Model compression methods are important to allow for easier deployment of deep learning models in compute, memory and energy-constrained environments such as mobile phones. Knowledge distillation is a class of model compression algorithm where knowledge from a large teacher network is transferred to a smaller student network thereby improving the student's performance. In this paper, we show how optimal transport-based loss functions can be used for training a student network which encourages learning student network parameters that help bring the distribution of student features closer to that of the teacher features. We present image classification results on CIFAR-100, SVHN and ImageNet and show that the proposed optimal transport loss functions perform comparably to or better than other loss functions.
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for either directed or undirected graphs, and its dual characterization is cast in terms of distributions over the nodes. The compression pertains to the support of node distributions and makes the problem challenging to solve directly. To this end, we introduce Boolean relaxations and specify conditions under which these relaxations are exact. The relaxations admit…
All Lossy compression algorithms employ similar compression schemes -- frequency domain transform followed by quantization and lossless encoding schemes. They target tradeoffs by quantizating high frequency data to increase compression rates which come at the cost of higher image distortion. We propose a new method of optimizing quantization tables using Deep Learning and a minimax loss function that more accurately measures the tradeoffs between rate and distortion parameters (RD) than previous methods. We design a convolutional neural network (CNN) that learns a mapping between image blocks …
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）；Ben-Gurion University（本-古里安大学）
We analyze a family of supervised learning algorithms based on sample compression schemes that are stable, in the sense that removing points from the training set which were not selected for the compression set does not alter the resulting classifier. We use this technique to derive a variety of novel or improved data-dependent generalization bounds for several learning algorithms. In particular, we prove a new margin bound for SVM, removing a log factor. The new bound is provably optimal. This resolves a long-standing open question about the PAC margin bounds achievable by SVM.
Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results on convergence rates under communication compression, a theoretical lower bound is still missing. Analyses of algorithms with communication compression have attributed convergence to two abstract properties: the unbiased property or the contractive property. They can be applied with either unidirectional compression (only messages from workers to server are compressed) or bidirectional compression. In…
A new data-enabled control technique for uncertain linear time-invariant systems, recently conceived by Coulson et\ al., builds upon the direct optimization of controllers over input/output pairs drawn from a large dataset. We adopt an optimal transport-based method for compressing such large dataset to a smaller synthetic dataset of representative behaviours, aiming to alleviate the computational burden of controllers to be implemented online. Specifically, the synthetic data are determined by minimizing the Wasserstein distance between atomic distributions supported on both the original data…
Stanford University（斯坦福大学）；University of New South Wales（新南威尔士大学）
In this paper, we compress convolutional neural network (CNN) weights post-training via transform quantization. Previous CNN quantization techniques tend to ignore the joint statistics of weights and activations, producing sub-optimal CNN performance at a given quantization bit-rate, or consider their joint statistics during training only and do not facilitate efficient compression of already trained CNN models. We optimally transform (decorrelate) and quantize the weights post-training using a rate-distortion framework to improve compression at any given quantization bit-rate. Transform quant…
South China University of Technology（华南理工大学）；Monash University（莫纳什大学）
Model compression aims to reduce the redundancy of deep networks to obtain compact models. Recently, channel pruning has become one of the predominant compression methods to deploy deep models on resource-constrained devices. Most channel pruning methods often use a fixed compression rate for all the layers of the model, which, however, may not be optimal. To address this issue, given a target compression rate for the whole model, one can search for the optimal compression rate for each layer. Nevertheless, these methods perform channel pruning for a specific target compression rate. When we c…
McMaster University（麦克马斯特大学）；Vector Institute（向量研究所）；University of Waterloo（滑铁卢大学）；University of British Columbia（不列颠哥伦比亚大学）；McGill University（麦吉尔大学）
We prove that $\tildeΘ(k d^2 / \varepsilon^2)$ samples are necessary and sufficient for learning a mixture of $k$ Gaussians in $\mathbb{R}^d$, up to error $\varepsilon$ in total variation distance. This improves both the known upper bounds and lower bounds for this problem. For mixtures of axis-aligned Gaussians, we show that $\tilde{O}(k d / \varepsilon^2)$ samples suffice, matching a known lower bound. Moreover, these results hold in the agnostic-learning/robust-estimation setting as well, where the target distribution is only approximately a mixture of Gaussians. The upper bound is shown us…
BayzAI；Volkswagen Group of America（美国大众汽车集团）；Innovation Center California（加州创新中心）
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that gives a solution. In this paper we propose a compression principle that states that an optimal predictive model is the one that minimizes a total compressed message length of all data and model definition while guarantees decodability. Following the compression principle we use Bayesian approach to build probabilistic models of data and network definitions. A me…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；University of Haifa（海法大学）
We present a novel global compression framework for deep neural networks that automatically analyzes each layer to identify the optimal per-layer compression ratio, while simultaneously achieving the desired overall compression. Our algorithm hinges on the idea of compressing each convolutional (or fully-connected) layer by slicing its channels into multiple groups and decomposing each group via low-rank decomposition. At the core of our algorithm is the derivation of layer-wise error bounds from the Eckart Young Mirsky theorem. We then leverage these bounds to frame the compression problem as…
Challenges and Solutions in Selecting Optimal Lossless Data Compression Algorithms
Department of Computer Science and Engineering（计算机科学与工程系）；East West University（东西方大学）；Bangladesh University of Business and Technology (BUBT)（孟加拉国商业技术大学）
To enhance image compression performance, recent deep neural network-based research can be divided into three categories: a learnable codec, a postprocessing network, and a compact representation network. The learnable codec has been designed for an end-to-end learning beyond the conventional compression modules. The postprocessing network increases the quality of decoded images using an example-based learning. The compact representation network is learned to reduce the capacity of an input image to reduce the bitrate while keeping the quality of the decoded image. However, these approaches ar…
