Accelerating Relative Entropy Coding with Space Partitioning
This work addresses the prohibitive runtime issue in REC for neural compression, making it more practical for applications like lossless and lossy compression.
The paper tackles the problem of slow encoding times in relative entropy coding (REC) algorithms by introducing a space partitioning scheme, achieving up to three times greater KL divergence handling and 5-15% bitrate reduction in neural compression tasks.
Relative entropy coding (REC) algorithms encode a random sample following a target distribution $Q$, using a coding distribution $P$ shared between the sender and receiver. Sadly, general REC algorithms suffer from prohibitive encoding times, at least on the order of $2^{D_{\text{KL}}[Q||P]}$, and faster algorithms are limited to very specific settings. This work addresses this issue by introducing a REC scheme utilizing space partitioning to reduce runtime in practical scenarios. We provide theoretical analyses of our method and demonstrate its effectiveness with both toy examples and practical applications. Notably, our method successfully handles REC tasks with $D_{\text{KL}}[Q||P]$ about three times greater than what previous methods can manage, and reduces the bitrate by approximately 5-15% in VAE-based lossless compression on MNIST and INR-based lossy compression on CIFAR-10, compared to previous methods, significantly improving the practicality of REC for neural compression.