Recently, deep neural networks (DNNs) have shown advantages in accelerating optimization algorithms. One approach is to unfold finite number of iterations of conventional optimization algorithms and to learn parameters in the algorithms. However, these are forward methods and are indeed neither iterative nor convergent. Here, we present a novel DNN-based convergent iterative algorithm that accelerates conventional optimization algorithms. We train a DNN to yield parameters in scaled gradient projection method. So far, these parameters have been chosen heuristically, but have shown to be crucial for good empirical performance. In simulation results, the proposed method significantly improves the empirical convergence rate over conventional optimization methods for various large-scale inverse problems in image processing.
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and then optimize these factors directly via simple iterative methods such as gradient descent and alternating minimization. Despite nonconvexity, recent literatures have shown that these simple heuristics in fact achieve linear convergence when initialized properly for a growing number of problems of interest. However, upon closer examination, existing approach…
Approximate Thompson sampling with Langevin Monte Carlo broadens its reach from Gaussian posterior sampling to encompass more general smooth posteriors. However, it still encounters scalability issues in high-dimensional problems when demanding high accuracy. To address this, we propose an approximate Thompson sampling strategy, utilizing underdamped Langevin Monte Carlo, where the latter is the go-to workhorse for simulations of high-dimensional posteriors. Based on the standard smoothness and log-concavity conditions, we study the accelerated posterior concentration and sampling using a spec…
JD Explore Academy, JD.com Inc.（京东探索研究院）；Faculty of Science, University of Hong Kong（香港大学理学院）
Complex-valued neural networks (CVNNs) have been widely applied to various fields, especially signal processing and image recognition. However, few works focus on the generalization of CVNNs, albeit it is vital to ensure the performance of CVNNs on unseen data. This paper is the first work that proves a generalization bound for the complex-valued neural network. The bound scales with the spectral complexity, the dominant factor of which is the spectral norm product of weight matrices. Further, our work provides a generalization bound for CVNNs when training data is sequential, which is also af…
Nesterov SGD is widely used for training modern neural networks and other machine learning models. Yet, its advantages over SGD have not been theoretically clarified. Indeed, as we show in our paper, both theoretically and empirically, Nesterov SGD with any parameter selection does not in general provide acceleration over ordinary SGD. Furthermore, Nesterov SGD may diverge for step sizes that ensure convergence of ordinary SGD. This is in contrast to the classical results in the deterministic scenario, where the same step size ensures accelerated convergence of the Nesterov's method over optim…
University of Illinois at Urbana–Champaign（伊利诺伊大学厄巴纳-香槟分校）
The matrix completion problem seeks to recover a $d\times d$ ground truth matrix of low rank $r\ll d$ from observations of its individual elements. Real-world matrix completion is often a huge-scale optimization problem, with $d$ so large that even the simplest full-dimension vector operations with $O(d)$ time complexity become prohibitively expensive. Stochastic gradient descent (SGD) is one of the few algorithms capable of solving matrix completion on a huge scale, and can also naturally handle streaming data over an evolving ground truth. Unfortunately, SGD experiences a dramatic slow-down …
University of Maryland, College Park（马里兰大学帕克分校）；Georgetown University（乔治城大学）
This paper considers the multi-agent distributed linear least-squares problem. The system comprises multiple agents, each agent with a locally observed set of data points, and a common server with whom the agents can interact. The agents' goal is to compute a linear model that best fits the collective data points observed by all the agents. In the server-based distributed settings, the server cannot access the data points held by the agents. The recently proposed Iteratively Pre-conditioned Gradient-descent (IPG) method has been shown to converge faster than other existing distributed algorith…
University of Maryland（马里兰大学）；École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
This paper studies a distributed multi-agent convex optimization problem. The system comprises multiple agents in this problem, each with a set of local data points and an associated local cost function. The agents are connected to a server, and there is no inter-agent communication. The agents' goal is to learn a parameter vector that optimizes the aggregate of their local costs without revealing their local data points. In principle, the agents can solve this problem by collaborating with the server using the traditional distributed gradient-descent method. However, when the aggregate cost i…
Carnegie Mellon University（卡内基梅隆大学）；University of Chicago（芝加哥大学）；Air Force Research Laboratory（美国空军研究实验室）
Tensors, which provide a powerful and flexible model for representing multi-attribute data and multi-way interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is to faithfully recover the tensor from highly incomplete measurements in a statistically and computationally efficient manner. Harnessing the low-rank structure of tensors in the Tucker decomposition, this paper develops a scaled gradient descent (ScaledGD) algorithm to directly recover the tensor factors with tailored spectral initializations, and shows tha…
The performance of a deep neural network is highly dependent on its training, and finding better local optimal solutions is the goal of many optimization algorithms. However, existing optimization algorithms show a preference for descent paths that converge slowly and do not seek to avoid bad local optima. In this work, we propose Learning Rate Dropout (LRD), a simple gradient descent technique for training related to coordinate descent. LRD empirically aids the optimizer to actively explore in the parameter space by randomly setting some learning rates to zero; at each iteration, only paramet…
MIT Media Laboratory（麻省理工学院媒体实验室）；Harvard University（哈佛大学）
Methods for neural network hyperparameter optimization and meta-modeling are computationally expensive due to the need to train a large number of model configurations. In this paper, we show that standard frequentist regression models can predict the final performance of partially trained model configurations using features based on network architectures, hyperparameters, and time-series validation performance data. We empirically show that our performance prediction models are much more effective than prominent Bayesian counterparts, are simpler to implement, and are faster to train. Our mode…
Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit exa…
German Aerospace Center (DLR)（德国航空航天中心）；Technical University of Munich（慕尼黑工业大学）
In robotics, deep learning (DL) methods are used more and more widely, but their general inability to provide reliable confidence estimates will ultimately lead to fragile and unreliable systems. This impedes the potential deployments of DL methods for long-term autonomy. Therefore, in this paper we introduce a scalable Laplace Approximation (LA) technique to make Deep Neural Networks (DNNs) more introspective, i.e. to enable them to provide accurate assessments of their failure probability for unseen test data. In particular, we propose a novel Bayesian Optimization (BO) algorithm to mitigate…
We propose the position-based scaled gradient (PSG) that scales the gradient depending on the position of a weight vector to make it more compression-friendly. First, we theoretically show that applying PSG to the standard gradient descent (GD), which is called PSGD, is equivalent to the GD in the warped weight space, a space made by warping the original weight space via an appropriately designed invertible function. Second, we empirically show that PSG acting as a regularizer to a weight vector is favorable for model compression domains such as quantization and pruning. PSG reduces the gap be…
We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks. The key ingredient is a new smoothness condition derived from practical neural network training examples. We observe that gradient smoothness, a concept central to the analysis of first-order optimization algorithms that is often assumed to be a constant, demonstrates significant variability along the training trajectory of deep neural networks. Further, this smoothness positively correlates with the gradient norm, and contrary to standard assumptions in the literature, it can grow…
Efi Arazi School of Computer Science（埃菲·阿拉齐计算机学院）；The Interdisciplinary Center（跨学科中心）
We present a selective sampling method designed to accelerate the training of deep neural networks. To this end, we introduce a novel measurement, the minimal margin score (MMS), which measures the minimal amount of displacement an input should take until its predicted classification is switched. For multi-class linear classification, the MMS measure is a natural generalization of the margin-based selection criterion, which was thoroughly studied in the binary classification setting. In addition, the MMS measure provides an interesting insight into the progress of the training process and can …
Carnegie Mellon University（卡内基梅隆大学）；University of Chicago（芝加哥大学）
An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key challenge is to develop computationally efficient and provably correct algorithms for extracting useful information from tensor data that are simultaneously robust to corruptions and ill-conditioning. This paper tackles tensor robust principal component analysis (RPCA), which aims to recover a low-rank tensor from its observations contaminated by sparse corru…
Princeton University（普林斯顿大学）；Zhongguancun Haihua Institute for Frontier Information Technology（中关村海华前沿信息技术研究院）；Peking University（北京大学）；Pazhou Lab（琶洲实验室）；Massachusetts Institute of Technology（麻省理工学院）；Microsoft Research（微软研究院）
Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets…
Massachusetts Institute of Technology（麻省理工学院）；Julia Computing（Julia Computing公司）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Modern design, control, and optimization often requires simulation of highly nonlinear models, leading to prohibitive computational costs. These costs can be amortized by evaluating a cheap surrogate of the full model. Here we present a general data-driven method, the continuous-time echo state network (CTESN), for generating surrogates of nonlinear ordinary differential equations with dynamics at widely separated timescales. We empirically demonstrate near-constant time performance using our CTESNs on a physically motivated scalable model of a heating system whose full execution time increase…
Despite the increasing interest in neural architecture search (NAS), the significant computational cost of NAS is a hindrance to researchers. Hence, we propose to reduce the cost of NAS using proxy data, i.e., a representative subset of the target data, without sacrificing search performance. Even though data selection has been used across various fields, our evaluation of existing selection methods for NAS algorithms offered by NAS-Bench-1shot1 reveals that they are not always appropriate for NAS and a new selection method is necessary. By analyzing proxy data constructed using various select…
Graduate School of Information, Production and Systems, Waseda University（早稻田大学信息生产系统研究生院）
Deep convolutional neural networks (CNN) have shown their good performances in many computer vision tasks. However, the high computational complexity of CNN involves a huge amount of data movements between the computational processor core and memory hierarchy which occupies the major of the power consumption. This paper presents Chain-NN, a novel energy-efficient 1D chain architecture for accelerating deep CNNs. Chain-NN consists of the dedicated dual-channel process engines (PE). In Chain-NN, convolutions are done by the 1D systolic primitives composed of a group of adjacent PEs. These systol…
The University of Arizona（亚利桑那大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
GMRES is a powerful numerical solver used to find solutions to extremely large systems of linear equations. These systems of equations appear in many applications in science and engineering. Here we demonstrate a real-time machine learning algorithm that can be used to accelerate the time-to-solution for GMRES. Our framework is novel in that is integrates the deep learning algorithm in an in situ fashion: the AI-accelerator gradually learns how to optimizes the time to solution without requiring user input (such as a pre-trained data set). We describe how our algorithm collects data and optimi…
University of Dhaka（达卡大学）；Purdue University（普渡大学）；University of South Carolina（南卡罗来纳大学）
Causal structure discovery from observational data is fundamental to the causal understanding of autonomous systems such as medical decision support systems, advertising campaigns and self-driving cars. This is essential to solve well-known causal decision making and prediction problems associated with those real-world applications. Recently, recursive causal discovery algorithms have gained particular attention among the research community due to their ability to provide good results by using Conditional Independent (CI) tests in smaller sub-problems. However, each of such algorithms needs a …
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Texas A&M University（德克萨斯农工大学）；Beijing Jiaotong University（北京交通大学）；University of Oregon（俄勒冈大学）；Facebook AI Applied Research（脸书AI应用研究部）；Zhejiang University（浙江大学）
This work targets designing a principled and unified training-free framework for Neural Architecture Search (NAS), with high performance, low cost, and in-depth interpretation. NAS has been explosively studied to automate the discovery of top-performer neural networks, but suffers from heavy resource consumption and often incurs search bias due to truncated training or approximations. Recent NAS works start to explore indicators that can predict a network's performance without training. However, they either leveraged limited properties of deep networks, or the benefits of their training-free i…
A Teacher-Student Perspective on the Dynamics of Learning Near the Optimal Point
CeFEMA-LaPMET & CAMGSD & IT（CeFEMA-LaPMET与CAMGSD及IT）；Instituto Superior Técnico University of Lisbon, Portugal（里斯本大学技术学院）；CAMGSD；Instituto de Telecomunicações（电信研究所）；CeFEMA-LaPMET
This paper studies the Variational Inference (VI) used for training Bayesian Neural Networks (BNN) in the overparameterized regime, i.e., when the number of neurons tends to infinity. More specifically, we consider overparameterized two-layer BNN and point out a critical issue in the mean-field VI training. This problem arises from the decomposition of the lower bound on the evidence (ELBO) into two terms: one corresponding to the likelihood function of the model and the second to the Kullback-Leibler (KL) divergence between the prior distribution and the variational posterior. In particular, …
Purdue University（普渡大学）；University of Southern California（南加州大学）
Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the energy function based on the full dataset and is not scalable to big data. The naïve implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive repl…
The University of Sydney Business School（悉尼大学商学院）；The University of Sydney（悉尼大学）
In this paper, we propose a simple yet effective graph neural network for directed graphs (digraph) based on the classic Singular Value Decomposition (SVD), named SVD-GCN. The new graph neural network is built upon the graph SVD-framelet to better decompose graph signals on the SVD ``frequency'' bands. Further the new framelet SVD-GCN is also scaled up for larger scale graphs via using Chebyshev polynomial approximation. Through empirical experiments conducted on several node classification datasets, we have found that SVD-GCN has remarkable improvements in a variety of graph node learning tas…
Gate functions in recurrent models, such as an LSTM and GRU, play a central role in learning various time scales in modeling time series data by using a bounded activation function. However, it is difficult to train gates to capture extremely long time scales due to gradient vanishing of the bounded function for large inputs, which is known as the saturation problem. We closely analyze the relation between saturation of the gate function and efficiency of the training. We prove that the gradient vanishing of the gate function can be mitigated by accelerating the convergence of the saturating f…
