Towards Auto-Regressive Next-Token Prediction: In-Context Learning Emerges from Generalization

TL;DR

This paper provides a theoretical framework for understanding how in-context learning emerges from generalization in large language models, focusing on auto-regressive next-token prediction and addressing limitations of previous analyses.

Contribution

It introduces a formal pre-training and ICL framework emphasizing sequence and topic dependencies, with new PAC-Bayesian generalization bounds for LLMs.

Findings

ICL emerges from sequence and topic generalization.

Theoretical bounds depend on data, topics, and optimization.

Experimental validation on synthetic and real datasets.

Abstract

Large language models (LLMs) have demonstrated remarkable in-context learning (ICL) abilities. However, existing theoretical analysis of ICL primarily exhibits two limitations: (a) Limited i.i.d. Setting. Most studies focus on supervised function learning tasks where prompts are constructed with i.i.d. input-label pairs. This i.i.d. assumption diverges significantly from real language learning scenarios where prompt tokens are interdependent. (b) Lack of Emergence Explanation. Most literature answers what ICL does from an implicit optimization perspective but falls short in elucidating how ICL emerges and the impact of pre-training phase on ICL. In our paper, to extend (a), we adopt a more practical paradigm, auto-regressive next-token prediction (AR-NTP), which closely aligns with the actual training of language models. Specifically, within AR-NTP, we emphasize prompt token-dependency, which involves predicting each subsequent token based on the preceding sequence. To address (b), we formalize a systematic pre-training and ICL framework, highlighting the layer-wise structure of sequences and topics, alongside a two-level expectation. In conclusion, we present data-dependent, topic-dependent and optimization-dependent PAC-Bayesian generalization bounds for pre-trained LLMs, investigating that ICL emerges from the generalization of sequences and topics. Our theory is supported by experiments on numerical linear dynamic systems, synthetic GINC and real-world language datasets.