基于注意力机制的神经网络用于采样二维 XY 模型
Sampling the XY model with an attention-based neural network
物理学家把 transformer 改造成统计力学采样器，96×96 格点的 XY 模型都能跑，还验证了不漏构型，做计算物理的可以看看。
研究团队提出一种基于 transformer 的变分自回归网络，用于采样具有连续自由度的格点系统，并以二维 XY 模型为对象，聚焦 Berezinskii-Kosterlitz-Thouless 相变附近区域。架构中引入了 locality-informed attention 和近似概率等物理先验成分。模型在最大 96×96 的格点上训练，通过 mode-dropping 估计器验证没有遗漏构型空间的任何区域。采样结果复现了传统马尔可夫链蒙特卡洛方法得到的能量、磁化和螺旋模量，性能显著超过现有神经采样器。
Sampling the XY model with an attention-based neural network
We present a transformer-based variational autoregressive network for sampling lattice systems with continuous degrees of freedom and apply it to the two-dimensional XY model near the Berezinskii-Kosterlitz-Thouless transition. The architecture is combined with physics-informed ingredients: locality-informed attention and approximate probabilities. The resulting sampler significantly outperforms existing neural samplers. We train the model on lattices up to $96\times96$, verify with a mode-dropping estimator that no parts of the configuration space are missed, and reproduce the energy, magnetization and helicity modulus obtained with the traditional Markov Chain Monte Carlo algorithm.
