Rate-Distortion Optimization

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7 papers in the last four weeks, against 1 the four weeks before. 0.1% of all new papers.

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Latest papers 44

Oct 8, 2026math.ST

Optimal random quantisers for spherically symmetric distributions

Zador's celebrated theorem is a cornerstone of optimal quantisation: it establishes both the weak limit of the empirical distribution of an optimal

n

-point quantiser in

R^d

and the decay rate of the associated

L_s

-mean quantisation error. In large dimension, however, observing this asymptotic behaviour requires an astronomically large sample size. We prove that, for spherically symmetric target distributions, optimisation over all spherically symmetric distributions is a convex problem and derive an equivalence theorem that both characterises global optimality and yields a constructive algorithm. We show that, for moderate

n

, random quantisers uniformly distributed on a sphere of suitably chosen radius

R

perform exceptionally well and, over a broad range of values of

n

, are numerically certified to be optimal among all random quantisers. Their expected distortion has an explicit integral representation that can be evaluated to arbitrary precision, and we prove concentration across random quantisers: the distortion variance tends to zero as

n\to\infty

for fixed

d

. For

s=2

, both the optimal radius and the associated minimum expected distortion admit exact expressions. For general

s

, the optimal radius can be determined efficiently, and extreme-value theory provides useful approximations when

n

grows with

d

. Depending on this growth rate,

R

either converges to zero or approaches a positive limit that is independent of

s

.

Luc Pronzato, Anatoly Zhigljavsky

Laboratoire I3S, CNRS-Université Côte d’Azur, Sophia Antipolis, France · School of Mathematics, Cardiff University, UK

Vector Quantization Rate-Distortion Optimization

Oct 6, 2026cs.IT

Task-Sufficient Contraction: Source Selection for Machine Information Interfaces

A declared task can sometimes certify a reduced source before a downstream encoder, codebook, rate, distortion target, or optimizer is chosen. This paper studies when one such reduction preserves the complete downstream problem family, a property termed Task-Sufficient Contraction. The reduced source is fixed by the task before the later operating point is selected. An exact contraction allows the later problem to be solved on that source with the same result as if the full source had been retained. For a machine with a fixed set of possible actions and a fixed loss, the paper identifies a consumer-specific source by merging states only when every available action has the same regret in both. For finite action sets, replacing the richer source by this reduced source preserves the complete one-step rate-regret curve, even though the reduction is fixed before the distortion target is chosen. A second result gives an exact characterization for quadratic loss on affine feasible-action sets: the canonical reduced source is the projection onto the directions in which feasible actions can differ. Under a fixed energy budget, this becomes centered load, while retaining only the optimal water-filled action is too coarse. Earlier Information Bottleneck, semantic rate-distortion, and goal-oriented quantization results are then used to distinguish exact, architecture-conditioned, approximate, failed, and corrected contractions. The framework suggests a way for heterogeneous machines to exchange what a receiving task needs without first aligning their full internal representations.

Joss Armstrong

Ericsson Ireland

Rate-Distortion Optimization

Oct 5, 2026cs.LG

Transmission Factors for Lossy Compression of PDE Training Data: Measuring What Reaches a Trained Operator

Operator-learning benchmarks ship as full-precision arrays, and they have grown to terabyte scale. A curator who wants to distribute one has to decide how coarsely to store it. That decision is usually made by fixing a tolerance on the reconstruction error of the stored field. We show that this quantity is measured in the wrong place. It compares the stored field with the original, before any model is trained. What the curator is buying is the accuracy of a model trained on the compressed copy, and the two can disagree: two PDEBench families stored to identical field error differ threefold downstream. A solution operator smooths, so only part of the codec error ever reaches the model's output. That part can be measured. Push a compressed field through a model already trained at full precision, and compare its output against the output on the clean field. The measurement costs forward passes and no training on compressed data. It spans more than two orders of magnitude across six PDE families, and it orders downstream cost where field error does not, inverting 12 of 104 cross-dataset comparisons against field error's 36. Read as a budget, the same curve nominates a storage rate for each dataset. A back-check against trained models finds those rates wrong in both directions by up to a factor of two in stored bits.

Huy Hoang Le

Powermore Ltd., Da Nang, Vietnam

Rate-Distortion Optimization PDE Operator Learning

Sep 30, 2026cs.LG

Semantic-Aware Joint Source-Channel Optimization for Encoder-Agnostic Digital Video Communication

Video semantic communication has attracted increasing attention as a promising approach to improving video transmission efficiency. However, most existing approaches rely on computationally intensive deep learning-based video encoders and decoders, which hinders their deployment in resource-constrained scenarios. To address this issue, we propose a lightweight semantic-aware joint source-channel optimization (SAJSCO) scheme that can be integrated into existing digital video communication systems as a plug-in module. Specifically, we develop a video communication system model in which the transmitter jointly optimizes source and channel coding parameters based on the inter-frame semantic importance of the input video and estimated channel state information. On this basis, we formulate an optimization problem that maximizes semantic importance weighted video reconstruction quality under a maximum bitrate constraint. To solve it, we first quantify inter-frame semantic importance using a cosine similarity-based metric with a shifted window mechanism. We then develop a multi-actor proximal policy optimization (MPPO) algorithm to solve the formulated problem by jointly adapting the source compression rate and channel coding rate. The learned policy can be directly applied to different video encoders without encoder-specific retraining or fine-tuning. SAJSCO achieves Bjøntegaard Delta rate reductions of 34.86% and 18.01% when integrated with H.265, a conventional video encoder, and DCVC-RT, a deep learning-based video encoder. Over-the-air experiments on a hardware testbed further demonstrate a PSNR gain of up to 1.448 dB with H.265 and an LPIPS reduction of up to 0.033 with DCVC-RT compared with the respective best-performing fixed-parameter baselines.

Xiangben Zhu, Caili Guo, Yang Yang +2

Beijing Key Laboratory of Network System Architecture and Convergence, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China · China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215011, China · Department of Engineering, King’s College London, London WC2R 2LS, U.K.

Semantic Communication Rate-Distortion Optimization Video Compression

Sep 29, 2026cs.MA

RAVEN: Receiver-Conditioned Action-Value Encoding for Finite-Alphabet Multi-Agent Communication

A message drawn from a small alphabet helps a teammate only if it keeps the distinctions that change that teammate's next decision. We show that scoring messages by action values averaged over the receiver's situation can erase exactly these distinctions, and we propose RAVEN (Receiver-conditioned Action-Value ENcoding), which trains a four-symbol, one-step-delayed channel to preserve each receiver's centered action-value profile within the receiver's own context. The sender never needs to know that context: the receiver decodes every symbol with its private information. We give two estimators of this target. With a teacher, offline RAVEN selects the codebook that exactly minimizes an empirical conditional distortion and distills it into a frozen sender; we bound the resulting codebook-selection error and one-step decision loss. Without a teacher, online RAVEN aligns, inside a QMIX learner, the deployed symbol pathway with a training-only continuous reference that shares its routing. Against five recent communication methods on eight navigation settings, offline RAVEN attains the highest return in seven, and removing receiver conditioning forfeits 83% of its communication gain. Online RAVEN raises predator-prey capture success from 53.2% to 96.0% over the same QMIX backbone without communication, and on SMAC and MPE it attains the best mean normalized score of 14 methods, including methods that exchange kilobit messages. Every RAVEN message costs 2 bits, 12-1,024x fewer than those of NDQ, CACOM and ExpoComm on navigation.

Shuwei Sun, Chenxi Wang, Jian Huang +2

Xi’an Jiaotong University Xi’an, China

Rate-Distortion Optimization Multi-Agent Communication Cooperative MARL Multi-Agent Coding

Sep 28, 2026cs.IT

The Hidden Perception Constraint in Task-Aware Compression

With the recent advancements of neural compressors, explicitly incorporating perception constraints into the design of compression schemes has gained significant attention. Traditionally, these perception constraints ensure that the distribution of the reconstruction does not significantly deviate from the distribution of the source, thus attesting to the perceptual quality of the reconstruction. In this work, we uncover several perception constraints that are naturally present in task-aware compression. In particular, we consider a problem where the primary task is reconstruction and the secondary task is classification (i.e., a statistical test). We study this problem at varying levels of domain information available to us and discuss how to utilize the naturally emerging perception constraints to design rate-minimal compression schemes that also maximize the utility of our secondary task. We show that in this setting, if the decision boundaries of the classifier are ill-defined (mismatch) for our source distribution, then matching onto a target distribution enhances our classification accuracy.

Sahan Liyanaarachchi, Semih Akkoc, Sennur Ulukus +1

University of Maryland College Park, MD, USA · The Ohio State University Columbus, OH, USA

Learned Image Compression Rate-Distortion Optimization Distortion-Perception Tradeoff

Sep 28, 2026cs.CV

Rate-Distortion Adaptive Primitive Selection for Omnidirectional Gaussian Splatting

Learned image codecs (LICs) achieve high reconstruction quality, but their decoding speed is often insufficient for immersive virtual reality (VR). Gaussian splatting (GS) codecs render much faster, yet still lag in reconstruction quality and typically decide primitive allocation without considering the coding cost of each primitive. We introduce OIC-GS, an omnidirectional GS codec with a new hierarchical HEALPix primitive grid representation. Gaussian primitives are anchored at predefined spherical locations, eliminating explicit coordinate coding. Finer levels refine their coarser ancestors, naturally supporting coarse-to-fine reconstruction and layered transmission. The predefined grid also enables efficient viewport decoding by selecting only view-relevant primitives. We further introduce a lightweight entropy model for quantized primitives and optimize the codec under a spherical rate-distortion objective. Primitives with insufficient rate-distortion benefit are automatically removed when their quantized opacity becomes zero, allowing OIC-GS to adapt both primitive density and level of detail without a fixed primitive budget. A single bitstream supports full-sphere, viewport-dependent, and progressive decoding. The first viewport reaches final quality after decoding only 52% of the bitstream, and is then rendered at 1,270 FPS. On a 100-image omnidirectional benchmark, OIC-GS outperforms all evaluated GS codecs, reducing WS-PSNR BD-rate by 49.6% over GaussianImage++ and 68.6% over SGI, which uses a learned entropy model.

Yulong Cheng, Youneng Bao, Junfeng Zhou +2

Harbin Institute of Technology, Shenzhen, China · Shenzhen University, Shenzhen, China

3DGS Compression 3D Gaussian Pruning Rate-Distortion Optimization Gaussian Splatting

Sep 28, 2026cs.AI

SemRD-V2X: Closure-Guided Communication with Bounded Inference for Cooperative Perception

Vehicle-to-Everything (V2X) cooperative perception improves 3-D detection by sharing intermediate features, but dense remote features may repeat context that the ego agent can infer locally. Most communication-efficient designs optimize masks or codes empirically, leaving a more basic question open: which remote evidence is indispensable given the receiver's own observation? We introduce a closure-fidelity perspective on ego conditioned remote perception. Under a finite deductive abstraction and explicit conditions, its rate--distortion function decomposes over an irredundant core, and the exact zero-distortion rate becomes

P_A H(π_A)

. This analysis suggests a concrete design principle: transmit compact evidence and recover derivable context with bounded receiver-side inference. Guided by this principle, SemRD-V2X is an operational neural proxy that combines exact-budget BEV support selection, pointwise channel compression, and masked shared-weight reconstruction before standard fusion. Experiments on simulated V2XSet and real-world DAIR-V2X validate the resulting design. In a controlled five-run V2XSet comparison against a locally reproduced V2X-ViT-v1 baseline on one Tesla V100, SemRD-V2X reduces the analytical feature payload by

26.6\times

while improving [email protected]/[email protected] by 4.13/8.57 points, with 3.81% additional mean compute latency. These results position closure fidelity as both an analytical lens and an actionable design principle for communication-efficient cooperative perception.

Hu Xu, Chun Li, Siyuan Qiu +2

Shanghai Jiao Tong University, Shanghai, China

Communication-Efficient Collaborative Perception Rate-Distortion Optimization V2X Communication Cooperative Perception

Sep 23, 2026cs.CV

Information Capacity of Generative Video Compression: Quantifying the Rate-Compute Exchange at Identical Quality

Under the AI Flow framework, communication networks distribute intelligence across devices, edge servers, and clouds, and computation at the receiver becomes a resource that can substitute for transmitted bits. Generative video compression (GVC) embodies this exchange by sending compact tokens with ultra-low bitrate and letting a generative decoder synthesize the video, yet how much bandwidth savings a unit of decoder compute actually achieves has never been quantified. To fill this vacancy, we model reconstruction quality as a two-factor power law in data rate and decoder compute, which fits measured DISTS of two GVC decoders with a mean error below 3%, and define the information capacity (IC) as the negative logarithmic slope along an iso-quality contour, namely the fraction of rate saved per fractional increase in compute at identical quality. IC is dimensionless and unit-invariant, thus enabling an architecture-agnostic comparison. It forms a field over the operating plane, locating where additional denoising steps are worth their cost. Across five datasets, the 14B decoder trades more compute for fewer rate about ten times more efficiently than the 1.3B decoder. IC also varies significantly across datasets, indicating imbalanced performance on the rate-compute trade-off in GVC methods.

Cheng Yuan, Jiawei Shao, Xuelong Li

Institute of Artificial Intelligence (TeleAI), China Telecom

Rate-Distortion Optimization Neural Video Compression Generative Video Compression

Sep 16, 2026eess.IV

Perceptual Refinement of an End-to-End Video Streaming Pipeline via Generative AI Layers

Traditional codecs treat every region of a frame alike; a generative layer can instead degrade the regions a viewer attends to least and reconstruct them at the client. We present PRESLEY, which extends the prior conference work ELVIS by replacing destructive block removal with adaptive in-place degradation under a removability mask, signaling per-block strength in a bit-packed side channel, and restoring via generative backbones conditioned on transmitted visual priors rather than unconditioned in-painting. We separate the problem into three goals: choosing which blocks to degrade, degrading them so the encoder spends fewer bits, and restoring them. Against its predecessor at matched rate, PRESLEY achieves a decisive mean -56.4% BD-rate reduction on delivered background quality across 13 rate ladders spanning multiple codecs and dataset families. Against pristine baselines, PRESLEY defines the operating regime of generative transport: delivering substantial bitrate savings (up to -29.4% BD-rate) and superior background quality (17/23 sequences) in the target bit-starved regime, while maintaining foreground fidelity bit-exact. We further map where the theoretical headroom in this class of architecture lies. Using an exact leave-one-superblock-out combinatorial oracle as an additive empirical bound, we show that existing complexity heuristics already capture 83.3% of bit-cost savings, bounding remaining cost-axis headroom at about 5% of total bitrate. We then identify and model the primary unaddressed axis -- post-restoration damage -- which disperses widely (4.9-8.4 dB). We prove that this damage is predictable before transmission (held-out rho = +0.400), establishing the feasibility of transmit-time restorability modeling and defining the roadmap for joint rate-distortion-restoration selection rules.

Emanuele Artioli, Farzad Tashtarian, Christian Timmerer

Christian Doppler Laboratory ATHENA, Institute of Information Technology (ITEC), Alpen-Adria-Universität Klagenfurt, Austria

Rate-Distortion Optimization Video Compression Video Restoration Generative Video Compression

Aug 11, 2026cs.CV

Flow Straight to Reality: Perceptually Consistent Flow Matching for Efficient Image Restoration

Image restoration is fundamentally constrained by the tradeoff between distortion and perception: minimizing pixel-wise error yields over-smoothed results, whereas optimizing for perceptual realism often introduces structural deviations. Recent approaches attempt to balance this tradeoff via posterior sampling or multi-stage generative pipelines, yet remain computationally expensive and architecturally complex. To overcome these limitations, we propose PCFlow (Perceptually Consistent Flow Matching), a unified framework that directly parameterizes a continuous transport from degraded observations to clean targets, jointly optimizing distortion and perceptual quality. While its latent consistency flow objective drives stable and efficient few-step inference, a Latent Consistency Perceptual Loss (LCPL) imposes semantic constraints directly on the guiding velocity field, steering the dynamics toward visually sharp data manifolds. Furthermore, recognizing the inherent conflict between structural and perceptual consistencies, we integrate a conflict-free gradient projection strategy to stabilize the multi-objective optimization landscape. Combined with lightweight, convolution-only backbone, PCFlow achieves competitive performance across diverse restoration tasks at a fraction of traditional computational costs.

Sangwoo Jo, Donggeun Ko, Jayeon Kang +3

Korea University, Seoul, South Korea · Aim Future, Seoul, South Korea

Flow Matching Perceptual Loss Rate-Distortion Optimization Image Restoration Distortion-Perception Tradeoff

Aug 4, 2026cs.CV

GVCCTurbo: Rate-Compute Quality Scheduling for Codebook Driven Generative Compression

Codebook-driven generative compression uses a pretrained image or video generator as a zero-shot visual prior and transmits compact codebook indices to guide reconstruction at ultra-low bitrate. Current codecs tie each finite-rate correction to a fresh prior evaluation, so shortening the sampler also removes correction slots that carry target-dependent information. We propose GVCCTurbo, a BPP-driven scheduler that separates expensive prior refreshes from codebook corrections: after calibrating an atom-count operating point and skip-gap ratio once per protocol, it maps a target codebook-payload bitrate to a trajectory length and refresh period, making BPP a schedule input instead of a fixed consequence of sampler length. The same endpoint-prediction and finite-rate steering interface covers GVCC-style rectified-flow video and DDCM-style diffusion image compression, preserving zero-training deployment and compatibility with future distilled priors. Native 1080p curves position the complete zero-shot codec in the ultra-low-bitrate regime. In a controlled 720p Wan-GVCC study, the scheduler cuts prior evaluations from 20 to 9 for a

\sim\!44\%

measured decoding-time reduction shared across the whole schedule family, at a small shared LPIPS cost on high-motion content; within that family, uniform refresh thinning (pure-skip) is a boundary point, and the BPP-aware interior point trades

2.9\%

fewer codebook-payload bits for consistently higher PSNR at comparable LPIPS. These results support BPP-to-compute scheduling as a controllable extension of sampler-length tuning, without requiring the allocated point to dominate every boundary point.

Ziyue Zeng, Dingjie Peng, Xun Su +1

Waseda University, Tokyo, Japan

Learned Image Compression Rate-Distortion Optimization Neural Video Compression Generative Image Compression Generative Video Compression

Aug 2, 2026cs.NI

Clear-Weighted Bit Allocation for Satellite Downlinks

Earth-observation satellites capture more imagery than intermittent ground contacts can transmit. Onboard systems threshold a cloud detector, discard frames or tiles, and compress the survivors with a fixed codec. On expert-labeled imagery, these rules remove more than one-fifth of clear pixels, primarily through detector false positives. We train a neural codec with a clear-probability-weighted reconstruction loss, reallocating coded bytes from clouds to clear ground without requiring or transmitting a cloud map onboard. Each capture is encoded into a resumable base layer and a dependent refinement layer, while clear content is estimated from features produced by the encoder. At each contact, we causally rank arrived layers using estimated clear content, unfinished bytes, deadline slack, and aggregate deadline pressure. The scheduler serves base and computational deadlines, bounds stored residual bytes, and resumes interrupted packets. We evaluate the onboard-to-downlink pipeline using real entropy-coded bytes, orbit-derived interruptible contact capacities, and measured service time and energy on resource-constrained embedded accelerators. Clear-weighted codecs require up to 47.8% fewer bytes than learned-compression baselines at matched clear-region quality. The optimized encoder consumes less time and energy than one pass of the cloud detector used by the frame-discard rules. Relative to fixed two-stage service on the same streams, our scheduler more than doubles deadline-full clear-content delivery for the interrupted combined cohort, reaches 83.6% of a certified clairvoyant upper bound, and exceeds replayed reference orders in deadline-usable delivery.

Alireza Furutanpey, Qiyang Zhang, Yujie Huang +2

Coovally, Barcelona, Spain · Technical University of Vienna, Austria · Peking University, China +2

Learned Image Compression Remote Sensing Rate-Distortion Optimization Wireless Resource Allocation

Jul 19, 2026cs.IT

Rate-Distortion-Perception Theory: Redefining the Fundamental Limits of Information Representation

Classical rate-distortion (RD) theory has long established the fundamental limits of lossy compression by quantifying the minimum number of bits required to represent a source under a prescribed distortion constraint. However, widely used distortion measures such as mean-squared error often fail to capture perceptual quality or semantic validity, which are increasingly central in modern learning-driven applications. Rate-distortion-perception (RDP) theory extends the RD framework by introducing perception as a third fundamental axis, quantified via distributional similarity between the source and reconstructed signals, leading to the rate-distortion-perception function (RDPF). This tutorial provides a structured overview of the coding principles underlying perception-aware lossy compression and surveys recent achievability results under different randomness assumptions. It then presents a unifying optimization viewpoint for computing the RDPF as defined by Blau and Michaeli, for both discrete and continuous sources under broad families of perceptual constraints, including f-divergences, alpha-divergences, and Wasserstein-based metrics. Special attention is given to computational tools such as alternating minimization schemes, Newton-based methods, and convex optimization formulations, as well as to analytically tractable cases such as Gaussian sources and the perfect-realism regime. Unlike recent broad surveys that emphasize generative architectures and AI-empowered communication systems, this tutorial focuses on the coding-theoretic and computational machinery needed to characterize, compute, and interpret the RDP limits. Finally, the tutorial outlines promising research directions at the intersection of information theory, neural compression, robust source coding, and perception-aware networked control systems.

Photios A. Stavrou, Giuseppe Serra, Marios Kountouris

Learned Image Compression Rate-Distortion Theory Rate-Distortion Optimization Distortion-Perception Tradeoff Information-Theoretic Lower Bounds

Jul 15, 2026cs.CV

MixCompress: Mixture of Experts for Variable Rate Learned Image Compression

Learned image compression (LIC) is bottlenecked by the need to store independent models for each rate-distortion operating point. Existing variable bit-rate (VBR) methods aim to reduce this overhead via dense parameter modulation, but forcing a shared backbone to approximate divergent mappings causes severe feature entanglement. Specifically, low-rate smoothing gradients inherently conflict with the preservation of high-frequency textural details, leading to sub-optimal performance. To resolve this, we propose MixCompress, a unified VBR framework based on sparse structural specialization. While sparsely gated Mixture-of-Experts (MoE) routing successfully mitigates gradient conflict, it operates on a fixed computational budget. To address the increased representational demands of higher bit-rates we introduce a Mixture-of-Depths (MoD) extension to dynamically scale model capacity. Combined with Conditional Auxiliary Transforms (CAT) for dynamic sub-band energy modulation, our hierarchical framework effectively dynamically scales capacity. Extensive evaluations demonstrate that MixCompress not only matches individually optimized single-rate baselines but can even surpass them, establishing a new Pareto frontier for computationally efficient image coding.

Calvin-Khang Ta, Praneet Singh, Tong Shao +1

Dolby Laboratories, USA

Learned Image Compression Rate-Distortion Optimization Mixture-of-Experts Models

Jul 11, 2026eess.IV

Differentiable Proxy Learning for Adaptive Quantization Control in H.264 Video Coding

H.264 has been the most widely used video coding format for the past two decades due to its relative simplicity, efficiency, and wide availability of software and hardware implementations. However, optimizing codec parameters such as the quantization parameter (QP) for specific objectives (e.g., perceptual quality or machine vision tasks) is challenging due to the non-differentiable nature of standard video codecs. While differentiable proxies have recently been used to enable gradient-based optimization around standard codecs, their fidelity to the target codec is rarely explicitly characterized. In this paper, we propose a differentiable proxy learning method for H.264 intra codec to enable adaptive quantization control. Built upon a variable-rate learned compression model, the proposed proxy is made differentiable with respect to codec QP through a soft-indexing mechanism. It is then trained to approximate the rate-distortion behavior of H.264 under two quantization settings: global-QP, which uses one QP per image, and spatial-QP, which assigns QPs at the macroblock level. Using the frozen trained proxy, we develop a proxy-based adaptive quantization (AQ) framework for both perceptual optimization and machine vision tasks. Experimental results demonstrate that the proposed proxies closely approximate the rate-distortion behavior of H.264 intra codec. The resulting proxy-based AQ framework consistently improves rate-task trade-offs over fixed-QP H.264 baselines, achieving BD-rate reduction of up to 17.12% for semantic segmentation and 15.30% for MS-SSIM.

Qihan Xu, Ivan V. Bajić

School of Engineering Science, Simon Fraser University Burnaby, BC, Canada

Learned Image Compression Rate-Distortion Optimization Video Compression

Jun 11, 2026cs.CV

Dual-Constrained Diffusion Image Compression for Operational Rate-Distortion-Perception Optimization

The rate-distortion-perception (RDP) trade-off extends classical rate--distortion theory by imposing a distributional constraint on reconstructions, providing a unified framework for neural image compression that jointly governs fidelity and perceptual realism. While prior work achieves near-optimal rate--perception trade-offs, practical frameworks explicitly realizing the full RDP surface remain scarce, primarily due to the difficulty of introducing common randomness at the decoder. We propose DCIC (Dual-Constrained Diffusion Image Compression), which integrates a learned codec with a diffusion-based decoder governed by joint distortion and idempotence constraints. The distortion constraint bounds reconstruction fidelity relative to the base codec output; the idempotence constraint -- requiring that re-encoding the restored image recovers the base codec reconstruction -- serves as a tractable surrogate for the distributional perception requirement. Together, they steer the reverse denoising process via iterative optimization with consistent noise injection, realizing common randomness without additional rate overhead. At fixed rate, dual attenuation factors

(K_D, K_P)

jointly navigate the Pareto frontier of the distortion-perception plane, enabling continuously adjustable fidelity-realism trade-offs from a single bitstream. DCIC

_{RD}

(

K_P{=}0

) and DCIC

_{RP}

(

K_D{=}0

) arise as boundary curves, with DCIC

_{RDP}

(

K_D = K_P=1

) realizing the optimal interior operating point. Experiments on CelebA-HQ, CLIC2020, and ImageNet-1K across CNN, Transformer, and hybrid architectures confirm that DCIC

_{RDP}

achieves superior BD-PSNR over all perceptual codecs, while DCIC

_{RP}

matches dedicated perception-oriented methods in BD-FID, validating the practical value of full RDP surface navigation.

Sanxin Jiang, Jiro Katto, Heming Sun

Department of Information Engineering Shanghai University of Electric Power Shanghai, China · Department of Computer Science and Communication Engineering Waseda University Tokyo, Japan · Faculty of Engineering Institute of Science Tokyo Tokyo, Japan

Learned Image Compression Rate-Distortion Optimization Distortion-Perception Tradeoff Generative Image Compression Diffusion Models

Jun 10, 2026eess.AS

Benchmarking Neural Speech Compression from a Rate-Distortion Perspective

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/

Jun Xu, Zhengxue Cheng, Fengxi Zhang +3

School of Information Science and Electronic Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Neural Audio Codecs Speech Processing Rate-Distortion Optimization Entropy Coding

Jun 9, 2026cs.IT

Minimum Distortion Quantization with Specified Output Distribution

We derive the optimal quantizer of a real-valued random variable

W

with distribution

P_W

such that 1) the distribution of the quantization output

X

that can take

k

values follows any specified distribution

P_X

over

\{1,\ldots,k\}

, and 2) the minimum mean squared error (MMSE) of estimating

W

from

X

is minimized. It is shown that the optimal quantizer takes the form

X=σ\big(F_{σ^{-1}(X)}^{-1}(F_W(W))\big)

, where

σ

is the optimal permutation of

\{1,\ldots,k\}

among all permutations to minimize the MMSE, and

F

is the cumulative distribution function. When

P_W

is uniform over an interval or

P_X

is uniform over

\{1,\ldots,k\}

, the quantizer takes a simple form

X=F_{X}^{-1}(F_W(W))

. The concept of majorization plays a key role in the optimality proof. Specifying the output distribution is useful for designing quantizers with explicitly controlled output entropy, maximized mutual information between input and output, tailored output distribution to match channel input requirements for communication, and data anonymization.

Aolin Xu

Rate-Distortion Theory Rate-Distortion Optimization

Jun 2, 2026cs.LG

A Geometric Lens on Physics-Aligned Data Compression

In AI for Science, physics-informed losses are increasingly used to train learned compressors for scientific data, but their rate-distortion implications remain poorly understood. At fixed bitrate, these objectives often improve preservation of a target physical observable while degrading standard reconstruction fidelity. We develop a local geometric theory showing that this tradeoff is governed by the interaction of latent-space sensitivities induced by the entropy model, the physical observable, and the distortion metric. At each operating point, these induce preferred directions along which compression noise should be suppressed, yielding an anisotropic error-allocation mechanism. When these directions are misaligned, improving the observable at fixed rate necessarily worsens standard distortion, establishing a fundamental limit on simultaneous preservation. We formalise this through a local tangent-space rate-distortion law and introduce a practical alignment diagnostic based on dominant eigenspace overlap. Experiments across scientific domains test the theory and validate that the alignment diagnostic correlates with observed data- and physics-space trade-offs.

Aleix Segui, Wesley Armour

Department of Engineering Science, University of Oxford, Oxford, UK.

Rate-Distortion Theory Rate-Distortion Optimization Scientific ML Physics-Informed ML

May 28, 2026stat.ML

Matching Rates and Optimal Allocation for Federated Probe-Logit Distillation under Heterogeneous Bandwidth Budgets

In federated language modeling,

K

nodes each hold

n

samples but cannot pool data or exchange full-precision gradients or weights. We study the minimax rate at which a conditional distribution over

V

tokens can be estimated when each node may upload at most

B

bits per query in a public probe set. In federated probe-logit distillation (FPLD), each node transmits a scalar-quantized logit vector on the probe set, and an aggregator distills a global parametric student. Prior work (Dubey and Huo, 2026) establishes a high-probability KL rate

O(d/(Kn) + ρ\sqrt{V \log V / m} + K^{-1} \cdot 2^{-2B/V})

plus optimization slack, with the bandwidth term in its trace-sharpened form. Whether this bandwidth-term rate is tight, and how the upper bound generalizes to heterogeneous per-node bandwidths, are left open. We close both gaps. First, the dithered FPLD construction has a matching single-round lower bound

Ω(K^{-1} \cdot 2^{-2B/V})

under non-degeneracy, pinning the bandwidth-axis rate at

Θ(K^{-1} \cdot 2^{-2B/V})

.

T

-round sequential refinement with nested/scaled residual quantizers achieves

O(K^{-1} \cdot 2^{-2TB/V})

; vanilla FPLD's

T

-independent bandwidth term is suboptimal for every

T > 1

. Second, we establish a heterogeneous-bandwidth upper bound for per-node budgets

B_i

, paired with a closed-form optimal allocation

B_i^* = B_{\mathrm{tot}}/K + (V/2) \log_2(w_i / \bar{w}_g)

, a log-tilted water-filling rule that is the per-node analogue of reverse water-filling for distortion-rate optimization. A plug-in adaptive variant estimates the weights from a short warm-up phase and attains

1 + O(\sqrt{\log(K/δ)/(m T_0)})

relative suboptimality. Synthetic n-gram simulations confirm that empirical KL is bracketed by the upper and lower bounds and that the optimal allocation strictly dominates uniform and inverse-weighted baselines under heterogeneous clipping.

Prasanjit Dubey, Xiaoming Huo

H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.

Federated Learning Aggregation Communication-Efficient Distributed Training Federated Knowledge Distillation Rate-Distortion Optimization Knowledge Distillation Heterogeneous Federated Learning

May 25, 2026cs.CV

TriDP-PTM: a three-stage distortion-perception tradeoff guides the pre-training model for radar cardiac sensing

Cardiovascular diseases (CVDs) remain a leading cause of death globally, necessitating continuous, accurate non-invasive cardiac monitoring. While non-contact radar-based approaches show great promise, they often employ a single "distortion-driven" or "perception-driven" paradigm, frequently facing a trade-off between "low distortion but weak semantic information" and "high perceptual fidelity but poor interpretability." To address this, we propose a Three-stage Distortion-Perception Pre-Training Model (TriDP-PTM), a radar-based multi-scale fusion dual-path framework that systematically compares the "direct radar-to-task" path against an "indirect radar-to-ECG-to-task" path. By integrating an ECG generator with a feature discriminator to form a composite loss function, our approach effectively incorporates medical priors - such as ECG morphology and rhythm - into downstream tasks. Through empirical analysis, we reveal that this trade-off manifests in three distinct phases (Positive-Sum, Coopetitive, and Negative-Sum), showing optimal downstream clinical accuracy typically emerges in the coopetitive stage. Extensive experiments on a dataset involving 30 subjects across 5 physiological states reveal that the indirect path consistently outperforms the direct path in diverse tasks, achieving 0.80 mean IoU in waveform segmentation, 98.3% average classification accuracy across four tasks, and a 56% MAE reduction in blood pressure regression compared to the strongest baselines. These findings validate our framework and indicate that, within the indirect radar-to-ECG pathway, appropriately weighting distortion and perception losses to operate in the coopetitive regime is critical for achieving both clinically interpretable ECG morphology and strong downstream accuracy in non-contact cardiac monitoring.

Jinye Li, Aidong Men, Yang Liu +1

National Institute of Health Data Science, Peking University, Beijing, China · Institute of Medical Technology, Peking University, Beijing, China · Beijing University of Posts and Telecommunications, Beijing, China +3

Electrocardiography Rate-Distortion Optimization Distortion-Perception Tradeoff

May 24, 2026cs.IT

Polynomial Context-Truncation Sensitivity in Autoregressive Language Models: Sequential Wyner-Ziv Bounds for KV Cache Compression

We study the rate-distortion limits of online KV cache compression in autoregressive language models, formulating it as sequential Wyner-Ziv source coding on the filtration induced by the model, with the next-step query as decoder side information. Empirically, across four models spanning two families and

0.5

-

3

B parameters, we find that the next-token distribution's sensitivity to context truncation decays \emph{polynomially} rather than \emph{geometrically}: a power law improves on an exponential fit by an order of magnitude in extrapolation, the fitted exponent is recovered independently from a sink-plus-recent KL measurement, and the decay is verified to be free of positional-encoding artifacts by a position-preserving ablation. Under a corresponding \emph{polynomial truncation-sensitivity} assumption, our main result characterizes the per-token memory requirement of \emph{suffix-only} cache policies: a sliding-window scheme attains distortion

\varepsilon

with window

w = O(\varepsilon^{-1/α})

, and -- under an additional two-sided Bayes-risk condition -- a converse shows

w = Ω(\varepsilon^{-1/α})

is necessary within this policy class, so the scaling is

Θ(\varepsilon^{-1/α})

for suffix-only policies. Whether recurrent or propagating cache summaries can beat this scaling is left open. An explicit block-Markov scheme achieves the upper bound; its rate-of-convergence exponent matches the converse under additional forward-decay and regularity hypotheses (not implied by truncation sensitivity alone), and differs by a factor of two otherwise. Empirically, the polynomial law predicts the degradation curves of concrete cache policies: recency-based eviction (sliding, sink-plus-recent) suppresses distortion by roughly two orders of magnitude over random retention at equal budget, with a power-law decay in the budget.

Munsik Kim

Independent Researcher.

KV Caching Rate-Distortion Theory Autoregressive Language Modeling Rate-Distortion Optimization KV-Cache Compression

May 18, 2026eess.IV

CATRF: Codec-Adaptive TriPlane Radiance Fields for Volumetric Content Delivery

Volumetric media promises next-generation content delivery applications, but its bandwidth demand remains a key bottleneck. Implicit and hybrid volumetric representations reduce model sizes, yet still require careful coding to reach 2D video-like bitrates. We present CATRF, a standard-codec-in-the-loop compression framework for plane-factorized radiance fields. During training, we quantize and pack 2D feature planes into codec-friendly canvases, run a standard codec roundtrip (JPEG/VP9/HEVC/AV1), then unpack and dequantize the decoded features before volume rendering. We use a straight-through estimator (STE) to insert the non-differentiable, standard codec pipeline into the training loop, allowing radiance-field features to adapt directly to the real, client-side codec distortions without introducing any learned codec parameters. On both static and dynamic benchmarks, CATRF consistently achieves a better rate-distortion trade-off over codec-agnostic and learned-codec-in-the-loop baselines, and also outperforms recent compressed 3DGS methods in both compression efficiency and decoding speed. These results highlight a practical path toward low-bitrate, compression-resilient volumetric representations for free-viewpoint video streaming.

Tung-I Chen, Lingdong Wang, Subhransu Maji +1

University of Massachusetts Amherst

Rate-Distortion Optimization 3D Scene Representation Video Compression Neural Radiance Fields

May 15, 2026cs.IT

PrismQuant: Rate-Distortion-Optimal Vector Quantization for Gaussian-Mixture Sources

For a Gaussian source under mean-squared error (MSE), classical transform coding is rate--distortion (RD) optimal: the Karhunen--Loeve transform (KLT) diagonalizes the covariance, reverse waterfilling allocates the bits, and scalar quantization closes the loop. This elegant story breaks down for multimodal sources, where no single covariance can capture heterogeneous local geometries, and the RD function loses its closed form. We revisit this problem through Gaussian-mixture sources and develop a constructive RD theory for them. Our key finding is that the mixture structure incurs only a component label cost. Conditioned on the active mixture component, each branch is Gaussian; the challenge is allocating bits across heterogeneous branches. We prove that the genie-aided conditional RD function is governed by a single global reverse-waterfilling level shared across all components and eigenmodes. Building on this result, we introduce PrismQuant, which transmits the component label losslessly and encodes the residual using the component-matched KLT, followed by scalar quantization, achieving a rate of H(C)/n bits per source dimension of the converse, with a vanishing asymptotic gap. We further develop a practical implementation based on EM-driven Gaussian-mixture learning, component-adaptive KLTs, and entropy-constrained scalar quantization (ECSQ). Experiments on synthetic Gaussian mixtures show that PrismQuant closely approaches the theoretical RD bound, while experiments on real-world channel-state-information (CSI) data demonstrate competitive or superior performance compared with transformer-based learned codecs at more than one order of magnitude smaller model size.

Bumsu Park, Chanho Park, Youngmok Park +1

Department of Electrical Engineering POSTECH Pohang, South Korea

Rate-Distortion Theory Gaussian Mixture Models Vector Quantization Rate-Distortion Optimization Information-Theoretic Lower Bounds

May 13, 2026cs.LG

SPHERICAL KV: Angle-Domain Attention and Rate-Distortion Retention for Efficient Long-Context Inference

Long-context inference is increasingly constrained by the KV cache: resident memory grows with context length, and decoding becomes limited by repeated High Bandwidth Memory (HBM) streaming rather than arithmetic. Existing methods such as eviction, windowing, quantization, and offloading reduce footprint, but often leave the critical-path bottleneck only partially addressed, especially when compressed states must still be reconstructed into dense vectors during decoding. We present Spherical KV, a long-context inference method that treats KV allocation as a rate-distortion problem grounded in attention geometry for efficient decoding. The method is built on two ideas: (i) represent directional information cheaply in the decode hot loop, and (ii) allocate retention and precision according to estimated future utility. Its first component, Angle-Domain Attention (ADA), stores keys in a spherical parameterization consisting of a scalar radius and compact angle codes, and computes attention logits directly from these codes without reconstructing dense keys. This preserves a paged, block-local, fusion-friendly decode path and directly targets HBM traffic in realistic serving settings. Its second component, Rate-Distortion Retention (RDR), jointly chooses keep/drop decisions and precision tiers per token and head under a fixed budget, producing tier-homogeneous pages with lightweight metadata and coalesced reads. Together, ADA and RDR provide a deployment-oriented mechanism for reducing KV residency while preserving decode efficiency.

Anay Chauhan, Gurucharan Marthi Krishna Kumar, Arion Das +4

1Synopsys, India · 2McGill University, Canada · 3IIIT Ranchi, India +4

KV Caching Long-Context Language Model Inference KV-Cache Management Efficient Attention Rate-Distortion Optimization KV-Cache Compression+1

May 13, 2026cs.LG

High-Rate Quantized Matrix Multiplication II

This is the second part of the work investigating quantized matrix multiplication (MatMul). In part I we considered the case of calibration-free quantization, whereas here we discuss the setting where covariance matrix

Σ_X

of the columns of the second factor is available. This setting arises in the ubiquitous task of weight-only post-training quantization of LLMs. Weight-only quantization is related to the problem of weighted mean squared error (WMSE) source coding, whose classical (reverse) waterfilling solution dictates how one should distribute rate between coordinates of the vector. We show how waterfilling can be used to improve practical LLM quantization algorithms (GPTQ), which at present allocate rate equally. A recent scheme (known as ``WaterSIC'') that only uses scalar INT quantizers is analyzed and its high-rate performance is shown to be (a) basis free (i.e., characterized by the determinant of

Σ_X

and, thus, unlike existing schemes, is immune to applying random rotations); and (b) within a multiplicative factor of

\frac{2πe}{12}

(or 0.25 bit/entry) of the information-theoretic distortion limit. GPTQ's performance, in turn, is affected by the choice of basis, but for a random rotation and actual

Σ_X

from Llama-3-8B we find it to be within 0.1 bit (depending on the layer type) of WaterSIC, suggesting that GPTQ with random rotation is also near optimal, at least in the high-rate regime.

Or Ordentlich, Yury Polyanskiy

the Hebrew University of Jerusalem, Israel · MIT, USA

LLM Quantization Rate-Distortion Theory Rate-Distortion Optimization Weight-Only Quantization Post-Training Quantization Neural Network Quantization

May 13, 2026cs.CV

Neural Video Compression with Domain Transfer

Content-adaptive compression has always been a key direction in neural video coding (NVC), aiming to mitigate the domain gap between training and testing data. Such gaps often arise from distributional discrepancies between training and inference data, which may cause noticeable performance degradation when the testing content differs from the training distribution. To tackle this challenge, we propose DCVC-DT, a domain transfer enhanced neural video compression framework. Specifically, we design a lightweight online domain transfer (DT) mechanism that dynamically adapts the encoded latent representation during inference, effectively bridging the domain gap without modifying the encoder or decoder parameters. In addition, we develop a frame-level dynamic RD (Rate and Distortion) adjustment scheme that actively regulates the ratio of R and D in the loss function based on quality fluctuation, thereby improving rate-distortion performance. Extensive experiments demonstrate that DCVC-DT achieves up to 6.21% bitrate savings over the baseline DCVC-DC, while significantly enhancing generalization to unseen testing data and alleviating error propagation. Our code is available at https://github.com/SunnyMass/DCVC-DT.

Tiange Zhang, Rongqun Lin, Xiandong Meng +4

Shenzhen Graduate School, Peking University, Shenzhen, China · Pengcheng Laboratory, Shenzhen, China · School of Computer Science, Peking University, Beijing, China

Test-Time Adaptation Cross-Domain Transfer Learning Rate-Distortion Optimization Neural Video Compression Video Compression Neural Network Compression

May 11, 2026cs.IT

Cross-Domain Lossy Compression via Constrained Minimum Entropy Coupling

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.

Nam Nguyen, Hassan Tavakoli, An Vuong +2

School of Electrical Engineering and Computer Science, Oregon State University, Corvallis, OR, 97331

Learned Image Compression Rate-Distortion Optimization Image Restoration

May 9, 2026cs.CV

AQMP: Image compression through Adaptive Quadtree Refinement and Matching Pursuit with Hyperparameter Optimization

We present AQMP, a novel image codec combining Adaptive Quadtree Refinement with Matching Pursuit. Unlike conventional Matching Pursuit methods that operate on fixed-size sub-images, AQMP dynamically adapts block sizes to local image structure, allocating finer partitions where the image is complex and coarser ones where it is smooth. This adaptivity yields superior compression ratios compared to fixed-size block Matching Pursuit at equivalent image quality, while offering significant parallelization opportunities at both the tree-leaf level and during compression of individual nodes. The algorithm is governed by user-specified accuracy and sparsity parameters alongside a small set of additional hyperparameters. To navigate the trade-off between compression efficiency and visual quality, we perform multi-objective hyperparameter optimization using the Tree-Structured Parzen Estimator, producing comprehensive Pareto fronts. Experimental results show that AQMP achieves up to

4\times

higher compression rates than JPEG at comparable SSIM values, while maintaining competitive quality across a broad range of compression regimes. Performance evaluation is provided using a representative set of test images. To ensure reproducibility and promote adoption, we have made our implementation publicly available on GitHub under the MIT license.

Franco Cerino, Emmanuel Tassone, Manuel Tiglio

CONICET. Facultad de Matem´atica, Astronom´ıa, F´ısica y Computaci´on, Universidad Nacional de C´ordoba (5000), Argentina

Rate-Distortion Optimization