Auto-Regressive Next-Token Predictors are Universal Learners
Eran Malach
Large language models display remarkable capabilities in logical and
mathematical reasoning, allowing them to solve complex tasks. Interestingly,
these abilities emerge in networks trained on the simple task of next-token
prediction. In this work, we present a theoretical framework for studying
auto-regressive next-token predictors. We demonstrate that even simple models
such as linear next-token predictors, trained on Chain-of-Thought (CoT) data,
can approximate any function efficiently computed by a Turing machine. We
introduce a new complexity measure -- length complexity -- which measures the
number of intermediate tokens in a CoT sequence required to approximate some
target function, and analyze the interplay between length complexity and other
notions of complexity. Finally, we show experimentally that simple next-token
predictors, such as linear networks and shallow Multi-Layer Perceptrons (MLPs),
display non-trivial performance on text generation and arithmetic tasks. Our
results demonstrate that the power of language models can be attributed, to a
great extent, to the auto-regressive next-token training scheme, and not
necessarily to a particular choice of architecture.