ACE: An Analytical Rate Proxy for Compression-aware Optimization

Gradient-based optimization over image codecs is hindered by the non-differentiability of quantization and entropy coding, and existing differentiable rate proxies require training a codec-specific surrogate network. We introduce ACE (AC-Entropy proxy), an analytical, training-free, differentiable entropy functional of pooled AC DCT coefficients, derived from the block-transform coding pipeline shared by standards such as JPEG and HEVC. Theoretically, we prove that a bin-width-corrected ACE consistently estimates the differential entropy of a smoothed, pooled AC-coefficient distribution. Empirically, we confirm that ACE closely tracks the measured coded bitrate of both HEVC and JPEG across quality levels. We show that ACE is an effective compression-aware regularizer for communication-efficient split inference, improving the transmitted feature rate--accuracy trade-off with no added parameters. We demonstrate ACE's further versatility across applications spanning pixel, perturbation, and generative sampling spaces in the appendix. In each setting, ACE requires no auxiliary training and adds no learned parameters, making it a lightweight, drop-in tool for any pipeline that needs a differentiable, compression-aware training signal.