# Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems

arXiv: https://arxiv.org/abs/2610.10213 · HTML: https://mlsanity.com/paper/2610.10213/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 14 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Builds on (most cited first, 1 of 1)

- [Optimizing Sensor Placement for Hydrogen Leak Detection in Enclosed Infrastructure: A Comparative Study Using CFD-informed Genetic Algorithm and DeepSets Neural Surrogate](https://mlsanity.com/paper/2607.26078/) (2026)

## Abstract (arXiv)

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 < n2 - kn, reducing sample complexity from O(n2) 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.