The information bottleneck principle (Shwartz-Ziv & Tishby, 2017) suggests that SGD-based training of deep neural networks results in optimally compressed hidden layers, from an information theoretic perspective. However, this claim was established on toy data. The goal of the work we present here is to test whether the information bottleneck principle is applicable to a realistic setting using a larger and deeper convolutional architecture, a ResNet model. We trained PixelCNN++ models as inverse representation decoders to measure the mutual information between hidden layers of a ResNet and input image data, when trained for (1) classification and (2) autoencoding. We find that two stages of learning happen for both training regimes, and that compression does occur, even for an autoencoder. Sampling images by conditioning on hidden layers' activations offers an intuitive visualisation to understand what a ResNets learns to forget.
New Jersey Institute of Technology（新泽西理工学院）；Tencent AI Lab（腾讯人工智能实验室）
Recent advances in deep neural networks (DNNs) lead to tremendously growing network parameters, making the deployments of DNNs on platforms with limited resources extremely difficult. Therefore, various pruning methods have been developed to compress the deep network architectures and accelerate the inference process. Most of the existing channel pruning methods discard the less important filters according to well-designed filter ranking criteria. However, due to the limited interpretability of deep learning models, designing an appropriate ranking criterion to distinguish redundant filters is…
Microsoft Research AI（微软研究院人工智能部门）；Stanford University（斯坦福大学）
How can neural networks such as ResNet efficiently learn CIFAR-10 with test accuracy more than 96%, while other methods, especially kernel methods, fall relatively behind? Can we more provide theoretical justifications for this gap? Recently, there is an influential line of work relating neural networks to kernels in the over-parameterized regime, proving they can learn certain concept class that is also learnable by kernels with similar test error. Yet, can neural networks provably learn some concept class BETTER than kernels? We answer this positively in the distribution-free setting. We pro…
Weizmann Institute of Science（魏茨曼科学研究所）；Microsoft Research（微软研究院）
A residual network (or ResNet) is a standard deep neural net architecture, with state-of-the-art performance across numerous applications. The main premise of ResNets is that they allow the training of each layer to focus on fitting just the residual of the previous layer's output and the target output. Thus, we should expect that the trained network is no worse than what we can obtain if we remove the residual layers and train a shallower network instead. However, due to the non-convexity of the optimization problem, it is not at all clear that ResNets indeed achieve this behavior, rather tha…
Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the recurrent application of proximal gradient algorit…
This paper presents a novel differentiable method for unstructured weight pruning of deep neural networks. Our learned-threshold pruning (LTP) method learns per-layer thresholds via gradient descent, unlike conventional methods where they are set as input. Making thresholds trainable also makes LTP computationally efficient, hence scalable to deeper networks. For example, it takes $30$ epochs for LTP to prune ResNet50 on ImageNet by a factor of $9.1$. This is in contrast to other methods that search for per-layer thresholds via a computationally intensive iterative pruning and fine-tuning proc…
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, …
The University of Hong Kong（香港大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Amazon Web Services（亚马逊云科技）；ByteDance Inc.（字节跳动有限公司）
Communication overhead severely hinders the scalability of distributed machine learning systems. Recently, there has been a growing interest in using gradient compression to reduce the communication overhead of the distributed training. However, there is little understanding of applying gradient compression to adaptive gradient methods. Moreover, its performance benefits are often limited by the non-negligible compression overhead. In this paper, we first introduce a novel adaptive gradient method with gradient compression. We show that the proposed method has a convergence rate of $\mathcal{O…
Large-scale distributed training requires significant communication bandwidth for gradient exchange that limits the scalability of multi-node training, and requires expensive high-bandwidth network infrastructure. The situation gets even worse with distributed training on mobile devices (federated learning), which suffers from higher latency, lower throughput, and intermittent poor connections. In this paper, we find 99.9% of the gradient exchange in distributed SGD is redundant, and propose Deep Gradient Compression (DGC) to greatly reduce the communication bandwidth. To preserve accuracy dur…
Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However, the stacking of many layers raises their computation costs. To address this problem, we propose Network Implosion, it erases multiple layers from Residual Networks without degrading accuracy. Our key idea is to introduce a priority term that identifies the importance of a layer; we can select unimportant layers according to the priority and erase them after…
Amazon Web Services（亚马逊云科技）；Hong Kong University of Science and Technology（香港科技大学）
Communication overhead is a major bottleneck hampering the scalability of distributed machine learning systems. Recently, there has been a surge of interest in using gradient compression to improve the communication efficiency of distributed neural network training. Using 1-bit quantization, signSGD with majority vote achieves a 32x reduction on communication cost. However, its convergence is based on unrealistic assumptions and can diverge in practice. In this paper, we propose a general distributed compressed SGD with Nesterov's momentum. We consider two-way compression, which compresses the…
A long-standing obstacle to progress in deep learning is the problem of vanishing and exploding gradients. Although, the problem has largely been overcome via carefully constructed initializations and batch normalization, architectures incorporating skip-connections such as highway and resnets perform much better than standard feedforward architectures despite well-chosen initialization and batch normalization. In this paper, we identify the shattered gradients problem. Specifically, we show that the correlation between gradients in standard feedforward networks decays exponentially with depth…
The current trend of pushing CNNs deeper with convolutions has created a pressing demand to achieve higher compression gains on CNNs where convolutions dominate the computation and parameter amount (e.g., GoogLeNet, ResNet and Wide ResNet). Further, the high energy consumption of convolutions limits its deployment on mobile devices. To this end, we proposed a simple yet effective scheme for compressing convolutions though applying k-means clustering on the weights, compression is achieved through weight-sharing, by only recording $K$ cluster centers and weight assignment indexes. We then intro…
This paper studies structured sparse training of CNNs with a gradual pruning technique that leads to fixed, sparse weight matrices after a set number of epochs. We simplify the structure of the enforced sparsity so that it reduces overhead caused by regularization. The proposed training methodology Campfire explores pruning at granularities within a convolutional kernel and filter. We study various tradeoffs with respect to pruning duration, level of sparsity, and learning rate configuration. We show that our method creates a sparse version of ResNet-50 and ResNet-50 v1.5 on full ImageNet whil…
Allen Institute for Artificial Intelligence（艾伦人工智能研究所）；University of Washington（华盛顿大学）
Training a neural network is synonymous with learning the values of the weights. By contrast, we demonstrate that randomly weighted neural networks contain subnetworks which achieve impressive performance without ever training the weight values. Hidden in a randomly weighted Wide ResNet-50 we show that there is a subnetwork (with random weights) that is smaller than, but matches the performance of a ResNet-34 trained on ImageNet. Not only do these "untrained subnetworks" exist, but we provide an algorithm to effectively find them. We empirically show that as randomly weighted neural networks w…
Peking University（北京大学）；MGH/BWH Center for Clinical Data Science（麻省总医院/布列根和妇女医院临床数据科学中心）；Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Beijing International Center for Mathematical Research, Peking University（北京大学北京国际数学研究中心）；Center for Data Science, Peking University（北京大学数据科学中心）；Beijing Institute of Big Data Research（北京大数据研究院）
In our work, we bridge deep neural network design with numerical differential equations. We show that many effective networks, such as ResNet, PolyNet, FractalNet and RevNet, can be interpreted as different numerical discretizations of differential equations. This finding brings us a brand new perspective on the design of effective deep architectures. We can take advantage of the rich knowledge in numerical analysis to guide us in designing new and potentially more effective deep networks. As an example, we propose a linear multi-step architecture (LM-architecture) which is inspired by the lin…
Training deep neural networks on large datasets containing high-dimensional data requires a large amount of computation. A solution to this problem is data-parallel distributed training, where a model is replicated into several computational nodes that have access to different chunks of the data. This approach, however, entails high communication rates and latency because of the computed gradients that need to be shared among nodes at every iteration. The problem becomes more pronounced in the case that there is wireless communication between the nodes (i.e. due to the limited network bandwidt…
Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of parameters and over a thousand layers. The trade-off is that these large architectures require an enormous amount of memory, storage, and computation, thus limiting their usability. Inspired by the recent tensor ring factorization, we introduce Tensor Ring Networks (TR-Nets), which significantly compress both the fully connected layers and the convolutional layers o…
Arm Inc（Arm公司）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
DenseNets introduce concatenation-type skip connections that achieve state-of-the-art accuracy in several computer vision tasks. In this paper, we reveal that the topology of the concatenation-type skip connections is closely related to the gradient propagation which, in turn, enables a predictable behavior of DNNs' test performance. To this end, we introduce a new metric called NN-Mass to quantify how effectively information flows through DNNs. Moreover, we empirically show that NN-Mass also works for other types of skip connections, e.g., for ResNets, Wide-ResNets (WRNs), and MobileNets, whi…
Filter pruning has been widely used for neural network compression because of its enabled practical acceleration. To date, most of the existing filter pruning works explore the importance of filters via using intra-channel information. In this paper, starting from an inter-channel perspective, we propose to perform efficient filter pruning using Channel Independence, a metric that measures the correlations among different feature maps. The less independent feature map is interpreted as containing less useful information$/$knowledge, and hence its corresponding filter can be pruned without affe…
Wrocław University of Science and Technology（弗罗茨瓦夫理工大学）
Convolutional neural networks applied for real-world classification tasks need to recognize inputs that are far or out-of-distribution (OoD) with respect to the known or training data. To achieve this, many methods estimate class-conditional posterior probabilities and use confidence scores obtained from the posterior distributions. Recent works propose to use multivariate Gaussian distributions as models of posterior distributions at different layers of the CNN (i.e., for low- and upper-level features), which leads to the confidence scores based on the Mahalanobis distance. However, this proc…
Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline, i.e., training, pruning and retraining (fine-tuning) significantly increases the overall training trails. In this paper, we develop a systematic weight-pruning optimization approach based on Surrogate Lagrangian relaxation (SLR), which is tailored to overcome difficulties caused by the discrete nature of the weight-pruning problem while ensuring fast convergence. We further accelerate the convergence of the SLR by using quadratic penalties. M…
