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Integer Linear Programming (ILP) provides a viable mechanism to encodeexplicit and controllable assumptions about explainable multi-hop inferencewith natural language. However, an ILP formulation is non-differentiable andcannot be integrated into broader deep learning architectures. Recently,Thayaparan et al. (2021a) proposed a novel methodology to integrate ILP withTransformers to achieve end-to-end differentiability for complex multi-hopinference. While this hybrid framework has been demonstrated to deliver betteranswer and explanation selection than transformer-based and existing ILPsolvers, the neuro-symbolic integration still relies on a convex relaxation ofthe ILP formulation, which can produce sub-optimal solutions. To improve theselimitations, we propose Diff-Comb Explainer, a novel neuro-symbolicarchitecture based on Differentiable BlackBox Combinatorial solvers (DBCS)(Pogan\v{c}i\'c et al., 2019). Unlike existing differentiable solvers, thepresented model does not require the transformation and relaxation of theexplicit semantic constraints, allowing for direct and more efficientintegration of ILP formulations. Diff-Comb Explainer demonstrates improvedaccuracy and explainability over non-differentiable solvers, Transformers andexisting differentiable constraint-based multi-hop inference frameworks.

Going Beyond Approximation: Encoding Constraints for Explainable Multi-hop Inference via Differentiable Combinatorial Solvers