AI 中文总结
研究二维哈伯德模型中Transformer回流神经量子态的优化动力学，基于多阶段训练工作流程，通过改变更新范数阈值等超参数，研究其对收敛的影响，确定了实际优化趋势，突出了假设表达能力等方面的平衡。
AI 中文摘要
基于多行列式Transformer回流神经量子态（NQS）假设和掺杂二维哈伯德模型的相关多阶段训练工作流程，研究NQS的优化动力学如何依赖于几个关键优化和架构超参数。工作流程包括神经网络回流初始化、监督Transformer预训练以及在变分蒙特卡罗中使用矩自适应重配置启发式方法进行主要能量优化。以U = 8的掺杂4×4周期哈伯德模型为基线，研究更新范数阈值、Transformer宽度、行列式通道数和蒙特卡罗批量大小如何影响收敛。发现适度的更新约束提高了MARCH优化效率，更大的Transformer宽度和更多行列式通道提高了假设的表达能力，更大的蒙特卡罗批量减少了更新方向上的采样噪声。还在半填充、较弱相互作用强度、开放边界条件以及更大的8×8掺杂晶格上测试了相同工作流程。这些结果确定了Transformer回流NQS的实际优化趋势，并突出了假设表达能力、MARCH更新稳定性和蒙特卡罗采样质量之间的平衡。
英文摘要
Building on the multi-determinant Transformer backflow neural quantum state (NQS) ansatz and the associated multi-stage training workflow for the doped two-dimensional Hubbard model, we investigate how the optimization dynamics of the NQS depend on several key optimization and architectural hyperparameters. The workflow consists of neural-network backflow (NNB) initialization, supervised Transformer pre-training, and main energy optimization using the Moment-Adaptive ReConfiguration Heuristic (MARCH) within variational Monte Carlo. Using the doped $4\times4$ periodic Hubbard model at $U=8$ as a baseline, we examine how the update-norm threshold, Transformer width, number of determinant channels, and Monte Carlo batch size affect convergence. We find that a moderate update constraint improves the efficiency of MARCH optimization, larger Transformer width and more determinant channels improve the expressive capacity of the ansatz, and larger Monte Carlo batches reduce sampling noise in the update direction. We further test the same workflow at half filling, weaker interaction strength, open boundary conditions, and on a larger $8\times8$ doped lattice. These results identify practical optimization trends for Transformer backflow NQSs and highlight the balance between ansatz expressivity, MARCH update stability, and Monte Carlo sampling quality.
Comments11 pages, 4 figures, 1 table
