发表机构
The Hong Kong University of Science and Technology (HKUST)（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究指出物理先验的代价由消融间隙界定，通过理论推导与野火严重度任务实验，发现代价受自由特征和验证拆分影响，提出两次拟合筛选方法以识别无法识别的实验。
AI 中文摘要
形状约束和物理引导学习报告了实施先验所带来的精度代价，并将其视为先验的一种属性。我们证明，这一代价主要是自由特征和验证拆分的属性。设P为将假设类限制为对特征S具有形状约束的函数时的超额风险，D为忽略S的消融模型的超额风险。由于对x_j为常数的函数既非x_j的非减函数也非非增函数，因此消融类包含在约束类中，故对于所有风险泛函，均有0 ≤ P ≤ D，且无需凸性、光滑性或可实现性假设。从经验上看，该界限是一个符号检验：约束模型绝不能被其自身的消融模型击败。我们在一个序数野火严重度任务（N = 26,681，K = 3）上实例化了该方法，对四个气象驱动因素施加了严格的单调约束，坐标保持自由，并使用从独立同分布重采样到2度空间分块的验证阶梯。坐标起到了屏障作用：在空间分块下，仅坐标就恢复了完整模型92.9%的宏F1值，将D从0.1288降至0.0427；相同的先验在有屏障时代价为0.0473，无屏障时为0.3470，在物理条件相同的情况下比值为7.3。由于D依赖于协议，因此无法迁移：将分块从1度粗化为10度，使D从0.0942降至0.0050，导致两种配置先验上无法识别。经认证的嵌套界限的反置限定了流水线的加性分辨率：在318次比较中，它们给出了0.0220宏F1的自校准下限，低于该下限的所有报告代价均不可解释，包括我们标题网格中的四个单元。代价与合规性无关：无约束模型违反先验的比率为0.48-0.49，而实施先验的代价为0.0473。我们提出了一种两次拟合筛选方法，在训练约束模型之前拒绝无法识别的实验。
英文摘要
Shape-constrained and physics-informed learning reports an accuracy cost of enforcing a prior and treats it as a property of the prior. We show it is mostly a property of the free features and the validation split. Let P be the excess risk of restricting a hypothesis class to functions with a shape constraint on features S, and D the excess risk of the ablated model that ignores S. Because a function constant in x_j is both non-decreasing and non-increasing in x_j, the ablated class is contained in the constrained class, so 0 <= P <= D for every risk functional, with no convexity, smoothness, or realizability assumption. Empirically the bound is a sign test: a constrained model must never be beaten by its own ablation. We instantiate it on an ordinal wildfire-severity task (N = 26,681, K = 3) with hard monotone constraints on four meteorological drivers, coordinates left free, and a validation ladder from i.i.d. resampling to 2-degree spatial blocking. Coordinates act as a shield: alone they recover 92.9% of the full model's macro-F1 under spatial blocking, collapsing D from 0.1288 to 0.0427; the same prior costs 0.0473 shielded and 0.3470 unshielded, a ratio of 7.3 with identical physics. Because D is protocol-dependent it does not transfer: coarsening blocks from 1 to 10 degrees drives D from 0.0942 to 0.0050, leaving two configurations unidentifiable a priori. Inversions of the certified nesting bound the pipeline's additive resolution: over 318 comparisons they give a self-calibrating floor of 0.0220 macro-F1, below which no reported price is interpretable, including four cells in our own headline grid. Cost and compliance are independent: the unconstrained model violates the prior at rate 0.48-0.49 while enforcing it costs 0.0473. We give a two-fit screen that rejects unidentifiable experiments before a constrained model is trained.
Comments15 pages, 7 tables, 6 figures
