# Learning Mathematical Properties of Integers

arXiv: https://arxiv.org/abs/2109.07230 · HTML: https://mlsanity.com/paper/2109.07230/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 15 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Enriching Word Vectors with Subword Information](https://mlsanity.com/paper/1607.04606/) (2016)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [What do Neural Machine Translation Models Learn about Morphology?](https://mlsanity.com/paper/1704.03471/) (2017)
- [Representing Numbers in NLP: a Survey and a Vision](https://mlsanity.com/paper/2103.13136/) (2021)
- [Probabilistic Latent Semantic Analysis](https://mlsanity.com/paper/1301.6705/) (2013)

## Built on by (most cited first, 4 of 4)

- [Deep Symbolic Regression for Recurrent Sequences](https://mlsanity.com/paper/2201.04600/) (2022)
- [Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning models](https://mlsanity.com/paper/2303.07735/) (2023)
- [FACT: Learning Governing Abstractions Behind Integer Sequences](https://mlsanity.com/paper/2209.09543/) (2022)
- [KitBit: A New AI Model for Solving Intelligence Tests and Numerical Series](https://mlsanity.com/paper/2206.08965/) (2022)

## Abstract (arXiv)

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora.