# Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction

arXiv: https://arxiv.org/abs/2203.10316 · HTML: https://mlsanity.com/paper/2203.10316/

## Key facts

- Cited by 44 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 75 references that are in the map.
- First posted on arXiv 19 Mar 2022.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 29 of 29)

- [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)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Unsupervised Cross-lingual Representation Learning at Scale](https://mlsanity.com/paper/1911.02116/) (2019)
- [Transformers are RNNs: Fast Autoregressive Transformers with Linear Attention](https://mlsanity.com/paper/2006.16236/) (2020)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems](https://mlsanity.com/paper/1705.04146/) (2017)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [Six Challenges for Neural Machine Translation](https://mlsanity.com/paper/1706.03872/) (2017)
- [Rationalizing Neural Predictions](https://mlsanity.com/paper/1606.04155/) (2016)
- [End-to-end Neural Coreference Resolution](https://mlsanity.com/paper/1707.07045/) (2017)
- [Lexically Constrained Decoding for Sequence Generation Using Grid Beam Search](https://mlsanity.com/paper/1704.07138/) (2017)
- [Neural-Symbolic Learning and Reasoning: A Survey and Interpretation](https://mlsanity.com/paper/1711.03902/) (2017)
- [Higher-order Coreference Resolution with Coarse-to-fine Inference](https://mlsanity.com/paper/1804.05392/) (2018)
- [Generate & Rank: A Multi-task Framework for Math Word Problems](https://mlsanity.com/paper/2109.03034/) (2021)
- [Neural Module Networks for Reasoning over Text](https://mlsanity.com/paper/1912.04971/) (2019)
- [Semantically-Aligned Equation Generation for Solving and Reasoning Math Word Problems](https://mlsanity.com/paper/1811.00720/) (2018)
- [MWPToolkit: An Open-Source Framework for Deep Learning-Based Math Word Problem Solvers](https://mlsanity.com/paper/2109.00799/) (2021)
- [Neural-Symbolic Solver for Math Word Problems with Auxiliary Tasks](https://mlsanity.com/paper/2107.01431/) (2021)
- [Mapping to Declarative Knowledge for Word Problem Solving](https://mlsanity.com/paper/1712.09391/) (2017)
- [Graph-to-Tree Neural Networks for Learning Structured Input-Output Translation with Applications to Semantic Parsing and Math Word Problem](https://mlsanity.com/paper/2004.13781/) (2020)
- [Seeking Patterns, Not just Memorizing Procedures: Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2110.08464/) (2021)
- [Investigating Math Word Problems using Pretrained Multilingual Language Models](https://mlsanity.com/paper/2105.08928/) (2021)
- [A Meaning-based Statistical English Math Word Problem Solver](https://mlsanity.com/paper/1803.06064/) (2018)

## Built on by (most cited first, 30 of 44)

- [WizardMath: Empowering Mathematical Reasoning for Large Language Models via Reinforced Evol-Instruct](https://mlsanity.com/paper/2308.09583/) (2023)
- [Scaling Relationship on Learning Mathematical Reasoning with Large Language Models](https://mlsanity.com/paper/2308.01825/) (2023)
- [REFINER: Reasoning Feedback on Intermediate Representations](https://mlsanity.com/paper/2304.01904/) (2023)
- [A Survey of Deep Learning for Mathematical Reasoning](https://mlsanity.com/paper/2212.10535/) (2022)
- [A Review of Large Language Models and Autonomous Agents in Chemistry](https://mlsanity.com/paper/2407.01603/) (2024)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [Self-Contrast: Better Reflection Through Inconsistent Solving Perspectives](https://mlsanity.com/paper/2401.02009/) (2024)
- [Interpreting and Improving Large Language Models in Arithmetic Calculation](https://mlsanity.com/paper/2409.01659/) (2024)
- [Let GPT be a Math Tutor: Teaching Math Word Problem Solvers with Customized Exercise Generation](https://mlsanity.com/paper/2305.14386/) (2023)
- [Mathematical Language Models: A Survey](https://mlsanity.com/paper/2312.07622/) (2023)
- [A Symbolic Character-Aware Model for Solving Geometry Problems](https://mlsanity.com/paper/2308.02823/) (2023)
- [Interpretable Math Word Problem Solution Generation Via Step-by-step Planning](https://mlsanity.com/paper/2306.00784/) (2023)
- [MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning](https://mlsanity.com/paper/2307.07951/) (2023)
- [Chaining Simultaneous Thoughts for Numerical Reasoning](https://mlsanity.com/paper/2211.16482/) (2022)
- [Multi-View Reasoning: Consistent Contrastive Learning for Math Word Problem](https://mlsanity.com/paper/2210.11694/) (2022)
- [Learning Multi-Step Reasoning by Solving Arithmetic Tasks](https://mlsanity.com/paper/2306.01707/) (2023)
- [Design of Chain-of-Thought in Math Problem Solving](https://mlsanity.com/paper/2309.11054/) (2023)
- [A Survey on Mathematical Reasoning and Optimization with Large Language Models](https://mlsanity.com/paper/2503.17726/) (2025)
- [Self-consistent Reasoning For Solving Math Word Problems](https://mlsanity.com/paper/2210.15373/) (2022)
- [DyRRen: A Dynamic Retriever-Reranker-Generator Model for Numerical Reasoning over Tabular and Textual Data](https://mlsanity.com/paper/2211.12668/) (2022)
- [A Survey in Mathematical Language Processing](https://mlsanity.com/paper/2205.15231/) (2022)
- [Fill in the Blank: Exploring and Enhancing LLM Capabilities for Backward Reasoning in Math Word Problems](https://mlsanity.com/paper/2310.01991/) (2023)
- [Three Questions Concerning the Use of Large Language Models to Facilitate Mathematics Learning](https://mlsanity.com/paper/2310.13615/) (2023)
- [Exploring the Limitations of Large Language Models in Compositional Relation Reasoning](https://mlsanity.com/paper/2403.02615/) (2024)
- [APOLLO: An Optimized Training Approach for Long-form Numerical Reasoning](https://mlsanity.com/paper/2212.07249/) (2022)
- [Non-Autoregressive Math Word Problem Solver with Unified Tree Structure](https://mlsanity.com/paper/2305.04556/) (2023)
- [Math Word Problem Solving by Generating Linguistic Variants of Problem Statements](https://mlsanity.com/paper/2306.13899/) (2023)
- [Learning by Applying: A General Framework for Mathematical Reasoning via Enhancing Explicit Knowledge Learning](https://mlsanity.com/paper/2302.05717/) (2023)
- [Chain-of-Translation Prompting (CoTR): A Novel Prompting Technique for Low Resource Languages](https://mlsanity.com/paper/2409.04512/) (2024)
- [Analogical Math Word Problems Solving with Enhanced Problem-Solution Association](https://mlsanity.com/paper/2212.00837/) (2022)

## Abstract (arXiv)

Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.