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

TL;DR

This study investigates how ALBERT language models internally represent numerical concepts, revealing they encode basic quantitative reasoning through learned embeddings and PCA analysis.

Contribution

The paper introduces a method to analyze internal numerical representations in language models and demonstrates ALBERT's ability to encode numerical orderings.

Findings

ALBERT models encode numerical orderings along principal axes.

Numerals and textual numbers form separate but similarly oriented clusters.

Language models can implicitly learn basic mathematical concepts.

Abstract

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.