# Unit Dependency Graph and its Application to Arithmetic Word Problem Solving

arXiv: https://arxiv.org/abs/1612.00969 · HTML: https://mlsanity.com/paper/1612.00969/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Dec 2016.

## Built on by (most cited first, 25 of 25)

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- [Towards Tractable Mathematical Reasoning: Challenges, Strategies, and Opportunities for Solving Math Word Problems](https://mlsanity.com/paper/2111.05364/) (2021)
- [World Models for Math Story Problems](https://mlsanity.com/paper/2306.04347/) (2023)
- [Why are NLP Models Fumbling at Elementary Math? A Survey of Deep Learning based Word Problem Solvers](https://mlsanity.com/paper/2205.15683/) (2022)
- [Solving Arithmetic Word Problems with Transformers and Preprocessing of Problem Text](https://mlsanity.com/paper/2106.00893/) (2021)
- [Math Word Problem Solving by Generating Linguistic Variants of Problem Statements](https://mlsanity.com/paper/2306.13899/) (2023)
- [Semantic-based Data Augmentation for Math Word Problems](https://mlsanity.com/paper/2201.02489/) (2022)
- [Learning by Applying: A General Framework for Mathematical Reasoning via Enhancing Explicit Knowledge Learning](https://mlsanity.com/paper/2302.05717/) (2023)
- [Generating Pedagogically Meaningful Visuals for Math Word Problems: A New Benchmark and Analysis of Text-to-Image Models](https://mlsanity.com/paper/2506.03735/) (2025)
- [Improving Compositional Generalization in Math Word Problem Solving](https://mlsanity.com/paper/2209.01352/) (2022)
- [WARM: A Weakly (+Semi) Supervised Model for Solving Math word Problems](https://mlsanity.com/paper/2104.06722/) (2021)
- [ComSearch: Equation Searching with Combinatorial Strategy for Solving Math Word Problems with Weak Supervision](https://mlsanity.com/paper/2210.07017/) (2022)
- [Textual Enhanced Contrastive Learning for Solving Math Word Problems](https://mlsanity.com/paper/2211.16022/) (2022)
- [Multi-tool Integration Application for Math Reasoning Using Large Language Model](https://mlsanity.com/paper/2408.12148/) (2024)
- [OLGA : An Ontology and LSTM-based approach for generating Arithmetic Word Problems (AWPs) of transfer type](https://mlsanity.com/paper/2211.12164/) (2022)

## Abstract (arXiv)

Math word problems provide a natural abstraction to a range of natural language understanding problems that involve reasoning about quantities, such as interpreting election results, news about casualties, and the financial section of a newspaper. Units associated with the quantities often provide information that is essential to support this reasoning. This paper proposes a principled way to capture and reason about units and shows how it can benefit an arithmetic word problem solver. This paper presents the concept of Unit Dependency Graphs (UDGs), which provides a compact representation of the dependencies between units of numbers mentioned in a given problem. Inducing the UDG alleviates the brittleness of the unit extraction system and allows for a natural way to leverage domain knowledge about unit compatibility, for word problem solving. We introduce a decomposed model for inducing UDGs with minimal additional annotations, and use it to augment the expressions used in the arithmetic word problem solver of (Roy and Roth 2015) via a constrained inference framework. We show that introduction of UDGs reduces the error of the solver by over 10 %, surpassing all existing systems for solving arithmetic word problems. In addition, it also makes the system more robust to adaptation to new vocabulary and equation forms .