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A Differentiable Integer Linear Programming Solver for Explanation-Based Natural Language Inference

Mokanarangan Thayaparan, Marco Valentino, André Freitas

TL;DR

This work addresses the challenge of integrating precise ILP-based reasoning with neural language representations for explanation-based Natural Language Inference. It introduces Diff-Comb Explainer, a neuro-symbolic framework that uses Differentiable BlackBox Combinatorial Solvers to perform end-to-end differentiable ILP optimization without relaxing semantic constraints, achieving improved answer accuracy and explanation faithfulness. The approach maintains the original ILP formulation while leveraging Transformer encoders to compute relevance scores, resulting in robust explanations and competitive performance against strong baselines including BERT-based and prior ILP models. The findings suggest that combining symbolic constraints with neural representations can yield more transparent, faithful, and robust NLI systems, with potential applicability to complex domains requiring explicit reasoning priors.

Abstract

Integer Linear Programming (ILP) has been proposed as a formalism for encoding precise structural and semantic constraints for Natural Language Inference (NLI). However, traditional ILP frameworks are non-differentiable, posing critical challenges for the integration of continuous language representations based on deep learning. In this paper, we introduce a novel approach, named Diff-Comb Explainer, a neuro-symbolic architecture for explanation-based NLI based on Differentiable BlackBox Combinatorial Solvers (DBCS). Differently from existing neuro-symbolic solvers, Diff-Comb Explainer does not necessitate a continuous relaxation of the semantic constraints, enabling a direct, more precise, and efficient incorporation of neural representations into the ILP formulation. Our experiments demonstrate that Diff-Comb Explainer achieves superior performance when compared to conventional ILP solvers, neuro-symbolic black-box solvers, and Transformer-based encoders. Moreover, a deeper analysis reveals that Diff-Comb Explainer can significantly improve the precision, consistency, and faithfulness of the constructed explanations, opening new opportunities for research on neuro-symbolic architectures for explainable and transparent NLI in complex domains.

A Differentiable Integer Linear Programming Solver for Explanation-Based Natural Language Inference

TL;DR

This work addresses the challenge of integrating precise ILP-based reasoning with neural language representations for explanation-based Natural Language Inference. It introduces Diff-Comb Explainer, a neuro-symbolic framework that uses Differentiable BlackBox Combinatorial Solvers to perform end-to-end differentiable ILP optimization without relaxing semantic constraints, achieving improved answer accuracy and explanation faithfulness. The approach maintains the original ILP formulation while leveraging Transformer encoders to compute relevance scores, resulting in robust explanations and competitive performance against strong baselines including BERT-based and prior ILP models. The findings suggest that combining symbolic constraints with neural representations can yield more transparent, faithful, and robust NLI systems, with potential applicability to complex domains requiring explicit reasoning priors.

Abstract

Integer Linear Programming (ILP) has been proposed as a formalism for encoding precise structural and semantic constraints for Natural Language Inference (NLI). However, traditional ILP frameworks are non-differentiable, posing critical challenges for the integration of continuous language representations based on deep learning. In this paper, we introduce a novel approach, named Diff-Comb Explainer, a neuro-symbolic architecture for explanation-based NLI based on Differentiable BlackBox Combinatorial Solvers (DBCS). Differently from existing neuro-symbolic solvers, Diff-Comb Explainer does not necessitate a continuous relaxation of the semantic constraints, enabling a direct, more precise, and efficient incorporation of neural representations into the ILP formulation. Our experiments demonstrate that Diff-Comb Explainer achieves superior performance when compared to conventional ILP solvers, neuro-symbolic black-box solvers, and Transformer-based encoders. Moreover, a deeper analysis reveals that Diff-Comb Explainer can significantly improve the precision, consistency, and faithfulness of the constructed explanations, opening new opportunities for research on neuro-symbolic architectures for explainable and transparent NLI in complex domains.
Paper Structure (27 sections, 13 equations, 3 figures, 3 tables, 1 algorithm)

This paper contains 27 sections, 13 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Constraint-based multi-hop inference
  4. Hybrid reasoning with Transformers
  5. Diff-Comb Explainer: Differentiable Integer Linear Programming Solver for Explanation-Based Natural Language Inference
  6. Graph Construction
  7. Semantic Relevance ($s$)
  8. Lexical Relevance ($l$)
  9. Subgraph Selection
  10. Answer selection constraint
  11. Edge and Node selection constraint
  12. Abstract fact selection constraint
  13. Adopting Differentiable Blackbox Combinatorial Optimisation Solvers
  14. Answer and Explanation Selection
  15. Empirical Evaluation
  16. ...and 12 more sections

Figures (3)

  • Figure 1: Example of a hypothesis (i.e., question + answer) and an explanation graph constructed via an ILP-based NLI model xie2020worldtreejansen2018worldtree.
  • Figure 2: End-to-end architectural diagram of Diff-Comb Explainer. The integration of Differentiable Blackbox Combinatorial solvers will result in better explanation generation and answer prediction.
  • Figure 3: Comparison of accuracy for different number of retrieved facts.

Theorems & Definitions (1)

  • Definition 3.1: ILP-Based NLI