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.
翻译:鉴于大量信息隐藏在文本中无处不在的数字背后,对文本的数字推理应该是AI系统的基本技能。为了得出解决数字推理问题的精确方程式,先前的工作侧重于模拟方程结构结构,并提出了各种结构解码器。虽然结构模型证明是有效的,但这些结构化解码器在预先定义的自动递减顺序下构建了一个单一方程式,可能对模型如何掌握推理过程施加不必要的限制。自然,人类可能有许多想法在不预先界定的顺序下涌现出来;思想并不局限于手头的问题,甚至可以关注其他相关问题。通过比较各种不同的想法和链条,人类不太容易出现错误。在本文中,我们利用这种启发和提议CANtor,一个数字解释器,即模型推理步骤使用定向的单行图,在不预先界定解码依赖的情况下同时产生不同的推理步骤,比较相关的步骤,以达成解决办法。广泛的实验展示了在完全监督和薄弱的封闭环境中的CANTOR的有效性。