Rate-Distortion Optimization

Streaming rendered content is an attractive way to bring high-quality graphics to billions of mobile devices that do not have sufficient rendering power. Existing solutions render content on a server at a fixed frame rate, typically 30 or 60 frames per second, and reduce resolution when bandwidth is restricted. However, this strategy leads to suboptimal rendering quality under the bandwidth constraints. In this work, we exploit the spatio-temporal limits of the human visual system to improve perceived quality while reducing rendering costs by adaptively adjusting both frame rate and resolution based on scene content and motion. Our approach is codec-agnostic and requires only minimal modifications to existing rendering infrastructure. We propose a system in which a lightweight neural network predicts the optimal combination of frame rate and resolution for a given transmission bandwidth, content, and motion velocity. This prediction significantly enhances perceptual quality while minimizing computational cost under bandwidth constraints. The network is trained on a large dataset of rendered content labeled with a perceptual video quality metric. The dataset and further information can be found at the project web page: https://www.cl.cam.ac.uk/research/rainbow/projects/adaptive_streaming/.

Large language models (LLMs) have shown strong performance across diverse tasks, but their inference with long input contexts is bottlenecked by memory size and bandwidth. The Key-Value (KV) cache size grows linearly with sequence length and needs to be re-read from off-chip high-bandwidth memory (HBM) to on-chip memory at every decoding step, resulting in memory-bound inference. Existing methods reduce the cache by either eviction or quantization, but typically treat the two in isolation. In this paper, we cast KV cache compression as a rate-distortion problem, under which eviction and quantization are two end-points of the same bit allocation scheme. This exposes the need to optimize them jointly, motivating our method, RDKV (Rate-Distortion KV cache compression). RDKV derives the weight of each token or channel from the distortion that compression induces on the attention computation. Based on these weights, it assigns each token or channel a bit-width ranging from full precision down to zero bits guided by reverse water-filling, applied once after the prefilling stage. Experiments on LongBench, RULER, and InfiniteBench show that RDKV outperforms the best evaluated baseline by 9.1% on average. On LongBench it recovers 97.81% of full-cache accuracy with only 2.48% cache retention. Compared with full-cache FlashAttention-2 decoding, it achieves 4.5x decode speedup and 1.9x peak memory reduction with 128K context length, while maintaining comparable performance.

Modern sensors generate rich, high-fidelity data, yet applications operating on wearable or remote sensing devices remain constrained by bandwidth and power budgets. Standardized codecs such as JPEG and MPEG achieve efficient trade-offs between bitrate and perceptual quality but are designed for human perception, limiting their applicability to machine-perception tasks and non-traditional modalities such as spatial audio arrays, hyperspectral images, and 3D medical images. General-purpose compression schemes based on scalar quantization or resolution reduction are broadly applicable but fail to exploit inherent signal redundancies, resulting in suboptimal rate-distortion performance. Recent generative neural codecs, or tokenizers, model complex signal dependencies but are often over-parameterized, data-hungry, and modality-specific, making them impractical for resource-constrained environments. We introduce a Lightweight, Versatile, and Asymmetric neural codec architecture (LiVeAction), that addresses these limitations through two key ideas. (1) To reduce the complexity of the encoder to meet the resource constraints of the execution environments, we impose an FFT-like structure and reduce the overall size and depth of the neural-network-based analysis transform. (2) To allow arbitrary signal modalities and simplify training, we replace adversarial and perceptual losses with a variance-based rate penalty. Our design produces codecs that deliver superior rate-distortion performance compared to state-of-the-art generative tokenizers, while remaining practical for deployment on low-power sensors. We release our code, experiments, and python library at https://github.com/UT-SysML/liveaction .

Semantic communication (SemCom) with learned encoder-decoder architectures enables end-to-end learning of compact task-oriented representations optimized for the wireless channel, reducing channel resources needed to convey task-relevant information and improving spectrum efficiency. This paper studies semantic image transmission over block Rayleigh fading with AWGN using a multi-task semantic autoencoder that jointly reconstructs images and predicts labels from the received waveform. The latent dimension (complex channel uses per source sample) serves as a cross-layer control variable governing semantic fidelity and channel resource usage. We characterize the resulting latency-task fidelity tradeoff: larger latent representations improve inference accuracy but increase service time, channel uses, and queueing delay. Building on this insight, we develop online semantic-rate controllers that adapt the latent dimension per update under a long-term semantic error constraint. A queue-aware drift-plus-penalty policy minimizes delay subject to an average semantic error cap, while a complementary age-aware policy minimizes time-average Age of Information (AoI). By adapting the semantic rate to congestion and fidelity requirements, the proposed framework improves spectrum utilization and enables timely semantic updates with significantly lower delay and AoI than fixed-rate baselines.

One of the major differentiators unlocked by learned codecs relative to their hard-coded traditional counterparts is their ability to be optimized directly to appeal to the human visual system. Despite this potential, a perceptual yet practical image codec is yet to be proposed. In this work, we aim to close this gap. We conduct a comprehensive study of the key modeling choices that govern the design of a practical learned image codec, jointly optimized for perceptual quality and runtime -- including within the ablations several novel techniques. We then perform performance-aware neural architecture search over millions of backbone configurations to identify models that achieve the target on-device runtime while maximizing compression performance as captured by perceptual metrics. We combine the various optimizations to construct a new codec that achieves a significantly improved tradeoff between speed and perceptual quality. Based on rigorous subjective user studies, it provides 2.3-3x bitrate savings against AV1, AV2, VVC, ECM and JPEG-AI, and 20-40% bitrate savings against the best learned codec alternatives. At the same time, on an iPhone 17 Pro Max, it encodes 12MP images as fast as 230ms, and decodes them in 150ms -- faster than most top ML-based codecs run on a V100 GPU.

Scalable compression is essential for bandwidth-adaptive transmission, yet most learned codecs are optimized for a fixed rate-distortion point, making rate adaptation costly due to re-encoding or maintaining multiple bitstreams. In this work, we propose TAFA-GSGC, a scalable learned point cloud geometry codec that enables multi-quality decoding from a single bitstream and a single trained model. TAFA-GSGC combines layered residual refinement with channel-group entropy coding, and introduces a Target-Aligned Feature Aggregation module to reduce cross-layer redundancy in enhancement residuals. Our framework supports up to 9 decodable quality levels with monotonic quality improvement as more subbitstreams are received, while maintaining strong compression efficiency. Compared with the PCGCv2 baseline, TAFA-GSGC demonstrates improved RD performance, achieving average BD-rate reductions of 4.99% and 5.92% in terms of D1-PSNR and D2-PSNR, respectively.

We analyse three KV cache quantization schemes under a fair bit budget: \textbf{KV} (scalar MSE baseline), \textbf{KQV} (WHT + MSE on $K$; WHT + MSE + QJL on $V$), and \textbf{QKQV} (WHT + MSE + QJL on both). Starting from the Beta distribution on the hypersphere, we trace how QJL on $K$ inflates inner product variance by $π/2$, which softmax amplifies nonlinearly via Jensen's inequality, and we present statistical inference and information metrics to highlight practical differences. Three empirical findings emerge. (1)~At $n=4$ (the practically dominant budget), KQV wins on every measure -- KL divergence, geometric $K$ error, and 6D distance -- across all distributions and ranks tested. (2)~The K--V asymmetry is unconditional: QKQV is consistently worse than KQV in KL divergence at every budget and distribution. (3)~A budget-dependent crossover exists: QKQV achieves better geometric $K$ reconstruction at $n \in \{2,3,5\}$, KQV at $n \in \{4,6\}$, invariant to rank and tail weight -- an open rate-distortion problem. $\mathrm{KL}(p_{\mathrm{ref}} \| p_{\mathrm{quant}})$, K-only by construction, bridges K direction error to routing corruption and output collapse. We present a sufficient condition when the Jensen mechanism amplifies superlinearly through the softmax. At $n \in \{2,3,5\}$, QKQV wins geometrically because this assumption does not bind. At $n=4$, elevated K error and KL divergence for QKQV strongly suggest the Jensen mechanism is the operative cause of the crossover, providing a new perspective and explanation.

Fundamental rate-distortion-perception (RDP) trade-offs arise in applications requiring maintained perceptual quality of reconstructed data, such as neural image compression. When compressed data is transmitted over public communication channels, security risks emerge. We therefore study secure RDP under negligible information leakage over both noiseless channels and broadcast channels, BCs, with correlated noise components. For noiseless channels, the exact secure RDP region is characterized. For BCs, an inner bound is derived and shown to be tight for a class of more-capable BCs. Separate source-channel coding is further shown to be optimal for this exact secure RDP region with unlimited common randomness available. Moreover, when both encoder and decoder have access to side information correlated with the source and the channel is noiseless, the exact RDP region is established. If only the decoder has correlated side information in the noiseless setting, an inner bound is derived along with a special case where the region is exact. Binary and Gaussian examples demonstrate that common randomness can significantly reduce the communication rate in secure RDP settings, unlike in standard rate-distortion settings. Thus, our results illustrate that random binning-based coding achieves strong secrecy, low distortion, and high perceptual quality simultaneously.

Large language models cache all previously computed key-value (KV) pairs during generation, and this KV cache grows linearly with sequence length, making it a primary memory bottleneck for serving. Quantizing the KV cache to fewer bits reduces this cost, yet all current quantizers assign the same bit-width to every attention head, ignoring the large variation in head importance. A natural idea is to allocate more bits to important heads and fewer to the rest. We show, however, that such mixed-precision allocation has a hidden pitfall: each quantizer follows a different distortion curve D(b)=alpha*beta^{-b}, and the decay rate beta varies from 3.6 to 5.3 across quantizer designs. Applying one quantizer's distortion model to another inverts the allocation order and makes performance worse than uniform quantization. We call this failure mode distortion model mismatch and propose RateQuant to resolve it. RateQuant fits a per-quantizer distortion model from a small calibration set, then solves the resulting bit-allocation problem in closed form via reverse waterfilling from rate-distortion theory. On Qwen3-8B at 2.5 average bits, calibrated RateQuant reduces KIVI's perplexity from 49.3 to 14.9 (70% reduction) and improves QuaRot by 6.6 PPL. The entire calibration takes 1.6 s on a single GPU and adds zero overhead at inference time.

The fundamental limit of natural signal compression has traditionally been characterized by classical rate-distortion (RD) theory through the tradeoff between coding rate and reconstruction distortion, while the rate-distortion-perception (RDP) framework introduces a divergence-based measure of perceptual quality as a modeling principle, leaving its theoretical origin unclear. In this paper, motivated by a synonymity-based semantic information perspective, we reformulate perceptual reconstruction as recovering any admissible sample within an ideal synonymous set (synset) associated with the source, rather than the source sample itself, and establish a synonymous source coding architecture. On this basis, we develop a synonymous variational inference (SVI) analysis framework with a synonymous variational lower bound (SVLBO) for tractable analysis of synset-oriented compression. Within this framework, we establish a synonymity-perception consistency principle, showing that optimal identification of semantic information is theoretically consistent with perceptual optimization. Based on this result, we further derive a tight-bound synonymous source coding rate characterization and show that its Jensen-limit relaxation leads to a synonymous rate-distortion-perception form for practical optimization. These analytical results show that the distributional divergence term arises naturally from the synset-based reconstruction objective, clarify its compatibility with existing RDP formulations and classical RD theory, and suggest the potential advantages of synonymous source coding.

Efficient coding theory predicts that biological perceptual systems compress sensory input optimally under resource constraints, with the systematic structure of errors reflecting the geometry of that compression. Here we operationalize this principle using rate-distortion theory (RDT) to characterize how any system - biological or artificial - trades representational fidelity for informational efficiency. Treating stimulus-response behavior as an effective communication channel, we infer rate-distortion (RD) frontiers directly from confusion matrices and summarize each system with three geometric signatures: slope (beta), curvature (kappa), and area under the RD curve (AUC), capturing the marginal cost, abruptness, and overall efficiency of the accuracy-compression trade-off respectively. Applying this framework to human psychophysical data and 18 deep vision models across 12 families of controlled image perturbations at graded severities, we find that both biological and artificial systems follow a common lossy-compression principle but occupy systematically different regions of RD space. Humans exhibit smooth, flexible trade-offs characteristic of near-optimal efficient coding, while deep networks operate in steeper, more brittle regimes even at matched accuracy, with geometry dissociable from performance across training regimes. Critically, behavioral RD signatures track internal representational geometry, evidenced by the behaviorally inferred compression structure correlating with internal representational dissimilarity across all models. These results establish RD geometry as a compact diagnostic of perceptual compression strategy that recovers mechanistically interpretable structure in internal representations from behavioral input alone and extends naturally to the direct characterization of compression geometry in neural population activity.

The structure of naming systems in natural languages hinges on a trade-off between high informativeness and low complexity. Focusing on the domain of kinship naming, we analyze such trade-off while addressing simplifying assumptions of prior work, namely: (i) universal communicative need across languages, and (ii) optimal listeners. To that aim, we collect data from four different languages, and analyze how different communicative needs and variations in the listener model influence the informativeness--complexity trade-off. Adopting a referential game setup from emergent communication, we further show that trade-off optimality is not only theoretically achievable but also emerges empirically in learned communication systems.

Given encoded 3D point cloud geometry available at the decoder, we study the problem of lossy attribute compression in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_{L}$, where $\mathcal{F}^{(p)}_{l}$ is a family of functions spanned by a B-spline basis function of order $p$ at a chosen scale and its integer shifts. The projected low-pass coefficients $F_l^*$ are computed by variable-complexity unrolling of a rate-distortion (RD) optimization algorithm into a feed-forward network, where the rate term is the sparsity-promoting $\ell_1$-norm. Thus, the projection operation is end-to-end differentiable. For a chosen coarse-to-fine predictor, the coefficients are then adjusted to account for the prediction from a lower-resolution to a higher-resolution, which is also optimized in a data-driven manner.

Recently, numerous end-to-end optimized image compression neural networks have been developed and proved themselves as leaders in rate-distortion performance. The main strength of these learnt compression methods is in powerful nonlinear analysis and synthesis transforms that can be facilitated by deep neural networks. However, out of operational expediency, most of these end-to-end methods adopt uniform scalar quantizers rather than vector quantizers, which are information-theoretically optimal. In this paper, we present a novel Lattice Vector Quantization scheme coupled with a spatially Adaptive Companding (LVQAC) mapping. LVQ can better exploit the inter-feature dependencies than scalar uniform quantization while being computationally almost as simple as the latter. Moreover, to improve the adaptability of LVQ to source statistics, we couple a spatially adaptive companding (AC) mapping with LVQ. The resulting LVQAC design can be easily embedded into any end-to-end optimized image compression system. Extensive experiments demonstrate that for any end-to-end CNN image compression models, replacing uniform quantizer by LVQAC achieves better rate-distortion performance without significantly increasing the model complexity. Code is available at: https://github.com/xzhang9308/LVQAC.