Weakly Supervised Neuro-Symbolic Module Networks for Numerical Reasoning

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.

One-sentence Summary: A weak supervised neural module network for numerical reasoning based Reading Comprehension which learns to execute a noisy generalized program form of the query over both neural and symbolic reasoning modules with the answer as the sole supervision.

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