Auto-Regressive Next-Token Predictors are Universal Learners

TL;DR

This paper presents a theoretical framework showing that simple auto-regressive next-token predictors, like linear models, can approximate complex functions and exhibit advanced reasoning abilities, highlighting the fundamental power of the next-token training scheme.

Contribution

The work introduces a new complexity measure called length complexity and demonstrates that simple models trained on next-token prediction can perform complex reasoning tasks.

Findings

Linear next-token predictors can approximate Turing-complete functions.

Simple models show non-trivial performance on reasoning and arithmetic tasks.

The power of large language models largely stems from the auto-regressive training scheme.

Abstract

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 today's LLMs can be attributed, to a great extent, to the auto-regressive next-token training scheme, and not necessarily to a particular choice of architecture.