Investigating the Limitations of Transformers with Simple Arithmetic Tasks

TL;DR

This paper examines how the surface form of numbers affects the ability of transformer-based language models to learn simple arithmetic tasks, revealing that representation choices significantly impact accuracy and generalization.

Contribution

It demonstrates that proper surface representations enable models to learn and generalize arithmetic operations, highlighting limitations of current tokenization and positional encoding methods.

Findings

Number representation strongly influences model accuracy

Position tokens improve learning of long-number arithmetic

Models fail to generalize addition rules across different number lengths

Abstract

The ability to perform arithmetic tasks is a remarkable trait of human intelligence and might form a critical component of more complex reasoning tasks. In this work, we investigate if the surface form of a number has any influence on how sequence-to-sequence language models learn simple arithmetic tasks such as addition and subtraction across a wide range of values. We find that how a number is represented in its surface form has a strong influence on the model's accuracy. In particular, the model fails to learn addition of five-digit numbers when using subwords (e.g., "32"), and it struggles to learn with character-level representations (e.g., "3 2"). By introducing position tokens (e.g., "3 10e1 2"), the model learns to accurately add and subtract numbers up to 60 digits. We conclude that modern pretrained language models can easily learn arithmetic from very few examples, as long as we use the proper surface representation. This result bolsters evidence that subword tokenizers and positional encodings are components in current transformer designs that might need improvement. Moreover, we show that regardless of the number of parameters and training examples, models cannot learn addition rules that are independent of the length of the numbers seen during training. Code to reproduce our experiments is available at https://github.com/castorini/transformers-arithmetic