Exploring Internal Numeracy in Language Models: A Case Study on ALBERT
This provides insight into how language models trained on text can develop basic mathematical understanding, potentially benefiting NLP applications requiring quantitative reasoning.
The researchers investigated how ALBERT language models internally represent numerical data by analyzing learned embeddings for number tokens using Principal Component Analysis. They found that different ALBERT models consistently use the principal axes to represent approximate numerical ordering, with numerals and their textual counterparts forming separate clusters but increasing along the same direction.
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.