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Register a new userRate-Distortion Theoretic Model Compression: Successive Refinement for Pruning
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Berivan Isik
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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We study the neural network (NN) compression problem, viewing the tension between the compression ratio and NN performance through the lens of rate-distortion theory. We choose a distortion metric that reflects the effect of NN compression on the model output and then derive the tradeoff between rate (compression ratio) and distortion. In addition to characterizing theoretical limits of NN compression, this formulation shows that emph{pruning}, implicitly or explicitly, must be a part of a good compression algorithm. This observation bridges a gap between parts of the literature pertaining to NN and data compression, respectively, providing insight into the empirical success of pruning for NN compression. Finally, we propose a novel pruning strategy derived from our information-theoretic formulation and show that it outperforms the relevant baselines on CIFAR-10 and ImageNet datasets.
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Previous AutoML pruning works utilized individual layer features to automatically prune filters. We analyze the correlation for two layers from different blocks which have a short-cut structure. It is found that, in one block, the deeper layer has many redundant filters which can be represented by filters in the former layer so that it is necessary to take information from other layers into consideration in pruning. In this paper, a graph pruning approach is proposed, which views any deep model as a topology graph. Graph PruningNet based on the graph convolution network is designed to automatically extract neighboring information for each node. To extract features from various topologies, Graph PruningNet is connected with Pruned Network by an individual fully connection layer for each node and jointly trained on a training dataset from scratch. Thus, we can obtain reasonable weights for any size of sub-network. We then search the best configuration of the Pruned Network by reinforcement learning. Different from previous work, we take the node features from well-trained Graph PruningNet, instead of the hand-craft features, as the states in reinforcement learning. Compared with other AutoML pruning works, our method has achieved the state-of-the-art under same conditions on ImageNet-2012. The code will be released on GitHub.
A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.
The overall predictive uncertainty of a trained predictor can be decomposed into separate contributions due to epistemic and aleatoric uncertainty. Under a Bayesian formulation, assuming a well-specified model, the two contributions can be exactly expressed (for the log-loss) or bounded (for more general losses) in terms of information-theoretic quantities (Xu and Raginsky, 2020). This paper addresses the study of epistemic uncertainty within an information-theoretic framework in the broader setting of Bayesian meta-learning. A general hierarchical Bayesian model is assumed in which hyperparameters determine the per-task priors of the model parameters. Exact characterizations (for the log-loss) and bounds (for more general losses) are derived for the epistemic uncertainty - quantified by the minimum excess meta-risk (MEMR)- of optimal meta-learning rules. This characterization is leveraged to bring insights into the dependence of the epistemic uncertainty on the number of tasks and on the amount of per-task training data. Experiments are presented that compare the proposed information-theoretic bounds, evaluated via neural mutual information estimators, with the performance of a novel approximate fully Bayesian meta-learning strategy termed Langevin-Stein Bayesian Meta-Learning (LS-BML).
End-to-end optimization capability offers neural image compression (NIC) superior lossy compression performance. However, distinct models are required to be trained to reach different points in the rate-distortion (R-D) space. In this paper, we consider the problem of R-D characteristic analysis and modeling for NIC. We make efforts to formulate the essential mathematical functions to describe the R-D behavior of NIC using deep network and statistical modeling. Thus continuous bit-rate points could be elegantly realized by leveraging such model via a single trained network. In this regard, we propose a plugin-in module to learn the relationship between the target bit-rate and the binary representation for the latent variable of auto-encoder. Furthermore, we model the rate and distortion characteristic of NIC as a function of the coding parameter $lambda$ respectively. Our experiments show our proposed method is easy to adopt and obtains competitive coding performance with fixed-rate coding approaches, which would benefit the practical deployment of NIC. In addition, the proposed model could be applied to NIC rate control with limited bit-rate error using a single network.
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.
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