Chaining Simultaneous Thoughts for Numerical Reasoning
Zhihong Shao, Fei Huang, Minlie Huang The CoAI group, DCST, Tsinghua University, Institute for Artificial Intelligence; State Key Lab of Intelligent Technology and Systems; Beijing National Research Center for Information Science and Technology; Tsinghua University, Beijing 100084, China {szh19, *Corresponding author: Minlie Huang.
Abstract
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 effectivene
中文速览
文本中的数字往往蕴含丰富信息，让AI系统真正"读懂数字"并完成数值推理（numerical reasoning）一直是个难题。以往的方法都依赖预先设定好的顺序（从上到下或从下到上）来逐步构建方程，这种强制性的解码顺序可能反而妨碍模型自由地理解数字之间的逻辑关系。受人类思维"多线并发、比较筛选"的启发，本文提出了CANTOR模型：它用有向无环图（DAG）同时生成多条推理步骤，不规定任何解码顺序，再通过比较和串联这些步骤来得出最终方程。在有标注方程和仅有最终答案两种监督设置下，CANTOR均超越了此前最优方法，甚至在部分数据集上以小模型之身胜过参数量大出数百倍、使用思维链提示的PaLM-62B，为数值推理提供了全新的建模思路。
原文 arXiv:2211.16482;中英对照 + 大白话阅读 https://aha.fim.ai/paper/2211.16482v1