arXiv：cs.LG· Nicholas Tan Jerome, Fangnian Wang·· 6 小时前AI 评分48
边准确率并不足够：为何动力学学习到的结构无法迁移到逆问题
Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems
AI 导读
研究表明，从动力学预测中通过 NRI 学到的关系结构无法迁移到逆问题，即使其边误差满足 Δ < n²-kn 的理论条件。在 180 个 CFD 氢气泄漏与 180 个声学场景的源定位任务中，该结构比任务优化注意力基线性能下降 116% 和 201%。作者提出一种基于 Jaccard 相似度的轻量可迁移性测试，使用不到一小时计算和 15-20% 目标域数据即可区分迁移成败。
正文
Abstract: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 $\Delta < n^2 - kn$, reducing sample complexity from $O(n^2)$ to $O(kn+\Delta)$. 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.
| Comments: | 13 pages, 8 tables. Code: this https URL |
| Subjects: | Machine Learning (cs.LG) |
| MSC classes: | 68T07 |
| ACM classes: | I.2.6 |
| Cite as: | arXiv:2610.10213 [cs.LG] |
| (or arXiv:2610.10213v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10213 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Nicholas Tan Jerome [view email]
[v1]
Wed, 7 Oct 2026 15:10:31 UTC (49 KB)
来源：arXiv：cs.LG · arxiv.org