Chaining Simultaneous Thoughts for Numerical Reasoning (2022)

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 effectiveness of CANTOR under both fully-supervised and weakly-supervised settings.

## introduction numerical reasoning over text is an essential skill for a neural model to help analyze rich numerical information from large-scale textual data @xcite . many question answering benchmarks @xcite have been created to promote the numerical reasoning ability of neural models, where, typically, models are required to answer questions about given contexts with numerical answers. this is challenging, as it requires comprehensive structural analyses of text as well as precise and possibly complex deduction. * *corresponding author: minlie huang. ## task definition given a problem description x which mentions a list of numbers @xmath0, n 2 , ..., n |n | }, our task is to return the numerical answer a which is derived from an equation y that takes arithmetic operations (e.g., addition, subtraction, multiplication, division, and exponentiation) on n as well as a set of predefined constants @xmath1, c 2 , ..., c |c| }. for scenarios that consider only binary operators foot_0 , a ground-truth equation y can be formally defined as follows: ## conclusion we propose a numerical reasoner called cantor. unlike previous structured decoders that model a single equation with pre-defined restrictions on the decoding dependencies, cantor models diverse reasoning steps using a directed acyclic graph without a pre-defined decoding order, and derives equations by comparing and chaining relevant reasoning steps. with our training methods, cantor is capable of capturing the logical dependencies among reasoning steps internally, and produces equations that are more consistent with the reasoning problems by comparing diverse reasoning steps. can-tor achieves state-of-the-art results on two math word problem datasets under the fully-supervised setting, and is applicable to weakly-supervised scenarios with significant improvements. in future work, we plan to extend cantor for general structured prediction tasks, e.g., sequence labeling and parsing.