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Register a new userLossy Compression with Distortion Constrained Optimization
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When training end-to-end learned models for lossy compression, one has to balance the rate and distortion losses. This is typically done by manually setting a tradeoff parameter $beta$, an approach called $beta$-VAE. Using this approach it is difficult to target a specific rate or distortion value, because the result can be very sensitive to $beta$, and the appropriate value for $beta$ depends on the model and problem setup. As a result, model comparison requires extensive per-model $beta$-tuning, and producing a whole rate-distortion curve (by varying $beta$) for each model to be compared. We argue that the constrained optimization method of Rezende and Viola, 2018 is a lot more appropriate for training lossy compression models because it allows us to obtain the best possible rate subject to a distortion constraint. This enables pointwise model comparisons, by training two models with the same distortion target and comparing their rate. We show that the method does manage to satisfy the constraint on a realistic image compression task, outperforms a constrained optimization method based on a hinge-loss, and is more practical to use for model selection than a $beta$-VAE.
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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 samples follow the distribution of the training data. The resulting compression system recovers both ends of the spectrum: On one hand, at zero bitrate it learns a generative model of the data, and at high enough bitrates it achieves perfect reconstruction. Furthermore, for intermediate bitrates it smoothly interpolates between learning a generative model of the training data and perfectly reconstructing the training samples. We study several methods to approximately solve the proposed optimization problem, including a novel combination of Wasserstein GAN and Wasserstein Autoencoder, and present an extensive theoretical and empirical characterization of the proposed compression systems.
The field of deep generative modeling has succeeded in producing astonishingly realistic-seeming images and audio, but quantitative evaluation remains a challenge. Log-likelihood is an appealing metric due to its grounding in statistics and information theory, but it can be challenging to estimate for implicit generative models, and scalar-valued metrics give an incomplete picture of a models quality. In this work, we propose to use rate distortion (RD) curves to evaluate and compare deep generative models. While estimating RD curves is seemingly even more computationally demanding than log-likelihood estimation, we show that we can approximate the entire RD curve using nearly the same computations as were previously used to achieve a single log-likelihood estimate. We evaluate lossy compression rates of VAEs, GANs, and adversarial autoencoders (AAEs) on the MNIST and CIFAR10 datasets. Measuring the entire RD curve gives a more complete picture than scalar-valued metrics, and we arrive at a number of insights not obtainable from log-likelihoods alone.
Deep Neural Networks (DNNs) are applied in a wide range of usecases. There is an increased demand for deploying DNNs on devices that do not have abundant resources such as memory and computation units. Recently, network compression through a variety of techniques such as pruning and quantization have been proposed to reduce the resource requirement. A key parameter that all existing compression techniques are sensitive to is the compression ratio (e.g., pruning sparsity, quantization bitwidth) of each layer. Traditional solutions treat the compression ratios of each layer as hyper-parameters, and tune them using human heuristic. Recent researchers start using black-box hyper-parameter optimizations, but they will introduce new hyper-parameters and have efficiency issue. In this paper, we propose a framework to jointly prune and quantize the DNNs automatically according to a target model size without using any hyper-parameters to manually set the compression ratio for each layer. In the experiments, we show that our framework can compress the weights data of ResNet-50 to be 836$times$ smaller without accuracy loss on CIFAR-10, and compress AlexNet to be 205$times$ smaller without accuracy loss on ImageNet classification.
In the context of lossy compression, Blau & Michaeli (2019) adopt a mathematical notion of perceptual quality and define the information rate-distortion-perception function, generalizing the classical rate-distortion tradeoff. We consider the notion of universal representations in which one may fix an encoder and vary the decoder to achieve any point within a collection of distortion and perception constraints. We prove that the corresponding information-theoretic universal rate-distortion-perception function is operationally achievable in an approximate sense. Under MSE distortion, we show that the entire distortion-perception tradeoff of a Gaussian source can be achieved by a single encoder of the same rate asymptotically. We then characterize the achievable distortion-perception region for a fixed representation in the case of arbitrary distributions, identify conditions under which the aforementioned results continue to hold approximately, and study the case when the rate is not fixed in advance. This motivates the study of practical constructions that are approximately universal across the RDP tradeoff, thereby alleviating the need to design a new encoder for each objective. We provide experimental results on MNIST and SVHN suggesting that on image compression tasks, the operational tradeoffs achieved by machine learning models with a fixed encoder suffer only a small penalty when compared to their variable encoder counterparts.
Deep model compression has been extensively studied, and state-of-the-art methods can now achieve high compression ratios with minimal accuracy loss. This paper studies model compression through a different lens: could we compress models without hurting their robustness to adversarial attacks, in addition to maintaining accuracy? Previous literature suggested that the goals of robustness and compactness might sometimes contradict. We propose a novel Adversarially Trained Model Compression (ATMC) framework. ATMC constructs a unified constrained optimization formulation, where existing compression means (pruning, factorization, quantization) are all integrated into the constraints. An efficient algorithm is then developed. An extensive group of experiments are presented, demonstrating that ATMC obtains remarkably more favorable trade-off among model size, accuracy and robustness, over currently available alternatives in various settings. The codes are publicly available at: https://github.com/shupenggui/ATMC.
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