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         author = {Thayaparan, Mokanarangan and Valentino, Marco and Mendes, Deborah and Rozanova, Julia and Freitas, Andre},
       projects = {Idiap},
          title = {Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-Hop Inference},
        journal = {Transactions of the Association for Computational Linguistics},
           year = {2022},
            doi = {https://doi.org/10.1162/tacl_a_00508},
       abstract = {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.}