Compression with Bayesian Implicit Neural Representations

TL;DR

This paper introduces a Bayesian neural network-based data compression method that optimizes rate-distortion trade-offs directly, outperforming traditional quantization approaches in image and audio compression tasks.

Contribution

It proposes a novel Bayesian variational approach with relative entropy coding for neural network-based data compression, improving efficiency and quality.

Findings

Achieves strong image and audio compression performance.

Enables direct rate-distortion optimization via $eta$-ELBO.

Employs iterative prior learning and progressive refinement.

Abstract

Many common types of data can be represented as functions that map coordinates to signal values, such as pixel locations to RGB values in the case of an image. Based on this view, data can be compressed by overfitting a compact neural network to its functional representation and then encoding the network weights. However, most current solutions for this are inefficient, as quantization to low-bit precision substantially degrades the reconstruction quality. To address this issue, we propose overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding instead of quantizing and entropy coding it. This strategy enables direct optimization of the rate-distortion performance by minimizing the $\beta$-ELBO, and target different rate-distortion trade-offs for a given network architecture by adjusting $\beta$. Moreover, we introduce an iterative algorithm for learning prior weight distributions and employ a progressive refinement process for the variational posterior that significantly enhances performance. Experiments show that our method achieves strong performance on image and audio compression while retaining simplicity.