L$^2$M: Mutual Information Scaling Law for Long-Context Language Modeling
This provides a principled foundation for designing more efficient architectures with stronger long-context capabilities, potentially benefiting natural language processing and beyond.
The paper tackled the problem of understanding long-context language modeling by developing a theoretical framework based on bipartite mutual information scaling laws, which they validated on transformer and state-space models, showing it captures multi-token interactions distinct from conventional methods.
We present a universal theoretical framework for understanding long-context language modeling based on a bipartite mutual information scaling law that we rigorously verify in natural language. We demonstrate that bipartite mutual information captures multi-token interactions distinct from and scaling independently of conventional two-point mutual information, and show that this provides a more complete characterization of the dependencies needed for accurately modeling long sequences. Leveraging this scaling law, we formulate the Long-context Language Modeling (L$^2$M) condition, which lower bounds the necessary scaling of a model's history state -- the latent variables responsible for storing past information -- for effective long-context modeling. We validate the framework and its predictions on transformer and state-space models. Our work provides a principled foundation to understand long-context modeling and to design more efficient architectures with stronger long-context capabilities, with potential applications beyond natural language.