Diff-Explainer: Differentiable Convex Optimization for Explainable Multi-hop Inference (2022)

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.

## introduction explainable question answering (qa) in complex domains is often modeled as a multi-hop inference problem @xcite @xcite . in this context, the goal is to answer a given question through the construction of an explanation, typically represented as a graph of multiple interconnected sentences supporting the answer (figure 1 ). @xcite @xcite . however, explainable qa models exhibit lower performance when compared to state-of-the-art approaches, which are generally represented by transformer-based architectures @xcite @xcite . while transformers are able to achieve high accuracy due to their ability to transfer linguistic and semantic information to downstream tasks, they are typically regarded as black-boxes @xcite , posing concerns about the interpretability and transparency of their predictions @xcite . to alleviate the aforementioned limitations and find a better trade-off between explainability and inference performance, this paper proposes diff-explainer (∂-explainer), a novel hybrid framework for multi-hop and explainable qa that combines constraint satisfaction layers with pretrained neural representations, enabling end-toend differentiability. recent works have shown that certain convex optimization problems can be represented as individual layers in larger end-to-end differentiable networks @xcite , demonstrating that these layers can be adapted to encode constraints and dependencies between hidden states that are hard to capture via standard neural networks. in this paper, we build upon this line of research, showing that convex optimization layers can be integrated with transformers to improve explainability and robustness in multi-hop inference problems. to illustrate the impact of end-to-end differentiability, we integrate the constraints of existing ilp solvers (i.e., tupleilp @xcite , explanationlp @xcite ) into a hybrid framework. specifically, we propose a methodology to transform existing constraints into differentiable convex optimization layers and subsequently integrate them with pre-trained sentence embeddings based on transformers @xcite . figure 1 : example of a multi-hop qa problem with an explanation represented as a graph of multiple interconnected sentences supporting the answer @xcite . to evaluate the proposed framework, we perform extensive experiments on complex multiple-choice qa tasks requiring scientific and commonsense reasoning @xcite . in summary, the contributions of the paper are as follows: ## multi-hop question answering via differentiable convex optimization the problem of explainable multi-hop question answering can be stated as follows: definition 3.1 (explanations in multi-hop question answering). given a question q, answer a and a knowledge base f kb (composed of natural language sentences), we say that we may infer hypothesis h (where hypotheses h is the concatenation of q with a) if there exists a subset (f exp ) of supporting facts {f 1 , f 2 , . . .} ⊆ f kb of statements which would allow a human being to deduce h from {f 1 , f 2 , . . .}. we call this set of facts an explanation for h. given a question (q) and a set of candidate answers @xmath0, c 2 , c 3 , . . . , c n } ilp-based approaches @xcite @xcite , convert them into a list of hypothesis @xmath1, h 2 , h 3 , . . . , h n } by concatenating question and candidate answer. for each hypothesis h i these approaches typically adopt a retrieval model (e.g., bm25, faiss @xcite ), to select a list of candidate explanatory facts @xmath2, f 2 , f 3 , . . . , f k }, and construct a weighted graph @xmath3, e, w ) with edge weights w : @xmath4, edge weight w ik of each edge e ik denote how relevant a fact f k is with respect to the hypothesis h i . based on these definitions, ilp-based qa can be defined as follows: the ilp-based inference has two main challenges in producing convincing explanations. first, design edge weights w , ideally capturing a quantification of the relevance of the fact to the hypothesis. second, define constraints that emulate the multi-hop inference process. ## empirical evaluation question sets: we use the following multiplechoice question sets to evaluate the diff-explainer. ## conclusion we presented a novel framework for encoding explicit and controllable assumptions as an end-toend learning framework for question answering. we empirically demonstrated how incorporating these constraints in broader transformer-based architectures can improve answer and explanation selection. the presented framework adopts constraints from tupleilp and explanationlp, but diff-explainer can be extended to encode different constraints with varying degrees of complexity. this approach can also be extended to handle other forms of multi-hop qa, including opendomain, cloze style, and answer generation. ilp has also been employed for relation extraction @xcite @xcite , semantic role labeling @xcite , sentiment analysis @xcite , and explanation regeneration @xcite . we can adapt and improve the constraints presented in this approach to build explainable approaches for the respective tasks. diff-explainer is the first work investigating the intersection of explicit constraints and latent neural representations to the best of our knowledge. we hope this work will open the way for future lines of research on neuro-symbolic models, leading to more controllable, transparent and explainable nlp models.