边缘精度不够：为何动力学学习到的结构无法迁移到反问题
Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems
- Institute for Data Processing and Electronics (IPE)（数据处理与电子研究所）
- Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该论文证明，从动力学预测中学习到的结构即使满足理论条件，在反问题迁移中仍会失败，并提出了基于Jaccard相似度的轻量级可迁移性测试来预测迁移成败。
AI中文摘要：
对于标注数据稀缺的反问题，一个自然的策略是迁移从丰富的正向模拟数据中学习到的关系结构。我们表明，即使该策略满足结构应有助于求解的标准理论依据，它仍会系统性地失效。我们证明，只要边缘误差满足 $\Delta < n^2 - kn$，近似结构就能带来估计误差上的收益，将样本复杂度从 $O(n^2)$ 降低到 $O(kn+\Delta)$。通过神经关系推断（NRI）从动力学预测中学习到的结构满足这一条件，然而在跨越180个CFD模拟氢泄漏场景和180个声学场景的源定位任务中，相对于灵活且任务优化的注意力基线，它使性能分别下降了116%和201%，而基于物理的先验（格林函数）仅下降了69-72%。四条独立的证据表明这不是调参失败：当提供18倍多的训练数据时，NRI仅提升0.5%（而任务优化的基线提升16.6%，$p<0.001$）；性能在广泛的NRI边缘阈值范围内不敏感；动力学学习到的图与任务最优图仅在6%的边缘上重叠；另外两种基于动力学的结构估计器（基于相关性和基于互信息的）相对于无结构基线没有可测量的收益，其中基于相关性的估计器表现明显更差。我们将这一差距形式化为关于近似误差的陈述，而边缘精度条件无法控制该误差，并且我们提供了一个轻量级的可迁移性测试（与部分观测的目标任务图的Jaccard相似度），该测试在我们评估的所有四个域/结构组合中区分了成功与失败的迁移，使用不到一小时的计算和15-20%的目标域数据；我们将其作为在少数案例上校准的启发式方法，而非经过验证的通用阈值。
英文摘要：
A natural strategy for inverse problems with scarce labelled data is to transfer relational structure learned from abundant forward-simulation data. We show this strategy fails systematically, even when it satisfies the standard theoretical justification for why structure should help. We prove that approximate structure provides estimation-error benefits whenever the edge error satisfies $Δ< n^2 - kn$, reducing sample complexity from $O(n^2)$ to $O(kn+Δ)$. Structure learned via Neural Relational Inference (NRI) from dynamics prediction satisfies this condition, yet on a source-localisation task across 180 CFD-simulated hydrogen-leak scenarios and 180 acoustic scenarios, it degrades performance by 116% and 201% relative to a flexible, task-optimised attention baseline, while a physics-based prior (Green's function) degrades by only 69-72%. Four independent lines of evidence show this is not a tuning failure: NRI improves only 0.5% when given 18x more training data (versus 16.6% for the task-optimised baseline, $p<0.001$); performance is insensitive to the NRI edge threshold across a wide range; the dynamics-learned graph overlaps the task-optimal graph on only 6% of edges; and two further dynamics-derived structure estimators (correlation- and mutual-information-based) show no measurable benefit over a structure-free baseline, with the correlation-based estimator performing markedly worse. We formalise this gap as a statement about approximation error that the edge-accuracy condition cannot control, and we provide a lightweight transferability test (Jaccard similarity against a partially-observed target-task graph) that separates successful from failed transfer in all four domain/structure pairs we evaluate, using under an hour of computation and 15-20% of target-domain data; we present this as a heuristic calibrated on few cases, not a validated general threshold.
