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

Mokanarangan Thayaparan, Marco Valentino, Andre Freitas

Keywords: Explainable AI, Constrained Optimization, Integer Linear Programming, Question Answering

TL;DR: The paper presents a novel neuro-symbolic framework that integrates Integer Linear Programming with pre-trained transformers to perform end-to-end explainable multi-hop inference

Abstract: Integer Linear Programming (ILP) provides a viable mechanism to encode explicit and controllable assumptions about explainable multi-hop inference with natural language. However, an ILP formulation is non-differentiable and cannot be integrated into broader deep learning architectures. Recently, Thayaparan et al. (2021a) proposed a novel methodology to integrate ILP with Transformers to achieve end-to-end differentiability for complex multi-hop inference. While this hybrid framework has been demonstrated to deliver better answer and explanation selection than transformer-based and existing ILP solvers, the neuro-symbolic integration still relies on a convex relaxation of the ILP formulation, which can produce sub-optimal solutions. To improve these limitations, we propose Diff-Comb Explainer, a novel neuro-symbolic architecture based on Differentiable BlackBox Combinatorial solvers (DBCS) (Pogančić et al., 2019). Unlike existing differentiable solvers, the presented model does not require the transformation and relaxation of the explicit semantic constraints, allowing for direct and more efficient integration of ILP formulations. Diff-Comb Explainer demonstrates improved accuracy and explainability over non-differentiable solvers, Transformers and existing differentiable constraint-based multi-hop inference frameworks.

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