Weakly Supervised Neuro-Symbolic Module Networks for Numerical Reasoning
Authors: Amrita Saha, Shafiq Joty, Steven Hoi
Keywords: neural module networks, machine reading comprehension, numerical reasoning over text
Abstract: Neural Module Networks (NMNs) have been quite successful in incorporating explicit reasoning as learnable modules in various question answering tasks, including the most generic form of numerical reasoning over text  in Machine Reading Comprehension (MRC). However, to achieve this, contemporary NMNs need strong supervision in executing the query as a specialized program over the reasoning modules and fail to generalize to more open-ended settings where such supervision is not readily available. In this work, we propose Weakly Supervised Neuro-Symbolic Module Network (WNSMN) trained with answers as the sole supervision for numerical reasoning based MRC. It learns to execute a noisy heuristic program obtained from dependency parsing of the query as discrete actions over both neural and symbolic reasoning modules and trains it end-to-end in a reinforcement learning framework with discrete reward from answer matching. On the numerical-answer subset of the DROP dataset, WNSMN outperforms NMN by 32% and the reasoning-free language model GenBERT by 8% in exact match accuracy when trained under comparable weak supervised settings. This showcases the effectiveness and generalizability of modular networks that can handle explicit discrete reasoning over noisy programs in an end-to-end manner.