xInv: Explainable Optimization of Inverse Problems

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.

Kevin Denamganaï

Independent Researcher

My research investigates the conditions under which AI systems acquire and deploy structured symbolic representations — towards in-context grounding of novel atomic symbols and their systematic recombination into unseen configurations — spanning Compositional Generalisation, Formal Mathematics, Differentiable Language Models, and Physical Simulation. I have also investigated Language Emergence & Grounding (Emergent Communication), Unsupervised Representation Learning, Natural Language Processing, and Multi-Agent Deep Reinforcement Learning.