Joint Multi-Dimension Pruning

We present joint multi-dimension pruning (named as JointPruning), a new perspective of pruning a network on three crucial aspects: spatial, depth and channel simultaneously. The joint strategy enables to search a better status than previous studies that focused on individual dimension solely, as our method is optimized collaboratively across the three dimensions in a single end-to-end training. Moreover, each dimension that we consider can promote to get better performance through colluding with the other two. Our method is realized by the adapted stochastic gradient estimation. Extensive experiments on large-scale ImageNet dataset across a variety of network architectures MobileNet V1&V2 and ResNet demonstrate the effectiveness of our proposed method. For instance, we achieve significant margins of 2.5% and 2.6% improvement over the state-of-the-art approach on the already compact MobileNet V1&V2 under an extremely large compression ratio

Parsimonious Deep Learning: A Differential Inclusion Approach with Global Convergence

Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world applications and direct training of small networks may be trapped in local optima. In this paper, instead of pruning or distilling an over-parameterized model to compressive ones, we propose a parsimonious learning approach based on differential inclusions of inverse scale spaces, that generates a family of models from simple to complex ones with a better efficiency and interpretability than stochastic gradient descent in exploring the model space. It enjoys a simple discretization, the Split Linearized Bregman Iterations, with provable global convergence that from any initializations, algorithmic iterations converge to a critical point of empirical risks. One may exploit the proposed method to boost the complexity of neural networks progressively. Numerical experiments with MNIST, Cifar-10/100, and ImageNet are conducted to show the method is promising in training large scale models with a favorite interpretability.Comment: 25 pages, 7 figure

The Impact of Neural Network Overparameterization on Gradient Confusion and Stochastic Gradient Descent

This paper studies how neural network architecture affects the speed of training. We introduce a simple concept called gradient confusion to help formally analyze this. When gradient confusion is high, stochastic gradients produced by different data samples may be negatively correlated, slowing down convergence. But when gradient confusion is low, data samples interact harmoniously, and training proceeds quickly. Through theoretical and experimental results, we demonstrate how the neural network architecture affects gradient confusion, and thus the efficiency of training. Our results show that, for popular initialization techniques, increasing the width of neural networks leads to lower gradient confusion, and thus faster model training. On the other hand, increasing the depth of neural networks has the opposite effect. Our results indicate that alternate initialization techniques or networks using both batch normalization and skip connections help reduce the training burden of very deep networks.Comment: ICML 2020 camera-ready versio

A Selective Overview of Deep Learning

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks have a long history, recent advances have greatly improved their performance in computer vision, natural language processing, etc. From the statistical and scientific perspective, it is natural to ask: What is deep learning? What are the new characteristics of deep learning, compared with classical methods? What are the theoretical foundations of deep learning? To answer these questions, we introduce common neural network models (e.g., convolutional neural nets, recurrent neural nets, generative adversarial nets) and training techniques (e.g., stochastic gradient descent, dropout, batch normalization) from a statistical point of view. Along the way, we highlight new characteristics of deep learning (including depth and over-parametrization) and explain their practical and theoretical benefits. We also sample recent results on theories of deep learning, many of which are only suggestive. While a complete understanding of deep learning remains elusive, we hope that our perspectives and discussions serve as a stimulus for new statistical research

Ensemble Model Patching: A Parameter-Efficient Variational Bayesian Neural Network

Two main obstacles preventing the widespread adoption of variational Bayesian neural networks are the high parameter overhead that makes them infeasible on large networks, and the difficulty of implementation, which can be thought of as "programming overhead." MC dropout [Gal and Ghahramani, 2016] is popular because it sidesteps these obstacles. Nevertheless, dropout is often harmful to model performance when used in networks with batch normalization layers [Li et al., 2018], which are an indispensable part of modern neural networks. We construct a general variational family for ensemble-based Bayesian neural networks that encompasses dropout as a special case. We further present two specific members of this family that work well with batch normalization layers, while retaining the benefits of low parameter and programming overhead, comparable to non-Bayesian training. Our proposed methods improve predictive accuracy and achieve almost perfect calibration on a ResNet-18 trained with ImageNet

A Simple Baseline for Bayesian Uncertainty in Deep Learning

We propose SWA-Gaussian (SWAG), a simple, scalable, and general purpose approach for uncertainty representation and calibration in deep learning. Stochastic Weight Averaging (SWA), which computes the first moment of stochastic gradient descent (SGD) iterates with a modified learning rate schedule, has recently been shown to improve generalization in deep learning. With SWAG, we fit a Gaussian using the SWA solution as the first moment and a low rank plus diagonal covariance also derived from the SGD iterates, forming an approximate posterior distribution over neural network weights; we then sample from this Gaussian distribution to perform Bayesian model averaging. We empirically find that SWAG approximates the shape of the true posterior, in accordance with results describing the stationary distribution of SGD iterates. Moreover, we demonstrate that SWAG performs well on a wide variety of tasks, including out of sample detection, calibration, and transfer learning, in comparison to many popular alternatives including MC dropout, KFAC Laplace, SGLD, and temperature scaling.Comment: Published at NeurIPS 201

Understanding the Energy and Precision Requirements for Online Learning

It is well-known that the precision of data, hyperparameters, and internal representations employed in learning systems directly impacts its energy, throughput, and latency. The precision requirements for the training algorithm are also important for systems that learn on-the-fly. Prior work has shown that the data and hyperparameters can be quantized heavily without incurring much penalty in classification accuracy when compared to floating point implementations. These works suffer from two key limitations. First, they assume uniform precision for the classifier and for the training algorithm and thus miss out on the opportunity to further reduce precision. Second, prior works are empirical studies. In this article, we overcome both these limitations by deriving analytical lower bounds on the precision requirements of the commonly employed stochastic gradient descent (SGD) on-line learning algorithm in the specific context of a support vector machine (SVM). Lower bounds on the data precision are derived in terms of the the desired classification accuracy and precision of the hyperparameters used in the classifier. Additionally, lower bounds on the hyperparameter precision in the SGD training algorithm are obtained. These bounds are validated using both synthetic and the UCI breast cancer dataset. Additionally, the impact of these precisions on the energy consumption of a fixed-point SVM with on-line training is studied.Comment: 14 pages, 5 figures 4 of which have 2 subfigure

TernGrad: Ternary Gradients to Reduce Communication in Distributed Deep Learning

High network communication cost for synchronizing gradients and parameters is the well-known bottleneck of distributed training. In this work, we propose TernGrad that uses ternary gradients to accelerate distributed deep learning in data parallelism. Our approach requires only three numerical levels {-1,0,1}, which can aggressively reduce the communication time. We mathematically prove the convergence of TernGrad under the assumption of a bound on gradients. Guided by the bound, we propose layer-wise ternarizing and gradient clipping to improve its convergence. Our experiments show that applying TernGrad on AlexNet does not incur any accuracy loss and can even improve accuracy. The accuracy loss of GoogLeNet induced by TernGrad is less than 2% on average. Finally, a performance model is proposed to study the scalability of TernGrad. Experiments show significant speed gains for various deep neural networks. Our source code is available.Comment: NIPS 2017 Ora

Federated Learning with Cooperating Devices: A Consensus Approach for Massive IoT Networks

Federated learning (FL) is emerging as a new paradigm to train machine learning models in distributed systems. Rather than sharing, and disclosing, the training dataset with the server, the model parameters (e.g. neural networks weights and biases) are optimized collectively by large populations of interconnected devices, acting as local learners. FL can be applied to power-constrained IoT devices with slow and sporadic connections. In addition, it does not need data to be exported to third parties, preserving privacy. Despite these benefits, a main limit of existing approaches is the centralized optimization which relies on a server for aggregation and fusion of local parameters; this has the drawback of a single point of failure and scaling issues for increasing network size. The paper proposes a fully distributed (or server-less) learning approach: the proposed FL algorithms leverage the cooperation of devices that perform data operations inside the network by iterating local computations and mutual interactions via consensus-based methods. The approach lays the groundwork for integration of FL within 5G and beyond networks characterized by decentralized connectivity and computing, with intelligence distributed over the end-devices. The proposed methodology is verified by experimental datasets collected inside an industrial IoT environment.Comment: This work received support from the CHIST-ERA III Grant RadioSense (Big Data and Process Modelling for the Smart Industry - BDSI). The paper has been accepted for publication in the IEEE Internet of Things Journal. The current arXiv contains an additional Appendix C that describes the database and the Python scripts. Published version: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8950073&isnumber=670252

Edge Intelligence: Paving the Last Mile of Artificial Intelligence with Edge Computing

With the breakthroughs in deep learning, the recent years have witnessed a booming of artificial intelligence (AI) applications and services, spanning from personal assistant to recommendation systems to video/audio surveillance. More recently, with the proliferation of mobile computing and Internet-of-Things (IoT), billions of mobile and IoT devices are connected to the Internet, generating zillions Bytes of data at the network edge. Driving by this trend, there is an urgent need to push the AI frontiers to the network edge so as to fully unleash the potential of the edge big data. To meet this demand, edge computing, an emerging paradigm that pushes computing tasks and services from the network core to the network edge, has been widely recognized as a promising solution. The resulted new inter-discipline, edge AI or edge intelligence, is beginning to receive a tremendous amount of interest. However, research on edge intelligence is still in its infancy stage, and a dedicated venue for exchanging the recent advances of edge intelligence is highly desired by both the computer system and artificial intelligence communities. To this end, we conduct a comprehensive survey of the recent research efforts on edge intelligence. Specifically, we first review the background and motivation for artificial intelligence running at the network edge. We then provide an overview of the overarching architectures, frameworks and emerging key technologies for deep learning model towards training/inference at the network edge. Finally, we discuss future research opportunities on edge intelligence. We believe that this survey will elicit escalating attentions, stimulate fruitful discussions and inspire further research ideas on edge intelligence.Comment: Zhi Zhou, Xu Chen, En Li, Liekang Zeng, Ke Luo, and Junshan Zhang, "Edge Intelligence: Paving the Last Mile of Artificial Intelligence with Edge Computing," Proceedings of the IEE