接触过程的无监督机器学习
Unsupervised Machine Learning of the Contact Process
- Universidade Estadual do Piauí（皮奥伊州立大学）
- Universidade Federal do Piauí（皮奥伊联邦大学）
- Universidade Federal de Ouro Preto（欧罗普雷托联邦大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过数据增广和异方差先验改进PCA与VAE，使其能准确表征接触过程的活性-吸收相变，强调表示需适配物理结构。
AI中文摘要：
我们研究了无监督机器学习方法如何表征一维和二维空间中接触过程的活性-吸收相变。我们的分析聚焦于主成分分析（PCA）和变分自编码器（VAEs），并表明直接应用这些方法会遇到一个核心困难：接触过程构型本质上是正定的。在PCA情形下，标准的中心化步骤无法在前导分量中分离出序参量。为解决此问题，我们将数据扩充以包含符号反转的构型，从而创建一个均值为零的平衡数据集，同时保留描述相变所需的密度信息。这种预处理使得主导主成分能够恢复序参量，并在临界点附近重现预期的有限尺寸标度。对于VAEs，我们发现了一个相关的局限性：对于正定数据，固定的高斯先验无法在全部控制参数和系统尺寸范围内提供足够的潜在空间正则化。我们通过采用一种适应控制参数的异方差高斯先验来克服这一限制，从而在临界阈值附近基于重构的可观测量的有限尺寸标度得到显著改善。综合来看，这些结果凸显了一个关键教训：机器学习在相变问题中的成功不仅依赖于算法复杂性，还在于定制表示以尊重系统的物理结构，包括其内在约束和对称性。
英文摘要：
We investigate how unsupervised machine-learning methods can characterize the active-absorbing phase transition in the contact process in one and two spatial dimensions. Our analysis focuses on principal component analysis (PCA) and variational autoencoders (VAEs), and we show that direct applications of these methods encounter a central difficulty: contact process configurations are intrinsically positive-definite. In the PCA case, standard centering procedures fail to isolate the order parameter in the leading component. To address this, we augment the data with sign-reversed configurations, creating a balanced dataset with zero mean while preserving the density information required to describe the transition. This preprocessing allows the dominant principal component to recover the order parameter and reproduce the expected finite-size scaling near criticality. For VAEs, we find a related limitation: a fixed Gaussian prior does not provide sufficient latent regularization across the full range of control parameters and system sizes for positive-definite data. We overcome this by adopting a heteroscedastic Gaussian prior that adapts to the control parameter, leading to a substantial improvement in the finite-size scaling of reconstruction-based observables near the critical threshold. Taken together, these results highlight a key lesson: the success of machine learning in phase-transition problems does not rely on algorithmic complexity alone, but on tailoring the representation to respect the physical structure of the system, including its intrinsic constraints and symmetries.
