用自编码器解码伊辛模型的微观数据，揭示了磁化与能量的渐进学习规律。
Interpreting learning dynamics of autoencoders: Transient scaling and emerging concepts of the Ising model
- 通过多尺度粗粒化分析，发现磁化与能量分阶段学习的动态机制
- 深度模型在中等与快速学习率下会提前停滞，无法完成能量学习
- 首次用自递归轨迹解析重建误差与潜在表征的关系，具物理可解释性
我们研究了无监督自编码器在伊辛模型微观自旋构型上的学习过程，旨在捕捉数据生成机制中的宏观、理论相关变量。通过在多个空间尺度（粗粒化）上量化学习表现，揭示了两个相继出现的动态阶段：一个阶段学习磁化量，另一个阶段逐步学习能量。前者呈现有序的误差波动并仅学习全局平均值；后者则逐渐解析对能量表征至关重要的小尺度信息。在中等和快速学习率下训练的深层模型会提前陷入停滞，无法进入后一阶段。我们引入一种新的自递归轨迹分析方法，将重建误差与潜在表示相联系。这些内在动态由预测误差驱动，暴露了训练如何推动宏观概念的表征演化。我们基于训练数据波动引发远离平衡态的过程，建立了一个融合物理世界与机器模型的可解释框架。
原文摘要 · Abstract (English)
We study how unsupervised autoencoders trained on microscopic spin configurations from the Ising model learn macroscopic, theory-relevant variables underlying the data-generating process. We quantify learning across multiple spatial (coarse-graining) scales and reveal two distinct dynamical regimes that appear sequentially, controlled by the main hyperparameters (model depth, width, and learning rate): one in which magnetization and another in which energy is learned across scales. The first exhibits error fluctuations ordered to scale and learns global averages only; The second gradually resolves smaller scales relevant for the energy representation. Deep models trained at moderate and fast rates become arrested before reaching these regimes. We connect reconstruction errors with the latent representations using a novel analysis of self-recursive trajectories. These intrinsic dynamics are induced by prediction errors, exposing how training drives representation changes for macroscopic concepts. We utilize the intuition that learning operates as a process driven far from equilibrium by fluctuations from the training data to provide an interpretive basis grounded in both the physical world and the machine models that represent it.
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