# Weakly Supervised Neuro-Symbolic Module Networks for Numerical Reasoning

arXiv: https://arxiv.org/abs/2101.11802 · HTML: https://mlsanity.com/paper/2101.11802/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 25 references that are in the map.
- First posted on arXiv 28 Jan 2021.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [Seq2SQL: Generating Structured Queries from Natural Language using Reinforcement Learning](https://mlsanity.com/paper/1709.00103/) (2017)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Injecting Numerical Reasoning Skills into Language Models](https://mlsanity.com/paper/2004.04487/) (2020)
- [Neural Symbolic Machines: Learning Semantic Parsers on Freebase with Weak Supervision](https://mlsanity.com/paper/1611.00020/) (2016)
- [Neural Module Networks for Reasoning over Text](https://mlsanity.com/paper/1912.04971/) (2019)
- [NumNet: Machine Reading Comprehension with Numerical Reasoning](https://mlsanity.com/paper/1910.06701/) (2019)
- [Memory Augmented Policy Optimization for Program Synthesis and Semantic Parsing](https://mlsanity.com/paper/1807.02322/) (2018)
- [A Multi-Type Multi-Span Network for Reading Comprehension that Requires Discrete Reasoning](https://mlsanity.com/paper/1908.05514/) (2019)
- [Obtaining Faithful Interpretations from Compositional Neural Networks](https://mlsanity.com/paper/2005.00724/) (2020)
- [Learning a Natural Language Interface with Neural Programmer](https://mlsanity.com/paper/1611.08945/) (2016)

## Built on by (most cited first, 10 of 10)

- [From LSAT: The Progress and Challenges of Complex Reasoning](https://mlsanity.com/paper/2108.00648/) (2021)
- [DAGN: Discourse-Aware Graph Network for Logical Reasoning](https://mlsanity.com/paper/2103.14349/) (2021)
- [Summarization Programs: Interpretable Abstractive Summarization with Neural Modular Trees](https://mlsanity.com/paper/2209.10492/) (2022)
- [Neuro-Symbolic AI: Explainability, Challenges, and Future Trends](https://mlsanity.com/paper/2411.04383/) (2024)
- [MURMUR: Modular Multi-Step Reasoning for Semi-Structured Data-to-Text Generation](https://mlsanity.com/paper/2212.08607/) (2022)
- [Improving Numerical Reasoning Skills in the Modular Approach for Complex Question Answering on Text](https://mlsanity.com/paper/2109.02289/) (2021)
- [Unsupervised Numerical Reasoning to Extract Phenotypes from Clinical Text by Leveraging External Knowledge](https://mlsanity.com/paper/2204.10202/) (2022)
- [Discourse-Aware Graph Networks for Textual Logical Reasoning](https://mlsanity.com/paper/2207.01450/) (2022)
- [Teaching Neural Module Networks to Do Arithmetic](https://mlsanity.com/paper/2210.02703/) (2022)
- [Bridging the Gap: Representation Spaces in Neuro-Symbolic AI](https://mlsanity.com/paper/2411.04393/) (2024)

## Abstract (arXiv)

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 reasoning modules and fail to generalize to more open-ended settings without such supervision. Hence 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 the 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 DROP, WNSMN out-performs 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.