OpenNovelty.org

Cross-Domain Lossy Compression via Rate- and Classification-Constrained Optimal Transport

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Lossy CompressionImage CompressionImage RestorationImage InpaintingOptimal TransportMulti-task LearningRate-Distortion-Perception TradeoffRate-Distortion-Classification TradeoffDeep LearningUnsupervised Learning
Abstract:

We study cross-domain lossy compression, where the encoder observes a degraded source while the decoder reconstructs samples from a distinct target distribution. The problem is formulated as constrained optimal transport with two constraints on compression rate and classification loss. With shared common randomness, the one-shot setting reduces to a deterministic transport plan, and we derive closed-form distortion-rate-classification (DRC) and rate-distortion-classification (RDC) tradeoffs for Bernoulli sources under Hamming distortion. In the asymptotic regime, we establish analytic DRC/RDC expressions for Gaussian models under mean-squared error. The framework is further extended to incorporate perception divergences (Kullback-Leibler and squared Wasserstein), yielding closed-form distortion-rate-perception-classification (DRPC) functions. To validate the theory, we develop deep end-to-end compression models for super-resolution (MNIST), denoising (SVHN, CIFAR-10, ImageNet, KODAK), and inpainting (SVHN) problems, demonstrating the consistency between the theoretical results and empirical performance.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Overall Novelty Assessment

The paper develops a constrained optimal transport framework for cross-domain lossy compression, incorporating rate and classification constraints alongside distortion and perception metrics. It resides in the 'Rate-Distortion-Perception-Classification Functions' leaf, which contains only three papers total. This small sibling set indicates a relatively sparse research direction focused specifically on multi-objective tradeoffs that combine perceptual quality with classification accuracy, distinguishing it from the more populated 'Rate-Distortion-Classification Functions' leaf (four papers) that excludes perception metrics.

The taxonomy reveals neighboring work in 'Rate-Distortion-Perception Theory' (four papers) that addresses perceptual quality without classification objectives, and 'Cross-Domain and Optimal Transport Formulations' (two papers) that handle distribution mismatch without multi-constraint optimization. The paper bridges these directions by formulating cross-domain compression as entropy-constrained optimal transport with simultaneous perception and classification constraints. This positioning suggests the work synthesizes ideas from adjacent leaves rather than purely extending a single established direction, reflecting the field's emerging interest in unified multi-objective frameworks.

Among 30 candidates examined, the first contribution (constrained optimal transport framework) identified 2 refutable papers from 10 examined, and the second contribution (closed-form DRC/RDC characterizations) found 3 refutable papers from 10 examined. The third contribution (DRPC extension with perception divergences) showed no refutable candidates among 10 examined, suggesting stronger novelty in this specific theoretical extension. These statistics indicate that while the foundational framework and binary/Gaussian characterizations overlap with prior theoretical work, the perception-aware extension appears less anticipated within the limited search scope.

The analysis covers top-30 semantic matches and reveals moderate overlap in foundational multi-constraint formulations but clearer novelty in the perception-divergence extensions. The sparse taxonomy leaf (three papers) and the limited refutation evidence for the DRPC contribution suggest the work occupies a less crowded theoretical niche, though the search scope does not guarantee exhaustive coverage of all relevant prior art in optimal transport or multi-objective compression theory.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
5
Refutable Paper

Research Landscape Overview

Core task: cross-domain lossy compression with rate and classification constraints. This field addresses the challenge of compressing data while simultaneously satisfying bitrate budgets and preserving task-relevant information for downstream classification or perception. The taxonomy divides into two main branches: Information-Theoretic Foundations and Tradeoff Characterization, which develops theoretical frameworks for understanding fundamental limits and multi-objective tradeoffs (e.g., rate-distortion-perception-classification functions explored in works like Data Perception Classification[1] and Universal RDP[11]), and Implementation and Applications, which translates these principles into practical systems for domains such as scientific data (Error-Bounded Scientific[7], Scientific Data Applications[15]), remote sensing (Remote Sensing Classification[16]), and machine-oriented coding (Coding for Machines[8]). The theoretical branch often examines universal bounds and optimal transport formulations (Entropy Constrained Transport[4]), while the applied branch emphasizes end-to-end architectures (End-to-End Benchmark[10]) and domain-specific constraints. Recent work has intensified around multi-constraint optimization, where researchers balance reconstruction fidelity, perceptual quality, and classification accuracy under strict rate limits. Studies like RDC Approach[25] and RDC Model[27] formalize rate-distortion-classification tradeoffs, while Universal RDC Theory[14] and Zero Perception Error[36] push toward characterizing achievable regions with multiple simultaneous guarantees. Cross-Domain Optimal Transport[0] sits within this dense theoretical cluster, focusing on rate-distortion-perception-classification functions and leveraging optimal transport machinery to handle cross-domain scenarios—closely aligned with Universal RDC Theory[14] in its multi-constraint formulation but distinguished by its emphasis on domain shift and transport-based coupling. Compared to Zero Perception Error[36], which prioritizes perfect perceptual fidelity, Cross-Domain Optimal Transport[0] explores broader tradeoff surfaces where perception and classification constraints coexist under varying rate budgets, reflecting ongoing debates about which task metrics matter most in resource-constrained environments.

Claimed Contributions

Constrained lossy optimal transport framework with rate and classification constraints

The authors formulate cross-domain lossy compression as a constrained optimal transport problem that simultaneously minimizes expected distortion while satisfying both a compression rate constraint and a classification loss constraint. With shared common randomness, the framework decouples transport (reconstruction) from compression.

10 retrieved papers
Can Refute
Closed-form DRC and RDC characterizations for Bernoulli and Gaussian sources

The paper derives explicit distortion-rate-classification (DRC) and rate-distortion-classification (RDC) tradeoff functions for both one-shot Bernoulli sources with Hamming distortion and asymptotic Gaussian sources with MSE distortion, providing piecewise-linear and analytic expressions respectively.

10 retrieved papers
Can Refute
Extension to DRPC setting with perception divergences

The authors extend the framework to incorporate perception constraints using KL divergence and squared Wasserstein distance, deriving closed-form DRPC characterizations for Gaussian sources that explicitly incorporate classification constraints alongside perceptual quality measures.

10 retrieved papers

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Constrained lossy optimal transport framework with rate and classification constraints

The authors formulate cross-domain lossy compression as a constrained optimal transport problem that simultaneously minimizes expected distortion while satisfying both a compression rate constraint and a classification loss constraint. With shared common randomness, the framework decouples transport (reconstruction) from compression.

Contribution

Closed-form DRC and RDC characterizations for Bernoulli and Gaussian sources

The paper derives explicit distortion-rate-classification (DRC) and rate-distortion-classification (RDC) tradeoff functions for both one-shot Bernoulli sources with Hamming distortion and asymptotic Gaussian sources with MSE distortion, providing piecewise-linear and analytic expressions respectively.

Contribution

Extension to DRPC setting with perception divergences

The authors extend the framework to incorporate perception constraints using KL divergence and squared Wasserstein distance, deriving closed-form DRPC characterizations for Gaussian sources that explicitly incorporate classification constraints alongside perceptual quality measures.

Table of Contents