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

arXiv: https://arxiv.org/abs/2404.02625 · HTML: https://mlsanity.com/paper/2404.02625/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 30 references that are in the map.
- First posted on arXiv 3 Apr 2024.

## Builds on (most cited first, 23 of 23)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Billion-scale similarity search with GPUs](https://mlsanity.com/paper/1702.08734/) (2017)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [UnifiedQA: Crossing Format Boundaries With a Single QA System](https://mlsanity.com/paper/2005.00700/) (2020)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [WorldTree: A Corpus of Explanation Graphs for Elementary Science Questions supporting Multi-Hop Inference](https://mlsanity.com/paper/1802.03052/) (2018)
- [Quick and (not so) Dirty: Unsupervised Selection of Justification Sentences for Multi-hop Question Answering](https://mlsanity.com/paper/1911.07176/) (2019)
- [PRover: Proof Generation for Interpretable Reasoning over Rules](https://mlsanity.com/paper/2010.02830/) (2020)
- [CombOptNet: Fit the Right NP-Hard Problem by Learning Integer Programming Constraints](https://mlsanity.com/paper/2105.02343/) (2021)
- [A Survey on Explainability in Machine Reading Comprehension](https://mlsanity.com/paper/2010.00389/) (2020)
- [Answering Complex Questions Using Open Information Extraction](https://mlsanity.com/paper/1704.05572/) (2017)
- [Hybrid Autoregressive Inference for Scalable Multi-hop Explanation Regeneration](https://mlsanity.com/paper/2107.11879/) (2021)
- [Exploiting Explicit Paths for Multi-hop Reading Comprehension](https://mlsanity.com/paper/1811.01127/) (2018)
- [multiPRover: Generating Multiple Proofs for Improved Interpretability in Rule Reasoning](https://mlsanity.com/paper/2106.01354/) (2021)
- [Question Answering as Global Reasoning over Semantic Abstractions](https://mlsanity.com/paper/1906.03672/) (2019)
- [Question Answering via Integer Programming over Semi-Structured Knowledge](https://mlsanity.com/paper/1604.06076/) (2016)
- [Learning to Attend On Essential Terms: An Enhanced Retriever-Reader Model for Open-domain Question Answering](https://mlsanity.com/paper/1808.09492/) (2018)
- [KG^2: Learning to Reason Science Exam Questions with Contextual Knowledge Graph Embeddings](https://mlsanity.com/paper/1805.12393/) (2018)
- [Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-hop Inference](https://mlsanity.com/paper/2105.03417/) (2021)

## Built on by (most cited first, 1 of 1)

- [Generalizable Reasoning through Compositional Energy Minimization](https://mlsanity.com/paper/2510.20607/) (2025)

## Abstract (arXiv)

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.