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arXiv · 2506.11056

xInv: Explainable Optimization of Inverse Problems

Sean Memery·Kevin Denamganai·Anna Kapron-King·Kartic Subr
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Abstract

Inverse problems are central to a wide range of fields, including healthcare, climate science, and agriculture. They involve the estimation of inputs, typically via iterative optimization, to some known forward model so that it produces a desired outcome. Despite considerable development in the explainability and interpretability of forward models, the iterative optimization of inverse problems remains largely cryptic to domain experts. We propose a methodology to produce explanations, from traces produced by an optimizer, that are interpretable by humans at the abstraction of the domain. The central idea in our approach is to instrument a differentiable simulator so that it emits natural language events during its forward and backward passes. In a post-process, we use a Language Model to create an explanation from the list of events. We demonstrate the effectiveness of our approach with an illustrative optimization problem and an example involving the training of a neural network.

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Sean Memery, Kevin Denamganai, Anna Kapron-King, Kartic Subr. 2025-05-22. xInv: Explainable Optimization of Inverse Problems. https://arxiv.org/abs/2506.11056

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