Chaining Simultaneous Thoughts for Numerical Reasoning

TL;DR

CANTOR is a novel numerical reasoning model that generates diverse reasoning steps simultaneously in a graph structure, mimicking human-like flexible thought chaining to improve accuracy in solving problems.

Contribution

This paper introduces CANTOR, a new approach that models reasoning as a directed acyclic graph with parallel thought generation, moving beyond traditional sequential equation decoding.

Findings

CANTOR outperforms existing models on numerical reasoning benchmarks.

It effectively utilizes both fully-supervised and weakly-supervised training.

The approach reduces errors by comparing and chaining diverse reasoning steps.

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.