A Unified Rate-Distortion Perspective on Vector, Product, and Scalar Quantization

Discrete visual tokenization, predominantly driven by vector, scalar, and product quantization, lacks a unified conceptual framework for understanding quantization tradeoffs. In this paper, we propose a unified rate--distortion perspective on modern discrete visual tokenization. By viewing quantization as lossy compression, we characterize the nominal fixed-length coding rate through token count and codebook size, and quantization error as the distortion. Within this framework, we resolve three central questions. First, we theoretically and empirically show that minimizing distortion, rather than maximizing codebook utilization, is the primary intrinsic objective for reconstruction fidelity, with a direct connection to the STE-induced gradient discrepancy. Second, we establish two critical fairness conditions for intrinsic quantization comparison: controlling latent feature statistics and enforcing identical coding rates. Third, under these conditions, we recover the VQ--PQ--SQ distortion hierarchy in modern visual tokenization and show empirically that modern VQ methods achieve the lowest distortion. This work provides a foundational rate--distortion reframing of modern discrete visual tokenization, resolves ambiguities in quantizer evaluation, and provides a controlled framework for isolating intrinsic quantization effectiveness under fixed-rate constraints.

Lossy Event Compression: From Event Stream Distortion to Task Performance

Event cameras generate asynchronous, sparse data streams with microsecond temporal resolution, but in moderate-to-high motion scenes they can produce as many as hundreds of millions of events per second, creating significant bandwidth and storage challenges. Lossy compression is therefore essential for practical deployment, yet existing event stream distortion metrics fail to reliably predict compression-induced degradation at the task level, forcing codec optimization to rely on expensive task-specific evaluations. To address this gap, this paper introduces two fundamentally different event compression pipelines: i) an aggregation-based pipeline that converts the event stream into polarity-based histogram frames for compression with the conventional image codec JPEG 2000, and ii) a frame-free point cloud-based pipeline that codes events natively as 3D points using the octree-based codec G-PCC. Both pipelines are then assessed within a unified task-driven evaluation framework that relates event stream distortion to downstream application performance across four representative tasks: i) video reconstruction, ii) object detection, iii) optical flow estimation, and a delay-sensitive task iv) asynchronous feature tracking under a reference-relative protocol. Building on this framework, five classification-based distortion metrics are applied to event compression for the first time, to the best of the authors' knowledge, and benchmarked against existing event stream metrics. Experimental results demonstrate that the proposed metrics reliably predict compression-induced task degradation across different coding frameworks. This demonstrates that event stream distortion assessment can be an efficient alternative to repeated task-specific evaluation, providing direct guidance for the development and optimization of future event data coding solutions.

FDIR: Harmonizing Fidelity and Human-Machine Preference in Lossy Compression Image Restoration

Image restoration quality can be evaluated along three complementary facets: pixel-level fidelity, human perception, and downstream machine preference. However, existing lossy compression restoration methods optimize for at most one of these criteria: fidelity-oriented models often regress toward conditional means and produce over-smoothed outputs, while generative approaches hallucinate plausible but factually incorrect textures that degrade both ground-truth fidelity and downstream task accuracy. To navigate this three-way tradeoff, we propose FDIR, a two-stage architecture that decouples the conflicting demands through complementary inductive biases: Quality-Guided One-Step Flow Matching (QO-Flow) recovers global semantic structure in latent space via a single forward pass, while Flow-Conditioned Detail Refinement (FCDR) deterministically restores high-frequency textures and suppresses generative hallucinations in pixel space. Extensive experiments demonstrate that FDIR achieves superior fidelity, with a favorable perceptual-fidelity balance and competitive machine preference.

EVOLVE: Efficient Learned Volume Compression with Variable-Rate Encoding on a Cross-Domain Database

Large-scale scientific simulations generate volumetric data at rates that far outpace advances in storage and network bandwidth, making effective lossy compression increasingly critical. However, conventional compressors often struggle to preserve fine structural details at high compression ratios (CRs), and implicit neural representations (INRs) require costly per-volume optimization and produce models with fixed CRs. To respond, we present EVOLVE, an autoencoder (AE)-based volume-compression framework that targets high CRs for offline compression, with three key contributions. First, we construct a large-scale cross-domain database of 6,376 volumes from 21 scientific simulations, curated via perceptual hashing to ensure diversity, enabling the optimized model to extract features that generalize across volumes within the covered scientific simulation domains. Second, we reexamine the design space of AE-based compressors and incorporate several macro- and micro-designs into a vanilla AE to develop EVOLVE, which substantially improves the expressive power and compression capability. Third, we develop a learnable gain mechanism with a three-stage training strategy to enable variable-rate encoding, allowing a single model to support continuous CR adjustment at inference time. Experiments on multiple unseen scientific simulation datasets demonstrate that EVOLVE achieves substantially higher CRs than conventional compressors at comparable reconstruction quality, while delivering compression speeds that are orders of magnitude faster than INR-based methods, highlighting its promise as a strong alternative for compressing scientific data. The code, model weights, and results are available on our project page at https://evolve-vis.github.io.

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.

CGS: Configurable Graph Summarization with Bounded Neighborhood Loss and Query Support

Given a large graph, how to generate a compact summary graph that is configurable by the user and supports multiple graph queries with either no loss or with high accuracy? The ever growing size of graph datasets makes the above question on graph summarization very pertinent. Although, there are several approaches, there does not exist a configurable graph summarization method that offers high compression along with support for multiple graph queries on the summary graph with high accuracy, and allows the user to configure the summarization based on: (1) lossless or lossy summarization, (2) amount of tolerable neighborhood loss, (3) the type of loss it can tolerate, in terms of false positive edges (i.e., extra edges), false negative edges (i.e., missing edges), or neither, in both the (a) reconstructed graph and the (b) query answers. To overcome these limitations, we propose a novel graph summarization framework CGS (Configurable Graph Summarizer) that builds upon the idea of aggregating nodes with common neighborhoods. The CGS framework consists of three summarization variants, CGS-E, CGS-I and CGS-U. While CGS-E is a lossless scheme, CGS-I and CGS-U are lossy schemes that allow reconstruction of the input graph with no false positive edges and no false negative edges, respectively. To bound the graph reconstruction loss, we introduce a user-specified parameter neighborhood loss tolerance threshold, that limits the maximum loss allowed in the neighborhood of each node. This allows graph reconstruction and neighborhood query evaluation with either no loss or with bounded loss guarantees. Empirical evaluation on several synthetic and real-world graphs shows that CGS offers superior summarization than the state-of-the-art methods, and can answer graph queries with fairly high accuracy and efficiency.

Quantifying the Impact of Lossy Compression on Neural Generative Surrogate Modeling

Neural networks are used as generative surrogate models for scientific discovery, which are trainable approximations of scientific simulations. These models enable users to replace time-consuming numerical simulations with learned alternatives, providing quick solutions. However, high-fidelity generative surrogate models require massive training datasets, which can create storage and I/O challenges. Lossy compression is a promising way to reduce this burden, but compression errors may affect the model quality in subtle ways, making it challenging to quantify their impact. In this work, we examine how lossy compression of training data impacts the quality of generative surrogate models. We begin by characterizing the uncertainty inherent in training neural networks, showing that identical training configurations can produce different models. By exploiting this variability, we propose a method to estimate how much compression-induced error a surrogate model can tolerate without affecting its accuracy. Evaluation of two application simulations demonstrates that our approach significantly reduces memory/storage requirements and speeds up training while producing high-quality surrogate models. These results show that lossy compression saves data storage up to 23.7x and 39x with negligible impact on the quality of the surrogate model. Meanwhile, reducing the size of the training data set also enhances the data loading speed and reduces the training time by up to 3x.

Can Deep Neural Networks Improve Compression of Very Large Scientific Data?

Error-bounded lossy compression is a fundamental technique for managing the rapidly growing volumes of scientific data produced by modern simulations and observational instruments. Most state-of-the-art-compressors follow a prediction-residual paradigm, where compression effectiveness depends on the quality of the predictor: more accurate predictions generate smaller residuals that are easier to compress. This observation raises a question: can modern machine learning models serve as superior predictors for scientific data compression? Answering this question directly is challenging because developing compression-specific ML predictors requires substantial resources. Instead, we leverage the climate domain where highly accurate pretrained weather forecasting foundation models already exist, making them an ideal testbed. We present a framework that integrates spatial and temporal deep learning models into a conventional error-bounded compression pipeline. The framework supports auto-regressive forecasting models and avoids error accumulation. Using ERA5 climate data as a representative large-scale scientific dataset, we evaluate three distinct ML predictors: a VAEformer-based codec (CRA5), a graph neural network forecaster (GraphCast), and a vision-transformer forecaster (Aurora), against the state-of-the-art compressor SZ3.1 under identical quantization and entropy-coding backends. Our evaluation over approximately 1.7 TB of data reveals a surprising result: although ML predictors generate more accurate predictions and can improve reconstruction quality by up to 91% while achieving up to 9.6x higher compression ratios for highly predictable variables, they do not improve overall dataset-level compression ratio. We show that prediction accuracy alone is insufficient: the spatial structure of the resulting residuals plays a decisive role in entropy coding efficiency.

Few-step Generative Models as Lossy Compression

DiffC provides a principled way to reuse pre-trained diffusion models for lossy compression, but its encoding and decoding procedures remain slow because they require many discretized forward and reverse steps. We study whether few-step generative models -- Rectified Flow, Consistency Trajectory Models (CTM), and MeanFlow -- can be cast as codecs within the same reverse channel coding (RCC) framework. The main challenge is that RCC requires posterior and shared distribution parameters, whereas these models do not explicitly parameterize intermediate conditional distributions. For Rectified Flow and MeanFlow, we use the equivalence between velocity parameterization and diffusion-style denoising parameterization to derive the quantities required by RCC. For CTM, which is distilled from EDM, we adopt the EDM noise parameterization together with local Gaussian approximations of the sender and shared distributions at intermediate states. This yields a proof-of-concept probabilistic formulation that enables compression with pre-trained few-step generative models without retraining. On low-resolution benchmarks, the resulting codecs reduce encoding and decoding time and improve realism in the low-bit-rate regime.

Residual Modeling for High-Fidelity Learned Compression of Scientific Data

Lossy compression is essential for massive spatiotemporal data from scientific simulations. Learned compressors can achieve high compression ratios at moderate accuracy targets, but their aggregate reconstruction losses do not guarantee accuracy for each block. Existing Guaranteed Autoencoder (GAE) methods add a per-block residual correction by retaining SVD/PCA-style coefficients until the target is met. This works at moderate tolerances, but in the high-fidelity regime with block-level NRMSE from 10^-6 to 10^-4, the number of retained coefficients grows quickly and the correction stream dominates the total rate. We propose a residual-centric view: the learned residual is structurally different from the original scientific field and should be coded with a representation designed for that residual. We introduce two residual coders. LBRC is a deterministic, training-free pipeline that adaptively quantizes the learned residual to the target NRMSE and losslessly encodes the resulting integer residual using 3D Lorenzo differencing, zigzag mapping, bit-plane coding, and entropy coding. NGLR adds a causal neural predictor that outputs a normalized bias for an integer-rounded Lorenzo prediction in the same deterministic integer pipeline, reducing the entropy of the remaining residual code while preserving deterministic decoding. The predictor weights are serialized and counted in the bitstream. Across E3SM, JHTDB, and ERA5 at block-level NRMSE targets from 10^-6 to 10^-4, LBRC improves compression ratio over GAE by 30-60% and is broadly competitive with SZ. NGLR adds a further 10-40% over LBRC and outperforms SZ in the evaluated high-fidelity regime. These results show that residual representations tailored to learned-compressor residuals can preserve the advantage of learned compression when global residual correction becomes rate-dominant.