ARTICLE Thayaparan_TACL_2022/IDIAP Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-Hop Inference Thayaparan, Mokanarangan Valentino, Marco Mendes, Deborah Rozanova, Julia Freitas, Andre Transactions of the Association for Computational Linguistics 2022 https://doi.org/10.1162/tacl_a_00508 doi This paper presents Diff-Explainer, the first hybrid framework for explainable multi-hop inference that integrates explicit constraints with neural architectures through differentiable convex optimization. Specifically, Diff-Explainer allows for the fine-tuning of neural representations within a constrained optimization framework to answer and explain multi-hop questions in natural language. To demonstrate the efficacy of the hybrid framework, we combine existing ILP-based solvers for multi-hop Question Answering (QA) with Transformer-based representations. An extensive empirical evaluation on scientific and commonsense QA tasks demonstrates that the integration of explicit constraints in a end-to-end differentiable framework can significantly improve the performance of non-differentiable ILP solvers (8.91%–13.3%). Moreover, additional analysis reveals that Diff-Explainer is able to achieve strong performance when compared to standalone Transformers and previous multi-hop approaches while still providing structured explanations in support of its predictions.