Compression with Bayesian Implicit Neural Representations

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 β-ELBO, and target different rate-distortion trade-offs for a given network architecture by adjusting β. 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. Our code is available at https://github.com/cambridge-mlg/combiner . A recent line of work [10] [11] [12] proposes to solve this issue by reformulating it as a model compression problem: we treat a single datum as a continuous signal that maps coordinates to values, to which we overfit a small neural network called its implicit neural representation (INR). While INRs were originally proposed in [13] to study structural relationships in the data, Dupont et al. [10] have demonstrated that we can also use them for compression by encoding their weights. Since the data ˚Equal Contribution. 37th Conference on Neural Information Processing Systems (NeurIPS 2023).