Neural Entropy

Akhil Premkumar

Keywords: Diffusion models, thermodynamics, information theory, statistical mechanics

TL;DR: We introduce a measure of the information content stored in a neural network in the context of diffusion models.

Abstract: We explore the connection between deep learning and information theory through the paradigm of diffusion models. A diffusion model converts noise into structured data by reinstating, imperfectly, information that is erased when data was diffused to noise. This information is stored in a neural network during training. We quantify this information by introducing a measure called \textit{neural entropy}, which is related to the total entropy produced by diffusion. Neural entropy is a function of not just the data distribution, but also the diffusive process itself. Measurements of neural entropy on a few simple image diffusion models reveal that they are extremely efficient at compressing large ensembles of structured data.

Primary Area: Deep learning (e.g., architectures, generative models, optimization for deep networks, foundation models, LLMs)

Submission Number: 13518