发表机构
University of Toronto Scarborough; Alliance for AI-Accelerated Materials Discovery (A3MD); University of Toronto（多伦多大学士嘉堡校区; AI加速材料发现联盟; 多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文揭示残差尺度不足以衡量可学习性，提出尺度归一化图狄利克雷粗糙度作为诊断指标，并确立基线互补性为靶标设计核心原则，以提升科学机器学习泛化能力。
AI 中文摘要
在科学机器学习中，Δ学习在相对于物理基线的残差误差上训练模型，假设具有更小残差尺度的更准确基线固有地提升下游性能。在此，我们证明残差尺度单独不足以作为可学习性的启发式指标。通过评估分子图神经网络在总能量靶标上的表现，我们展示复杂的局部描述符基线可以产生小的残差靶标，这些靶标在架构感知的代理空间内不成比例地粗糙，并且相对于其尺度更难学习。相反，半经验基线同时降低尺度与归一化粗糙度，改善域内与域外预测。我们引入尺度归一化图狄利克雷粗糙度（D_IQR）作为残差可学习性的预训练诊断指标，并确立基线互补性作为核心靶标设计原则，将靶标空间表述提升为与模型架构并列的科学机器学习关键轴。
英文摘要
In scientific machine learning, $Δ$-learning trains models on residual errors relative to physical baselines, assuming that more accurate baselines with smaller residual scales inherently improve downstream performance. Here, we demonstrate that residual scale alone is an insufficient heuristic for learnability. Evaluating molecular graph neural networks on total energy targets, we show that complex local descriptor baselines can yield small residual targets that are disproportionately rough within architecture-informed proxy spaces and harder to learn relative to their scale. Conversely, semi-empirical baseline reduces both scale and normalized roughness, improving in-domain and out-of-domain prediction. We introduce scale-normalized graph Dirichlet roughness ($D_{\text{IQR}}$) as a pre-training diagnostic for residual learnability and establish baseline complementarity as a core target-design principle, elevating target space formulation alongside model architecture as a key axis for scientific machine learning.
Comments41 pages, including 24 pages of Supplementary Information; 4 main-text figures
