模型能否预测物理上不可能的材料性质，取决于一个设计细节。
A single design choice determines whether machine learning models of materials make physically impossible predictions
- 用奇偶性标签作为特征，可强制模型满足物理对称性
- 无奇偶性标签的模型在90%-96%的晶体上预测出禁戒响应
- 只需一次随机反射初始化即可验证标签有效性
机器学习模型正逐步取代材料发现中的第一性原理计算，物理对称性是其核心保障。关于是否应硬编码对称性而非让模型学习的争论主要集中在旋转对称性上，而对称性错误本质上是近似误差。但某些约束是精确的：对称性要求特定性质张量严格为零，非零预测即为物理上不可能。本文揭示，模型能否做出此类预测，由一个极少被提及的设计选择决定——其特征是否携带奇偶性标签，并推导出仅基于群论的奇偶性间隙判据，可判断哪些性质与晶体易受暴露。在仅差这一设计点的匹配架构对中，评估2000个中心对称晶体（其压电张量必须为零），带有奇偶性标签的分支处于浮点数下限，而仅依赖旋转的分支在90%-96%的晶体上预测出禁戒响应，差距达六数量级，且无精度损失。显式训练零值无法恢复精确性，且基于冻结通用势能的头部继承其主干的对称性群。在随机初始化时进行一次反射，可在数秒内验证标签有效性。
原文摘要 · Abstract (English)
Machine-learned models are replacing first-principles calculations across materials discovery, and physical symmetry is the central guarantee built into them. The debate over how much symmetry to hard-wire rather than learn has run on rotations, where a symmetry error is an approximation error. Some constraints are exact: symmetry forces certain property tensors to exactly zero, so a nonzero prediction is physically impossible rather than inaccurate. Here we show that whether a model can make such predictions is decided before training by one rarely reported design bit, whether its features carry parity labels, and derive a criterion, the parity gap, that computes from group theory alone which properties and crystals are exposed. Across matched architecture pairs differing only in that bit, evaluated on two thousand centrosymmetric crystals whose piezoelectric tensor must vanish, parity-labelled arms sit at the floating-point floor while rotation-only arms predict forbidden responses on 90-96% of crystals, six orders of magnitude apart, at no accuracy cost. Training on explicit zeros does not recover exactness, and a head on a frozen universal potential inherits its backbone's symmetry group. One reflection at random initialization verifies the label in seconds.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。