Investigating the Limitations of Transformers with Simple Arithmetic Tasks

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 seem to learn addition rules that are independent of the length of the numbers seen during training. Abstraction and composition are two important themes in the study of human languages, made possible by different linguistic representations. Although treatments in different linguistic traditions vary, representations at the lexical, syntactic, and semantic levels are a common feature in nearly all theoretical studies of human language, and until relatively recently, these representations are explicitly "materialized" in language processing pipelines (for example, semantic role labeling takes as input a syntactic parse).