Lossy compression algorithms are typically designed and analyzed through the lens of Shannon's rate-distortion theory, where the goal is to achieve the lowest possible distortion (e.g., low MSE or high SSIM) at any given bit rate. However, in recent years, it has become increasingly accepted that "low distortion" is no…
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48 results for “rate-distortion tradeoff”
New approach connects robust learning to privacy issues.
problem Vulnerability of deep neural networks to adversarial examples.
method Privacy-utility tradeoff and rate-distortion theory.
result Found saddle point via maximum conditional entropy problem.
The enormous size of modern deep neural networks makes it challenging to deploy those models in memory and communication limited scenarios. Thus, compressing a trained model without a significant loss in performance has become an increasingly important task. Tremendous advances has been made recently, where the main te…
New method optimizes lossy compression models more effectively.
problem Difficulty in manually setting a tradeoff parameter for lossy compression models.
method Constrained optimization method of Rezende and Viola, 2018.
result The method enables pointwise model comparisons and outperforms existing methods.
Extends likelihood ratio exponential families to analyze various optimization methods.
problem Analyzing optimization methods like rate-distortion and information bottleneck.
method Linking geometric mixture paths to exponential families and using hypothesis testing.
result Provides a common mathematical framework for understanding these methods.
New compression theory justifies model pruning for neural networks.
problem Improving neural network performance with reduced model size.
method Information-theoretic rate-distortion theory applied to NN compression.
result Pruning improves model performance on CIFAR-10 and ImageNet datasets.
Neural Estimation of the Rate-Distortion Function With Applications to Operational Source Codingcs.IT
Estimates rate-distortion function for large datasets using neural networks.
problem Designing lossy data compression schemes and comparing them with theoretical limits.
method Re-formulate rate-distortion objective and solve using neural networks.
result NERD accurately estimates the rate-distortion function for real-world datasets.
Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processescond-mat.stat-mech
Predictive rate-distortion analysis suffers from the curse of dimensionality: clustering arbitrarily long pasts to retain information about arbitrarily long futures requires resources that typically grow exponentially with length. The challenge is compounded for infinite-order Markov processes, since conditioning on fi…
New coding theorem shows achievable rate matches theoretical limit.
problem Unknown existence of encoders and decoders for RDPF.
method Used stochastic, variable-length codes to prove RDPF achievable.
result Achievable rate matches theoretical rate-distortion-perception function.
New bounds for optimal transport using Gaussian processes and rate-distortion functions.
problem Finding bounds for entropic optimal transport with mutual information constraints.
method Lifting technique to construct a Gaussian process and applying the majorizing measure theorem.
result Maximum expected inner product is equivalent to a truncated integral involving the rate-distortion function.
We propose and study the problem of distribution-preserving lossy compression. Motivated by recent advances in extreme image compression which allow to maintain artifact-free reconstructions even at very low bitrates, we propose to optimize the rate-distortion tradeoff under the constraint that the reconstructed sample…
High-dimensional VAEs inevitably collapse to prior, requiring large datasets for good performance.
problem Posterior collapse in VAEs leads to poor representation learning quality.
method Analyzed a minimal VAE in a high-dimensional limit, evaluating conditions for posterior collapse with respect to beta and dataset size.
result VAEs face 'inevitable posterior collapse' beyond a certain beta threshold, regardless of dataset size.
Fixing a Broken ELBOcs.LG
Recent work in unsupervised representation learning has focused on learning deep directed latent-variable models. Fitting these models by maximizing the marginal likelihood or evidence is typically intractable, thus a common approximation is to maximize the evidence lower bound (ELBO) instead. However, maximum likeliho…
Optimizing the Communication-Accuracy Trade-off in Federated Learning with Rate-Distortion Theorycs.LG
Optimizes communication in federated learning using rate-distortion theory.
problem Reduces communication cost in federated learning while maintaining model accuracy.
method Applies rate-distortion theory to model updates, proposing distortion as a proxy for accuracy.
result Near-optimal communication reduction, outperforming other methods on a FL benchmark.
Researchers prove inner product recovery is impossible in latent space models.
problem Recovering inner products in latent space models with random geometric graphs.
method Rate-distortion theory applied to Gaussian or spherical latent locations.
result Impossible to recover inner products if dimensionality exceeds , matching positive results' conditions.
This paper explores the problem of learning transforms for image compression via autoencoders. Usually, the rate-distortion performances of image compression are tuned by varying the quantization step size. In the case of autoen-coders, this in principle would require learning one transform per rate-distortion point at…
New bounds on generalization error for distributed learning using rate-distortion theory.
problem Establishing upper bounds on generalization error for distributed learning algorithms.
method Using rate-distortion theory, the paper introduces new bounds that depend on the compressibility of each client's algorithm.
result The bounds suggest that the generalization error of the distributed setting decays faster than that of the centralized one with a factor of .
Learning useful representations with little or no supervision is a key challenge in artificial intelligence. We provide an in-depth review of recent advances in representation learning with a focus on autoencoder-based models. To organize these results we make use of meta-priors believed useful for downstream tasks, su…
Paper studies fundamental limits of communication in distributed learning.
problem Communication efficiency in model aggregation for distributed learning.
method Rate-Distortion approach to model aggregation as a vector Gaussian CEO problem.
result Derives rate region bound and sum-rate-distortion function for model aggregation.
We show that model compression can improve the population risk of a pre-trained model, by studying the tradeoff between the decrease in the generalization error and the increase in the empirical risk with model compression. We first prove that model compression reduces an information-theoretic bound on the generalizati…
Simplifies VAE for anomaly detection using rate-distortion theory.
problem Anomaly detection in unsupervised learning systems.
method Revisit VAE from information theory, incorporate model uncertainty.
result Competitive performance on benchmark datasets.
This paper studies communication efficiency in federated learning by optimizing the sum-rate-distortion function for indirect multiterminal source coding.
problem Indirect multiterminal source coding in federated learning where edge devices send noisy gradients to the server.
method Analyzes the rate region for the quadratic vector Gaussian CEO problem under unbiased estimator and derives an explicit formula for the sum-rate-distortion function.
result Derives an explicit formula for the sum-rate-distortion function in the special case of identical gradients over edge devices.
Lower bounds on Bayes risk for realizable models derived using information theory.
problem Deriving lower bounds on Bayes risk for realizable machine learning models.
method Information-theoretic analysis using rate-distortion theory and mutual information.
result Lower bounds on Bayes risk for realizable models, matching known bounds up to logarithmic factors.
We formulate the notion of minimax estimation under storage or communication constraints, and prove an extension to Pinsker's theorem for nonparametric estimation over Sobolev ellipsoids. Placing limits on the number of bits used to encode any estimator, we give tight lower and upper bounds on the excess risk due to qu…
New method estimates rate-distortion function using optimal transport.
problem Estimating the fundamental performance limit of data compression.
method Wasserstein gradient descent to learn optimal reproduction distribution.
result Local convergence and sample complexity analysis of R-D estimator.
In this article we use rate-distortion theory, a branch of information theory devoted to the problem of lossy compression, to shed light on an important problem in latent variable modeling of data: is there room to improve the model? One way to address this question is to find an upper bound on the probability (equival…
Unified bounds linking compressibility, fractal dimensions, and mutual information.
problem Understanding generalization in stochastic learning algorithms.
method Rate-distortion theory applied to machine learning generalization.
result Unified bounds linking compressibility, fractal dimensions, and mutual information.
This paper develops a method to estimate the rate-distortion function for general data sources.
problem Estimating the rate-distortion function for general data sources.
method Develops an algorithm for sandwiching the R-D function of a general (not necessarily discrete) source using i.i.d. data samples.
result Estimates R-D sandwich bounds for various data sources, including natural images, indicating potential for improving compression methods.
New method improves bivariate causal discovery by accurately estimating cause variable complexity.
problem Improper estimation of cause variable complexity in current MDL-based methods.
method Rate-distortion MDL (RDMDL) using information dimension for cause variable complexity estimation.
result RDMDL achieves competitive performance on Tübingen dataset.
This work adapts RDT for mental program construction, showing benefits and costs.
problem Applying RDT to mental programs with trade-offs between description length, error, and computational costs.
method Proposed a three-way trade-off and used simulations and partial information decomposition.
result Constructing a shared program library provides global benefits but is sensitive to curricula.
A distinctive property of human and animal intelligence is the ability to form abstractions by neglecting irrelevant information which allows to separate structure from noise. From an information theoretic point of view abstractions are desirable because they allow for very efficient information processing. In artifici…
This paper proposes a new method for efficient data compression using Bayesian neural networks.
problem Efficient compression of data represented as functions mapping coordinates to signal values.
method Overfitting variational Bayesian neural networks to the data and compressing an approximate posterior weight sample using relative entropy coding.
result Our method achieves strong performance on image and audio compression while retaining simplicity.
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average distance between the learned classifier and the true maximum a posteriori classifier, which are well-established surrogates for th…
The paper proposes a principle for dynamically adjusting the granularity of reinforcement learning abstractions.
problem Lack of general principles for dynamically adjusting the granularity of reinforcement learning abstractions.
method The paper proposes a principle based on rate-distortion theory, formalized through a performance certificate decomposing value error into learning and abstraction error bounds.
result Soft state-action abstractions can achieve near-optimal performance under substantial lossy compression of state and action information.
Single training run learns optimal VAE parameters for various β values.
problem Training VAEs with varying β values for optimal trade-off between distortion and rate.
method Introduced Multi-Rate VAE (MR-VAE) using hypernetworks to map β to optimal parameters.
result MR-VAEs can construct the full rate-distortion curve without additional training.
Improved Monte-Carlo models by constraining mutual information between latent and observable variables.
problem Training density models leads to latent variables being useless.
method Weave tighter Monte-Carlo bounds with mutual information constraints.
result Improved training of models with continuous and discrete latent variables.
New insights into image compression trade-offs with private randomness.
problem Trade-off between compression rate and perceptual quality in image compression.
method Characterization of rate-distortion trade-off with private randomness under different realism constraints.
result Encoder private randomness is not useful if compression rate is below source entropy, even with limited common and decoder private randomness.
A new approach for efficient data compression in split DNN computing.
problem Optimizing data compression for DNN models split between mobile devices and edge servers.
method Systematic design and training of bottleneck units that can be inserted at the split point.
result Achieves excellent rate-distortion performance with minimal compute and storage overhead.
Compression is at the heart of effective representation learning. However, lossy compression is typically achieved through simple parametric models like Gaussian noise to preserve analytic tractability, and the limitations this imposes on learning are largely unexplored. Further, the Gaussian prior assumptions in model…
Modified BA algorithm computes RD and DR functions efficiently.
problem Computing rate-distortion and distortion-rate functions.
method A novel modification of the BA algorithm using Newton's method for root-finding.
result The modified algorithm converges to RD and DR function solutions with rate and provides -approximations.
We formalise the widespread idea of interpreting neural network decisions as an explicit optimisation problem in a rate-distortion framework. A set of input features is deemed relevant for a classification decision if the expected classifier score remains nearly constant when randomising the remaining features. We disc…
A new framework for neural network classification using vector quantization.
problem Learning a neural network classifier under the IB principle.
method Aggregated Learning framework, combining vector quantization and variational techniques.
result The effectiveness of Aggregated Learning verified through experiments.
This study analyzes communication constraints in MoE architectures using information theory.
problem Communication constraints in Mixture-of-Experts (MoE) architectures.
method Developed a rate-distortion characterization of finite-rate gating in MoE architectures using information theory.
result Yielded capacity-aware limits for communication-constrained MoE systems.
Rate-Distortion Optimization Guided Autoencoder for Isometric Embedding in Euclidean Latent Spacecs.LG
To analyze high-dimensional and complex data in the real world, deep generative models, such as variational autoencoder (VAE) embed data in a low-dimensional space (latent space) and learn a probabilistic model in the latent space. However, they struggle to accurately reproduce the probability distribution function (PD…
The bias-variance tradeoff doesn't always apply in neural networks, contradicting textbook claims.
problem The bias-variance tradeoff is not universally applicable in neural networks, contradicting textbook teachings.
method Extensive experiments and analysis on neural networks, revisiting Geman et al. (1992) experiments.
result Neural networks do not exhibit a bias-variance tradeoff when increasing network width, contradicting textbook claims.
BS-VAE separates decoder variance and beta to improve VAE performance.
problem Blurriness in VAE outputs and difficulty in analyzing model performance.
method Explicitly separates beta and decoder variance in Beta-Sigma VAE.
result Superior performance in natural image synthesis and controllable parameters.
DiffC compresses images by diffusing Gaussian noise, outperforming state-of-the-art methods.
problem Efficient lossy image compression without transform coding.
method Unconditional diffusion generative models to encode and denoise corrupted pixels.
result DiffC outperforms HiFiC on ImageNet 64x64, achieving a 3 dB gain at high bitrates.
Diffusion models improve image compression at low bit-rates.
problem Efficiently compressing images at very low bit-rates.
method Encoding into an embedding, using diffusion models to refine the embedding iteratively.
result Realistic reconstructions can be generated at extremely low bit-rates.