# OLGA : An Ontology and LSTM-based approach for generating Arithmetic Word Problems (AWPs) of transfer type

arXiv: https://arxiv.org/abs/2211.12164 · HTML: https://mlsanity.com/paper/2211.12164/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 43 references that are in the map.
- First posted on arXiv 22 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Bag of Tricks for Efficient Text Classification](https://mlsanity.com/paper/1607.01759/) (2016)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Solving General Arithmetic Word Problems](https://mlsanity.com/paper/1608.01413/) (2016)
- [word2vec Explained: deriving Mikolov et al.'s negative-sampling word-embedding method](https://mlsanity.com/paper/1402.3722/) (2014)
- [Gmail Smart Compose: Real-Time Assisted Writing](https://mlsanity.com/paper/1906.00080/) (2019)
- [Gated Feedback Recurrent Neural Networks](https://mlsanity.com/paper/1502.02367/) (2015)
- [Unit Dependency Graph and its Application to Arithmetic Word Problem Solving](https://mlsanity.com/paper/1612.00969/) (2016)
- [A Theme-Rewriting Approach for Generating Algebra Word Problems](https://mlsanity.com/paper/1610.06210/) (2016)

## Abstract (arXiv)

Machine generation of Arithmetic Word Problems (AWPs) is challenging as they express quantities and mathematical relationships and need to be consistent. ML-solvers require a large annotated training set of consistent problems with language variations. Exploiting domain-knowledge is needed for consistency checking whereas LSTM-based approaches are good for producing text with language variations. Combining these we propose a system, OLGA, to generate consistent word problems of TC (Transfer-Case) type, involving object transfers among agents. Though we provide a dataset of consistent 2-agent TC-problems for training, only about 36% of the outputs of an LSTM-based generator are found consistent. We use an extension of TC-Ontology, proposed by us previously, to determine the consistency of problems. Among the remaining 64%, about 40% have minor errors which we repair using the same ontology. To check consistency and for the repair process, we construct an instance-specific representation (ABox) of an auto-generated problem. We use a sentence classifier and BERT models for this task. The training set for these LMs is problem-texts where sentence-parts are annotated with ontology class-names. As three-agent problems are longer, the percentage of consistent problems generated by an LSTM-based approach drops further. Hence, we propose an ontology-based method that extends consistent 2-agent problems into consistent 3-agent problems. Overall, our approach generates a large number of consistent TC-type AWPs involving 2 or 3 agents. As ABox has all the information of a problem, any annotations can also be generated. Adopting the proposed approach to generate other types of AWPs is interesting future work.