Interpretable Proof Generation via Iterative Backward Reasoning (2022)

Abstract: We present IBR, an Iterative Backward Reasoning model to solve the proof generation tasks on rule-based Question Answering (QA), where models are required to reason over a series of textual rules and facts to find out the related proof path and derive the final answer. We handle the limitations of existed works in two folds: 1) enhance the interpretability of reasoning procedures with detailed tracking, by predicting nodes and edges in the proof path iteratively backward from the question; 2) promote the efficiency and accuracy via reasoning on the elaborate representations of nodes and history paths, without any intermediate texts that may introduce external noise during proof generation. There are three main modules in IBR, QA and proof strategy prediction to obtain the answer and offer guidance for the following procedure; parent node prediction to determine a node in the existing proof that a new child node will link to; child node prediction to find out which new node will be added to the proof. Experiments on both synthetic and paraphrased datasets demonstrate that IBR has better in-domain performance as well as cross-domain transferability than several strong baselines. Our code and models are available at https://github.com/find-knowledge/IBR .

## introduction endowing machines with reasoning capabilities is a longstanding problem @xcite in the field of ai. though existing tasks such as multi-hop qa @xcite or logical-reasoning qa @xcite impose a higher requirement on the reasoning capabilities, they usually just request for an answer without the reasoning procedure that would make it interpretable. recently, @xcite proposed new datasets and tasks for interpretable figure 1 : illustration of generating proof iteratively. regarding the proof path as a graph, and using the question as the initial node, other nodes and edges will be added step by step. (the gold proof is the obtained path in a reverse order exclude the question). the main challenges are wrong (cannot derive the answer) or redundant (can derive the answer, but the path is longer than the optimal one) branches may be involved. inspired by the top-down amr parsing @xcite , where a sentence is divided into sub-meanings iteratively, we present iterative backward reasoning (ibr) for better proof generation. it generates a proof path iteratively starting from the core component for qa, i.e. the question, making the process interpretable with trackable intermediate states. regarding a higher efficiency and accuracy, and two challenges mentioned in figure 1 , the proof generation module of ibr simplifies the intermediate process of reasoning as well as avoids the unnecessary search for a possible unsuitable branch. to add a new node and edge to the path, there are two steps in ibr for each iteration: 1) finding out the next parent node, i.e. one existing rule or fact in the parsed history path that a new node will become its child; 2) determine which rule or fact that will be the new child node and added to the path. equipped with question-aware representations from a pre-trained encoder, along with structure-aware node and path features, our model can choose the optimal endpoint. it accomplishes reasoning with the highest possibility to obtain a correct subsequent proof path based on relevant features, getting rid of intermediate texts while avoiding redundancy on all possible texts than previous iterative works. in addition, to make ibr applicable for samples with incomplete proof paths, which are abandoned in the former backward iterative model evr @xcite , we employ a proof strategy predictor to output a proof type. this prediction is then integrated into the later proof generation actions, making the process more controllable under different conditions. we validate our approach on several datasets that are widely used in previous studies (i.e. du0-du5, birds-electricity, and pararules) spanning different settings (i.e. fully-supervised, fewer training data, and out-of-domain). experimental results show that, compared to existing strong baselines including both non-iterative and iterative ones, ibr can achieve the best overall performance of proof generation and comparable answer prediction accuracy, along with noticeable generalization capability. extensive analyses show that 1) the improvements come from our elaborately designed iterative and simplified proof generation modules, and 2) both the reasoning ability and latency could be significantly improved compared to former iterative models, making a better trade-off considering its reasonable interpretability. lately, question answering (qa) is employed as an important task for machine reasoning. numerous datasets were proposed, including synthesized data @xcite , comprehension on natural texts @xcite @xcite or more complex relationship reasoning @xcite . there are also multi-hop qa tasks like hot-potqa @xcite or qangaroo @xcite , and logical qa datasets such as re-clor @xcite and logiqa @xcite , in which textual rules need to be inferred implicitly from a long supporting context. plenty of studies try to solve these problems via neural networks and achieve remarkable performance @xcite @xcite . nevertheless, nearly all of them only focus on the prediction of final answers and neglect the acquisition of interpretable proofs. although some datasets provide proof paths for better interpretability, these paths are only short chains with very few entities and cannot teach models to generate complex proofs. proof generation. nlprolog @xcite first employs logic programming to search for a proof and then predicts the answer in multi-hop qa. recently, @xcite propose new rulebased qa datasets for this line of research that include more complex proof paths, and present rule-taker to answer questions. @xcite argue that producing answer proofs makes models more reliable and propose prover, a transformer-based model that enumerates all possible nodes and edges of a proof path and predicts whether each one exists at once based on their embeddings. probr @xcite further improves this framework using the probabilistic graph to model more variables. there has been also an increasing interest in solving proof generation iteratively. evr @xcite splits the question into sub-questions, using generated intermediate texts to guide proof generation step by step. proofwriter @xcite shares a similar idea but uses intermediate textual conclusions instead and a more powerful t5-11b model @xcite for generation, which makes it hard to reproduce. ibr is also an iterative model, being more interpretable than at-once models. despite getting rid of intermediate texts and directly using various representations to finish each step, it improves efficiency and effectiveness. ## experiments following former studies @xcite , we evaluate our ibr 2 on three datasets and four settings including fully-supervised training, training using fewer samples, testing on out-ofdomain samples, and generalization to more complex proofs or language. ## conclusion this paper presents ibr, a proof generation model via iterative backward reasoning for rule-based qa tasks. we equip the reasoning procedure with detailed hidden state tracking by predicting nodes and edges in the proof path iteratively backward from the question, and allow the model to reason on the elaborate representations of nodes and his-