Question answering requiring numerical reasoning, which generally involves symbolic operations such as sorting, counting, and addition, is a challenging task. To address such a problem, existing mixture-of-experts (MoE)-based methods design several specific answer predictors to handle different types of questions and achieve promising performance. However, they ignore the modeling and exploitation of fine-grained reasoning-related operations to support numerical reasoning, encountering the inadequacy in reasoning capability and interpretability. To alleviate this issue, we propose OPERA, an operation-augmented numerical reasoning framework. Concretely, we systematically define a scalable operation set to model numerical reasoning. We first identify reasoning-related operations based on context and then softly execute them to imitate the answer reasoning procedure via an operation-aware cross-attention mechanism. Finally, we utilize the operation-augmented semantic representation of execution results to support answer prediction. We verify the effectiveness and generalization of OPERA in two scenarios with different knowledge sources and reasoning capabilities. Specifically, we conduct extensive experiments on two textual datasets, DROP and RACENum, and a table-text hybrid dataset TAT-QA. Experiment results show that OPERA outperforms previous strong methods on the DROP, RACENum, and TAT-QA datasets. Further, we statistically and visually analyze its interpretability.

Question answering requiring discrete reasoning, e.g., arithmetic computing, comparison, and counting, over knowledge is a challenging task.In this paper, we propose UniRPG, a semantic-parsing-based approach advanced in interpretability and scalability, to perform Unified discrete Reasoning over heterogeneous knowledge resources, i.e., table and text, as Program Generation.Concretely, UniRPG consists of a neural programmer and a symbolic program executor, where a program is the composition of a set of pre-defined general atomic and higher-order operations and arguments extracted from table and text.First, the programmer parses a question into a program by generating operations and copying arguments, and then, the executor derives answers from table and text based on the program.To alleviate the costly program annotation issue, we design a distant supervision approach for programmer learning, where pseudo programs are automatically constructed without annotated derivations.Extensive experiments on the TAT-QA dataset show that UniRPG achieves tremendous improvements and enhances interpretability and scalability compared with previous state-of-theart methods, even without derivation annotation.Moreover, it achieves promising performance on the textual dataset DROP without derivation annotation. 1

Yongwei Zhou, Junwei Bao, Chaoqun Duan, Haipeng Sun, Jiahui Liang, Yifan Wang, Jing Zhao, Youzheng Wu, Xiaodong He, Tiejun Zhao. Proceedings of the 2022 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2022.

According to the matrix representation of cubic NURBS surface, this paper presents a sufficient condition of G1continuity between two patches of adjacent cubic NURBS surface and provides specific algorithm for control points and weights of NURBS surface.