L^2M: Mutual Information Scaling Law for Long-Context Language
  Modeling
Authors: name: Zhuo Chen; name: Oriol Mayné i Comas; name: Zhuotao Jin; name: Di Luo; name: Marin Soljačić
Published: 2025-03-06 18:59:48

Abstract: We rigorously establish a bipartite mutual information scaling law in natural
language that governs long-range dependencies. This scaling law, which we show
is distinct from and scales independently of the conventional two-point mutual
information, is the key to understanding long-context language modeling. Using
this scaling law, we formulate the Long-context Language Modeling (L^2M)
condition, which relates a model's capacity for effective long context length
modeling to the scaling of its latent state size for storing past information.
Our results are validated through experiments on both transformers and state
space models. This work establishes a theoretical foundation that guides the
development of large language models toward longer context lengths.