用，用奇异值谱给分子、蛋白复合物做点群识别，还能追踪对称性破缺，做结构分析的朋友可以看看。
arXiv 论文提出 Spectral symmetry fingerprints（SymFP），利用等变图神经网络（GNN）表示的奇异值谱作为结构对称性指纹。该方法通过秩模板匹配实现离散点群识别，并通过量化超出目标秩约束的谱能量来分析连续对称性破缺。SymFP 具有方向不变性和架构无关性，可构建无参数的 GNN 实现，其谱可跨多个目标群复用。在合成结构、分子、配位化合物和大型生物组装体等数据上，SymFP 能准确识别点群并追踪受控的对称性破缺，还可揭示被全局几何度量掩盖的局部与按度分辨的对称性变化。
Spectral symmetry fingerprints in equivariant representations
Symmetry governs the organization of physical structures, while symmetry breaking reveals their transformations. In geometric deep learning, symmetry imposes rank constraints on equivariant representations, limiting the expressive capacity of equivariant graph neural networks (GNNs). Here we show that these constraints can instead be exploited: the singular-value spectra of equivariant representations provide a unified fingerprint of structural symmetry. We introduce spectral symmetry fingerprints (SymFP), which enable discrete point-group identification through rank-template matching and continuous symmetry analysis by quantifying spectral energy beyond target rank constraints. SymFP is orientation invariant and architecture agnostic, enabling a parameter-free GNN implementation. Its spectra can be reused across multiple target groups, and the resulting leakage scores satisfy subgroup monotonicity. Across synthetic structures, molecules, coordination complexes and large biological assemblies, SymFP accurately identifies point groups, tracks controlled symmetry breaking and reveals local and degree-resolved symmetry changes that can be obscured by global geometric measures. These results establish the spectral structure of equivariant representations as a general framework for characterizing symmetry across physical systems.