# DISK: Domain-constrained Instance Sketch for Math Word Problem Generation

arXiv: https://arxiv.org/abs/2204.04686 · HTML: https://mlsanity.com/paper/2204.04686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 52 references that are in the map.
- First posted on arXiv 10 Apr 2022.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [BART: Denoising Sequence-to-Sequence Pre-training for Natural Language Generation, Translation, and Comprehension](https://mlsanity.com/paper/1910.13461/) (2019)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [CTRL: A Conditional Transformer Language Model for Controllable Generation](https://mlsanity.com/paper/1909.05858/) (2019)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [Challenges in Data-to-Document Generation](https://mlsanity.com/paper/1707.08052/) (2017)
- [Survey of the State of the Art in Natural Language Generation: Core tasks, applications and evaluation](https://mlsanity.com/paper/1703.09902/) (2017)
- [Data-to-Text Generation with Content Selection and Planning](https://mlsanity.com/paper/1809.00582/) (2018)
- [Code Generation as a Dual Task of Code Summarization](https://mlsanity.com/paper/1910.05923/) (2019)
- [Skeleton-to-Response: Dialogue Generation Guided by Retrieval Memory](https://mlsanity.com/paper/1809.05296/) (2018)
- [Data-to-text Generation with Entity Modeling](https://mlsanity.com/paper/1906.03221/) (2019)
- [Response Generation by Context-aware Prototype Editing](https://mlsanity.com/paper/1806.07042/) (2018)
- [Densely Connected Graph Convolutional Networks for Graph-to-Sequence Learning](https://mlsanity.com/paper/1908.05957/) (2019)
- [Annotating Derivations: A New Evaluation Strategy and Dataset for Algebra Word Problems](https://mlsanity.com/paper/1609.07197/) (2016)
- [Math Word Problem Generation with Mathematical Consistency and Problem Context Constraints](https://mlsanity.com/paper/2109.04546/) (2021)
- [Order-Planning Neural Text Generation From Structured Data](https://mlsanity.com/paper/1709.00155/) (2017)
- [Table-to-Text Generation with Effective Hierarchical Encoder on Three Dimensions (Row, Column and Time)](https://mlsanity.com/paper/1909.02304/) (2019)
- [Mathematical Word Problem Generation from Commonsense Knowledge Graph and Equations](https://mlsanity.com/paper/2010.06196/) (2020)
- [Learning to generate one-sentence biographies from Wikidata](https://mlsanity.com/paper/1702.06235/) (2017)
- [Bootstrapping Generators from Noisy Data](https://mlsanity.com/paper/1804.06385/) (2018)
- [Generating Math Word Problems from Equations with Topic Controlling and Commonsense Enforcement](https://mlsanity.com/paper/2012.07379/) (2020)

## Built on by (most cited first, 1 of 1)

- [Towards Generating Controllable and Solvable Geometry Problem by Leveraging Symbolic Deduction Engine](https://mlsanity.com/paper/2506.02565/) (2025)

## Abstract (arXiv)

A math word problem (MWP) is a coherent narrative which reflects the underlying logic of math equations. Successful MWP generation can automate the writing of mathematics questions. Previous methods mainly generate MWP text based on inflexible pre-defined templates. In this paper, we propose a neural model for generating MWP text from math equations. Firstly, we incorporate a matching model conditioned on the domain knowledge to retrieve a MWP instance which is most consistent with the ground-truth, where the domain is a latent variable extracted with a domain summarizer. Secondly, by constructing a Quantity Cell Graph (QCG) from the retrieved MWP instance and reasoning over it, we improve the model's comprehension of real-world scenarios and derive a domain-constrained instance sketch to guide the generation. Besides, the QCG also interacts with the equation encoder to enhance the alignment between math tokens (e.g., quantities and variables) and MWP text. Experiments and empirical analysis on educational MWP set show that our model achieves impressive performance in both automatic evaluation metrics and human evaluation metrics.