宇宙学研究者终于有了一个能处理观测数据破缺对称性的AI工具——Velocityformer在速度重建上比线性理论提升35%，且数据效率极高，做kSZ效应测量的团队可以直接用。
Velocityformer是一种等变图Transformer架构，专门用于从光谱巡天数据中重建星系速度，以提升运动学SZ效应的测量信噪比。该模型通过匹配观测数据中因视线方向导致的破缺对称性，在归纳偏置上优于标准线性理论基线，将速度重建相关系数r提升35%。Velocityformer在仅4个低保真模拟上即可训练到高精度，并能零样本泛化到不同输入几何、宇宙学参数和星系样本。在高保真模拟星系目录上，该模型将r提升30%，直接转化为观测数据上相同的信噪比增益。
Velocityformer: Broken-Symmetry-Matched Equivariant Graph Transformers for Cosmological Velocity Reconstruction
Precise measurement of the kinematic Sunyaev-Zel'dovich (kSZ) effect - a probe of the large-scale distribution of baryonic matter, a key observable for cosmological inference - requires accurate reconstruction of galaxy velocities from spectroscopic surveys. The signal-to-noise ratio (SNR) of kSZ measurements scales directly with the correlation coefficient $r$ between reconstructed and true velocities. We introduce Velocityformer, an equivariant graph transformer architecture designed to match the specific symmetry of the observational data. While the underlying physics is equivariant with respect to translations and rotations, observational effects break this symmetry due to the preferred line-of-sight direction. Matching the model's inductive bias to the data's broken symmetry consistently improves performance across all model sizes and training volumes, with Velocityformer improving $r$ by 35% over the standard linear theory baseline and outperforming ML baselines at every data volume. By matching the model's inductive bias to the data and conditioning on the physics-based long-wavelength solution, Velocityformer is highly data-efficient, training to high accuracy on as few as 4 low-fidelity simulations, and generalises zero-shot across input geometry, cosmological parameters, and galaxy sample. On high-fidelity simulated galaxy catalogues, this yields a 30% improvement in $r$ over the physical baseline, directly translating to the same SNR gain on observational data.