Given that rich information is hidden behind ubiquitous numbers in text, numerical reasoning over text should be an essential skill of AI systems. To derive precise equations to solve numerical reasoning problems, previous work focused on modeling the structures of equations, and has proposed various structured decoders. Though structure modeling proves to be effective, these structured decoders construct a single equation in a pre-defined autoregressive order, potentially placing an unnecessary restriction on how a model should grasp the reasoning process. Intuitively, humans may have numerous pieces of thoughts popping up in no pre-defined order; thoughts are not limited to the problem at hand, and can even be concerned with other related problems. By comparing diverse thoughts and chaining relevant pieces, humans are less prone to errors. In this paper, we take this inspiration and propose CANTOR, a numerical reasoner that models reasoning steps using a directed acyclic graph where we produce diverse reasoning steps simultaneously without pre-defined decoding dependencies, and compare and chain relevant ones to reach a solution. Extensive experiments demonstrated the effectiveness of CANTOR under both fully-supervised and weakly-supervised settings.

Open-domain questions are likely to be open-ended and ambiguous, leading to multiple valid answers. Existing approaches typically adopt the rerank-then-read framework, where a reader reads top-ranking evidence to predict answers. According to our empirical analysis, this framework faces three problems: first, to leverage a large reader under a memory constraint, the reranker should select only a few relevant passages to cover diverse answers, while balancing relevance and diversity is non-trivial; second, the small reading budget prevents the reader from accessing valuable retrieved evidence filtered out by the reranker; third, when using a generative reader to predict answers all at once based on all selected evidence, whether a valid answer will be predicted also pathologically depends on evidence of some other valid answer(s). To address these issues, we propose to answer open-domain multi-answer questions with a recall-then-verify framework, which separates the reasoning process of each answer so that we can make better use of retrieved evidence while also leveraging large models under the same memory constraint. Our framework achieves state-of-the-art results on two multi-answer datasets, and predicts significantly more gold answers than a rerank-then-read system that uses an oracle reranker.

Weakly supervised question answering usually has only the final answers as supervision signals while the correct solutions to derive the answers are not provided. This setting gives rise to the spurious solution problem: there may exist many spurious solutions that coincidentally derive the correct answer, but training on such solutions can hurt model performance (e.g., producing wrong solutions or answers). For example, for discrete reasoning tasks as on DROP, there may exist many equations to derive a numeric answer, and typically only one of them is correct. Previous learning methods mostly filter out spurious solutions with heuristics or using model confidence, but do not explicitly exploit the semantic correlations between a question and its solution. In this paper, to alleviate the spurious solution problem, we propose to explicitly exploit such semantic correlations by maximizing the mutual information between question-answer pairs and predicted solutions. Extensive experiments on four question answering datasets show that our method significantly outperforms previous learning methods in terms of task performance and is more effective in training models to produce correct solutions.

Existing neural methods for data-to-text generation are still struggling to produce long and diverse texts: they are insufficient to model input data dynamically during generation, to capture inter-sentence coherence, or to generate diversified expressions. To address these issues, we propose a Planning-based Hierarchical Variational Model (PHVM). Our model first plans a sequence of groups (each group is a subset of input items to be covered by a sentence) and then realizes each sentence conditioned on the planning result and the previously generated context, thereby decomposing long text generation into dependent sentence generation sub-tasks. To capture expression diversity, we devise a hierarchical latent structure where a global planning latent variable models the diversity of reasonable planning and a sequence of local latent variables controls sentence realization. Experiments show that our model outperforms state-of-the-art baselines in long and diverse text generation.