Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling
Authors: Nam Nguyen, Hassan Tavakoli, An Vuong, Thinh Nguyen, Bella Bose
Organizations: School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, 97331
Abstract
This paper studies cross-domain lossy compression through the lens of minimum entropy coupling (MEC) with rate and classification constraints. In this setting, an encoder observes samples from a degraded source domain, while the decoder is required to generate outputs following a prescribed target distribution and to preserve information relevant to a downstream classification task. Motivated by logarithmic-loss distortion, we adopt an information-based objective that maximizes the coupling strength between the source and reconstruction, rather than minimizing a sample-wise distortion. Under common randomness, we formulate a rate-constrained MEC problem (MEC-B) and show that the intermediate representation can be removed without loss of optimality, yielding an equivalent deterministic coupling formulation. For Bernoulli sources, closed-form expressions are derived with and without classification constraints. In addition, we implement a neural restoration framework using quantization, entropy modeling, distribution matching, and classification regularization. Experiments on MNIST super-resolution and SVHN denoising show that increasing the available rate improves classification accuracy and yields more informative reconstructions.
Learning-based speech compression has achieved promising low-bitrate performance, but many neural speech codecs still describe quantized latents with preset-rate discrete symbols or apply entropy coding only after symbol generation. Such designs decouple representation learning from probability modeling, limiting their ability to exploit the non-uniform usage and temporal dependencies of learned speech latents. In this paper, we benchmark neural speech compression from a rate--distortion perspective and further investigate entropy-constrained coding for low-bitrate speech compression. We first formulate a unified learning-based speech coding pipeline and provide a benchmark-style analysis of recent neural speech codecs, showing that explicit probability modeling remains underexplored in learned speech compression. We then propose ECC, an Entropy-Constrained Codec that combines scalar quantization with a learned entropy model. ECC integrates hyperprior-based side information, channel-wise context modeling, latent residual prediction, and lightweight temporal modeling to estimate latent likelihoods for rate estimation during training and arithmetic coding during inference. To further improve low-bitrate efficiency, ECC introduces entropy skip, which omits highly predictable residual symbols using decoder-available scale estimates without transmitting additional skip masks. Extensive experiments show that ECC achieves a favorable low-bitrate rate--distortion trade-off over conventional and neural codec baselines, reducing BD-rate by 39.9% on ViSQOL and 76.3% on PESQ on average over two widely-used test sets. Ablation and diagnostic studies further validate the effectiveness of entropy modeling. Project Page: https://avery-xu.github.io/ECC-demo/
Entropy coding is widely used in typical learned image compression (LIC) that converts latents into a compact bitstream. However, entropy coding is typically sequential and becomes the coding latency bottleneck. To overcome it, we present Entropy-Coding Free Learned Image Compression (EF-LIC), a multi-rate framework that generates compact representation by removing statistical and correlation redundancy with low coding latency. First, we introduce unconstrained vector quantization and prove that its index distribution approaches the maximum-entropy bound, yielding minimal statistical redundancy. Second, we propose a context-conditioned autoregressive transform that directly reparameterizes the latents to reduce inter-dependency. Theoretical analysis shows that EF-LIC can remove correlation redundancy as effectively as typical LIC with entropy coding, leading to comparable compression performance. Experiments show EF-LIC achieves up to 67.86% bitrate reduction over MS-ILLM on Kodak with LPIPS. Ablation studies further show EF-LIC matches the compression performance of its entropy-coding based variant while achieving over 3× faster encoding and 5× faster decoding.
Deep joint source--channel coding (Deep JSCC) enables visual semantic transmission by mapping inputs directly to channel symbols and task outputs, but its performance can deteriorate under distribution shifts between training and deployment domains. We study single-source domain adaptation for task-oriented Deep JSCC and formulate a classification-capacity-invariance (CCI) function to characterize how the available channel capacity and class-conditional cross-domain invariance affect target domain classification accuracy. A scalar linear analysis of source-domain-optimal solutions and a controlled shallow nonlinear validation show that target domain classification accuracy can vary non-monotonically with the invariance constraint and with available capacity along separate control paths obtained by varying the transmitted dimension or CSNR. We then propose a domain-adaptive Deep JSCC framework that combines pseudo-label-based class-level adversarial alignment with supervised contrastive learning on confidence-filtered target samples. Experiments on digit and PACS datasets over AWGN and Rayleigh fading channels demonstrate improved target domain generalization without introducing additional inference-time networks. On SVHN → MNIST, the proposed method achieves 98.15% target-domain accuracy at a CSNR of 10 dB.