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-the-art methods, even without derivation annotation. Moreover, it achieves promising performance on the textual dataset DROP without derivation annotation.

Machine reading comprehension (MRC) that requires discrete reasoning involving symbolic operations, e.g., addition, sorting, and counting, is a challenging task. According to this nature, semantic parsing-based methods predict interpretable but complex logical forms. However, logical form generation is nontrivial and even a little perturbation in a logical form will lead to wrong answers. To alleviate this issue, multi-predictor -based methods are proposed to directly predict different types of answers and achieve improvements. However, they ignore the utilization of symbolic operations and encounter a lack of reasoning ability and interpretability. To inherit the advantages of these two types of methods, we propose OPERA, an operation-pivoted discrete reasoning framework, where lightweight symbolic operations (compared with logical forms) as neural modules are utilized to facilitate the reasoning ability and interpretability. Specifically, operations are first selected and then softly executed to simulate the answer reasoning procedure. Extensive experiments on both DROP and RACENum datasets show the reasoning ability of OPERA. Moreover, further analysis verifies its interpretability.

Transformer-based pre-trained models, such as BERT, have achieved remarkable results on machine reading comprehension. However, due to the constraint of encoding length (e.g., 512 WordPiece tokens), a long document is usually split into multiple chunks that are independently read. It results in the reading field being limited to individual chunks without information collaboration for long document machine reading comprehension. To address this problem, we propose RoR, a read-over-read method, which expands the reading field from chunk to document. Specifically, RoR includes a chunk reader and a document reader. The former first predicts a set of regional answers for each chunk, which are then compacted into a highly-condensed version of the original document, guaranteeing to be encoded once. The latter further predicts the global answers from this condensed document. Eventually, a voting strategy is utilized to aggregate and rerank the regional and global answers for final prediction. Extensive experiments on two benchmarks QuAC and TriviaQA demonstrate the effectiveness of RoR for long document reading. Notably, RoR ranks 1st place on the QuAC leaderboard (https://quac.ai/) at the time of submission (May 17th, 2021).