神经网络在物理反问题中可能依赖统计偏见而非真实规律。
Out-of-distribution Neural Inference in Dynamical Ising Models
- 用多种架构重建伊辛模型的相互作用图
- 变换拓扑或温度后，模型表现差异显著
- 不同架构有不同统计先验，可能误判异常数据
神经网络被广泛用于从动态观测中推断隐藏的物理结构，但其分布外性能是否反映可迁移的物理规律仍不明确。我们在一个受控的逆问题中研究此问题：从Glauber磁化轨迹重构动力学伊辛模型的相互作用图。在卷积、图、Transformer及混合架构中，我们发现数据驱动训练会产生不同且可重复的统计策略，面对拓扑和温度变化时表现各异。边密度诊断显示，基于Transformer的模型倾向于保持训练集的连接密度，而卷积模型则可能坍缩为稀疏或无连接的预测，这些预测看似在分布外稳定，实则利用了多数无连接类别的统计偏见。因此，高分布内准确率和看似鲁棒的分布外表现，并不意味着学习到了动力学到结构的规则。相反，神经重建可能由架构依赖的统计先验主导。我们的结果揭示了标准数据驱动学习在物理逆问题中的具体失效模式，为机器学习辅助科学发现提出了规则引导原则。
原文摘要 · Abstract (English)
Neural networks are increasingly used to infer hidden physical structure from dynamical observations, yet it remains unclear whether their out-of-distribution performance reflects transferable physical rule learning. We address this question in a controlled inverse problem: reconstructing interaction graphs of a kinetic Ising model from Glauber magnetization trajectories. Across convolutional, graph, Transformer, and hybrid architectures, we find that data-driven training produces distinct and reproducible statistical strategies under topology and temperature shifts. Edge-population diagnostics reveal that Transformer-based models tend to preserve the link density of the training ensemble, whereas convolutional models can collapse toward sparse- or no-link predictions that appear out-of-distribution stable by exploiting the majority no-link class. Thus, high in-distribution accuracy and apparent out-of-distribution robustness do not necessarily imply a learned dynamics-to-structure rule. Instead, neural reconstruction can be governed by architecture-dependent statistical priors. Our results identify a concrete failure mode of standard data-driven learning in physical inverse problems and motivate rule-guided principles for machine-learning-assisted scientific discovery.
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