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.

Regenerating natural language explanations in the scientific domain has been proposed as a benchmark to evaluate complex multi-hop and explainable inference. In this context, large language models can achieve state-of-the-art performance when employed as cross-encoder architectures and fine-tuned on human-annotated explanations. However, while much attention has been devoted to the quality of the explanations, the problem of performing inference efficiently is largely under studied. Cross-encoders, in fact, are intrinsically not scalable, possessing limited applicability to real-world scenarios that require inference on massive facts banks. To enable complex multi-hop reasoning at scale, this paper focuses on bi-encoder architectures, investigating the problem of scientific explanation regeneration at the intersection of dense and sparse models. Specifically, we present SCAR (for Scalable Autoregressive Inference), a hybrid framework that iteratively combines a Transformer-based bi-encoder with a sparse model of explanatory power, designed to leverage explicit inference patterns in the explanations. Our experiments demonstrate that the hybrid framework significantly outperforms previous sparse models, achieving performance comparable with that of state-of-the-art cross-encoders while being approx 50 times faster and scalable to corpora of millions of facts. Further analyses on semantic drift and multi-hop question answering reveal that the proposed hybridisation boosts the quality of the most challenging explanations, contributing to improved performance on downstream inference tasks.

Most of the contemporary approaches for multi-hop Natural Language Inference (NLI) construct explanations considering each test case in isolation. However, this paradigm is known to suffer from semantic drift, a phenomenon that causes the construction of spurious explanations leading to wrong conclusions. In contrast, this paper proposes an abductive framework for multi-hop NLI exploring the retrieve-reuse-refine paradigm in Case-Based Reasoning (CBR). Specifically, we present Case-Based Abductive Natural Language Inference (CB-ANLI), a model that addresses unseen inference problems by analogical transfer of prior explanations from similar examples. We empirically evaluate the abductive framework on commonsense and scientific question answering tasks, demonstrating that CB-ANLI can be effectively integrated with sparse and dense pre-trained encoders to improve multi-hop inference, or adopted as an evidence retriever for Transformers. Moreover, an empirical analysis of semantic drift reveals that the CBR paradigm boosts the quality of the most challenging explanations, a feature that has a direct impact on robustness and accuracy in downstream inference tasks.

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.

This paper presents a novel framework for reconstructing multi-hop explanations in science Question Answering (QA).While existing approaches for multi-hop reasoning build explanations considering each question in isolation, we propose a method to leverage explanatory patterns emerging in a corpus of scientific explanations.Specifically, the framework ranks a set of atomic facts by integrating lexical relevance with the notion of unification power, estimated analysing explanations for similar questions in the corpus.An extensive evaluation is performed on the Worldtree corpus, integrating k-NN clustering and Information Retrieval (IR) techniques.We present the following conclusions: (1) The proposed method achieves results competitive with Transformers, yet being orders of magnitude faster, a feature that makes it scalable to large explanatory corpora (2) The unificationbased mechanism has a key role in reducing semantic drift, contributing to the reconstruction of many hops explanations (6 or more facts) and the ranking of complex inference facts (+12.0Mean Average Precision) (3) Crucially, the constructed explanations can support downstream QA models, improving the accuracy of BERT by up to 10% overall.