# Exploring Internal Numeracy in Language Models: A Case Study on ALBERT

arXiv: https://arxiv.org/abs/2404.16574 · HTML: https://mlsanity.com/paper/2404.16574/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 25 Apr 2024.

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

- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Analysing Mathematical Reasoning Abilities of Neural Models](https://mlsanity.com/paper/1904.01557/) (2019)
- [LUKE: Deep Contextualized Entity Representations with Entity-aware Self-attention](https://mlsanity.com/paper/2010.01057/) (2020)
- [Do NLP Models Know Numbers? Probing Numeracy in Embeddings](https://mlsanity.com/paper/1909.07940/) (2019)
- [Phrase-Based & Neural Unsupervised Machine Translation](https://mlsanity.com/paper/1804.07755/) (2018)
- [Birds have four legs?! NumerSense: Probing Numerical Commonsense Knowledge of Pre-trained Language Models](https://mlsanity.com/paper/2005.00683/) (2020)
- [Meta-Learning for Low-Resource Neural Machine Translation](https://mlsanity.com/paper/1808.08437/) (2018)
- [Pre-Training Transformers as Energy-Based Cloze Models](https://mlsanity.com/paper/2012.08561/) (2020)
- [Take and Took, Gaggle and Goose, Book and Read: Evaluating the Utility of Vector Differences for Lexical Relation Learning](https://mlsanity.com/paper/1509.01692/) (2015)
- [The Case for Translation-Invariant Self-Attention in Transformer-Based Language Models](https://mlsanity.com/paper/2106.01950/) (2021)
- [How Much Coffee Was Consumed During EMNLP 2019? Fermi Problems: A New Reasoning Challenge for AI](https://mlsanity.com/paper/2110.14207/) (2021)
- [On the Transformation of Latent Space in Fine-Tuned NLP Models](https://mlsanity.com/paper/2210.12696/) (2022)
- [Mathematical Reasoning in Latent Space](https://mlsanity.com/paper/1909.11851/) (2019)
- [Learning Numeral Embeddings](https://mlsanity.com/paper/2001.00003/) (2019)
- [NumGPT: Improving Numeracy Ability of Generative Pre-trained Models](https://mlsanity.com/paper/2109.03137/) (2021)
- [Multi-Operational Mathematical Derivations in Latent Space](https://mlsanity.com/paper/2311.01230/) (2023)
- [Improving Downstream Task Performance by Treating Numbers as Entities](https://mlsanity.com/paper/2205.03559/) (2022)

## Abstract (arXiv)

It has been found that Transformer-based language models have the ability to perform basic quantitative reasoning. In this paper, we propose a method for studying how these models internally represent numerical data, and use our proposal to analyze the ALBERT family of language models. Specifically, we extract the learned embeddings these models use to represent tokens that correspond to numbers and ordinals, and subject these embeddings to Principal Component Analysis (PCA). PCA results reveal that ALBERT models of different sizes, trained and initialized separately, consistently learn to use the axes of greatest variation to represent the approximate ordering of various numerical concepts. Numerals and their textual counterparts are represented in separate clusters, but increase along the same direction in 2D space. Our findings illustrate that language models, trained purely to model text, can intuit basic mathematical concepts, opening avenues for NLP applications that intersect with quantitative reasoning.