When can transformers reason with abstract symbols?
Authors: name: Enric Boix-Adsera, name: Omid Saremi, name: Emmanuel Abbe, name: Samy Bengio, name: Etai Littwin, name: Joshua Susskind

We investigate the capabilities of transformer large language models (LLMs)
on relational reasoning tasks involving abstract symbols. Such tasks have long
been studied in the neuroscience literature as fundamental building blocks for
more complex abilities in programming, mathematics, and verbal reasoning. For
(i) regression tasks, we prove that transformers generalize when trained, but
require astonishingly large quantities of training data. For (ii)
next-token-prediction tasks with symbolic labels, we show an "inverse scaling
law": transformers fail to generalize as their embedding dimension increases.
For both settings (i) and (ii), we propose subtle transformer modifications
which can reduce the amount of data needed by adding two trainable parameters
per head.