Explaining Context Length Scaling and Bounds for Language Models

Long Context Language Models have drawn great attention in the past few years. There has been work discussing the impact of long context on Language Model performance: some find that long irrelevant context could harm performance, while some experimentally summarize loss reduction by relevant long context as Scaling Laws. This calls for a more thorough understanding on how long context impacts Language Modeling. In this work, we (1) propose a clean and effective theoretical framework for explaining the impact of context length on Language Modeling, from an Intrinsic Space perspective; and (2) conduct experiments on natural language and synthetic data, validating our proposed theoretical assumptions and deductions. Our theoretical framework can provide practical insights such as establishing that training dataset size dictates an optimal context length and bounds context length scaling for certain cases. We hope our work may inspire new long context Language Models, as well as future work studying Physics for Language Models. Code for our experiments is available at: this https URL.