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

Key points

• We show this strategy fails systematically, even when it satisfies the standard theoretical justification for why structure should help.1
• 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 $O(kn+Δ)$.1
• 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%.1

Sources (1)

• [1]Edge Accuracy Is Not Enough: Why Dynamics-Learned Structure Fails to Transfer to Inverse Problems
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 03:10 PM

  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.

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