We propose a first-order stochastic optimization algorithm incorporating adaptive regularization applicable to machine learning problems in deep learning framework. The adaptive regularization is imposed by stochastic process in determining batch size for each model parameter at each optimization iteration. The stochastic batch size is determined by the update probability of each parameter following a distribution of gradient norms in consideration of their local and global properties in the neural network architecture where the range of gradient norms may vary within and across layers. We empirically demonstrate the effectiveness of our algorithm using an image classification task based on conventional network models applied to commonly used benchmark datasets. The quantitative evaluation indicates that our algorithm outperforms the state-of-the-art optimization algorithms in generalization while providing less sensitivity to the selection of batch size which often plays a critical role in optimization, thus achieving more robustness to the selection of regularity.
Batch Normalization is a commonly used trick to improve the training of deep neural networks. These neural networks use L2 regularization, also called weight decay, ostensibly to prevent overfitting. However, we show that L2 regularization has no regularizing effect when combined with normalization. Instead, regularization has an influence on the scale of weights, and thereby on the effective learning rate. We investigate this dependence, both in theory, and experimentally. We show that popular optimization methods such as ADAM only partially eliminate the influence of normalization on the lea…
University of Waterloo（滑铁卢大学）；Vector Institute（向量研究所）
The variational autoencoder is a well defined deep generative model that utilizes an encoder-decoder framework where an encoding neural network outputs a non-deterministic code for reconstructing an input. The encoder achieves this by sampling from a distribution for every input, instead of outputting a deterministic code per input. The great advantage of this process is that it allows the use of the network as a generative model for sampling from the data distribution beyond provided samples for training. We show in this work that utilizing batch normalization as a source for non-determinism …
Department of Applied Mathematics, Harvard University（哈佛大学应用数学系）；Department of Computer Science, Harvard University（哈佛大学计算机科学系）；Department of Statistics, Harvard University（哈佛大学统计学系）
In batch reinforcement learning, there can be poorly explored state-action pairs resulting in poorly learned, inaccurate models and poorly performing associated policies. Various regularization methods can mitigate the problem of learning overly-complex models in Markov decision processes (MDPs), however they operate in technically and intuitively distinct ways and lack a common form in which to compare them. This paper unifies three regularization methods in a common framework -- a weighted average transition matrix. Considering regularization methods in this common form illuminates how the M…
Huazhong University of Science and Technology（华中科技大学）
Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which e…
Batch normalization is widely used in deep learning to normalize intermediate activations. Deep networks suffer from notoriously increased training complexity, mandating careful initialization of weights, requiring lower learning rates, etc. These issues have been addressed by Batch Normalization (\textbf{BN}), by normalizing the inputs of activations to zero mean and unit standard deviation. Making this batch normalization part of the training process dramatically accelerates the training process of very deep networks. A new field of research has been going on to examine the exact theoretical…
University of Utah（犹他大学）；Cornell University（康奈尔大学）
The minibatch stochastic gradient descent method (SGD) is widely applied in deep learning due to its efficiency and scalability that enable training deep networks with a large volume of data. Particularly in the distributed setting, SGD is usually applied with large batch size. However, as opposed to small-batch SGD, neural network models trained with large-batch SGD can hardly generalize well, i.e., the validation accuracy is low. In this work, we introduce a novel regularization technique, namely distinctive regularization (DReg), which replicates a certain layer of the deep network and enco…
A key component of most neural network architectures is the use of normalization layers, such as Batch Normalization. Despite its common use and large utility in optimizing deep architectures, it has been challenging both to generically improve upon Batch Normalization and to understand the circumstances that lend themselves to other enhancements. In this paper, we identify four improvements to the generic form of Batch Normalization and the circumstances under which they work, yielding performance gains across all batch sizes while requiring no additional computation during training. These co…
University of California, Berkeley（加州大学伯克利分校）；NVIDIA（英伟达）
Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer more parallelism and hence better computational efficiency. We have developed a new training approach that, rather than statically choosing a single batch size for all epochs, adaptively increases the batch size during the training process. Our method delivers the convergence rate of small batch sizes while achieving performance similar to large batch sizes. …
Huazhong University of Science and Technology（华中科技大学）
Takagi-Sugeno-Kang (TSK) fuzzy systems are very useful machine learning models for regression problems. However, to our knowledge, there has not existed an efficient and effective training algorithm that ensures their generalization performance, and also enables them to deal with big data. Inspired by the connections between TSK fuzzy systems and neural networks, we extend three powerful neural network optimization techniques, i.e., mini-batch gradient descent, regularization, and AdaBound, to TSK fuzzy systems, and also propose three novel techniques (DropRule, DropMF, and DropMembership) spe…
National University of Singapore（新加坡国立大学）；Northwestern University（西北大学）；Purdue University（普渡大学）；New Oriental AI Research Academy（新东方人工智能研究院）
Batch Normalization (BN)(Ioffe and Szegedy 2015) normalizes the features of an input image via statistics of a batch of images and hence BN will bring the noise to the gradient of the training loss. Previous works indicate that the noise is important for the optimization and generalization of deep neural networks, but too much noise will harm the performance of networks. In our paper, we offer a new point of view that self-attention mechanism can help to regulate the noise by enhancing instance-specific information to obtain a better regularization effect. Therefore, we propose an attention-ba…
Training deep neural networks is a very demanding task, especially challenging is how to adapt architectures to improve the performance of trained models. We can find that sometimes, shallow networks generalize better than deep networks, and the addition of more layers results in higher training and test errors. The deep residual learning framework addresses this degradation problem by adding skip connections to several neural network layers. It would at first seem counter-intuitive that such skip connections are needed to train deep networks successfully as the expressivity of a network would…
MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）；Body Labs Inc.（Body Labs公司）
Mini-batch stochastic gradient descent and variants thereof have become standard for large-scale empirical risk minimization like the training of neural networks. These methods are usually used with a constant batch size chosen by simple empirical inspection. The batch size significantly influences the behavior of the stochastic optimization algorithm, though, since it determines the variance of the gradient estimates. This variance also changes over the optimization process; when using a constant batch size, stability and convergence is thus often enforced by means of a (manually tuned) decre…
UC San Diego（加州大学圣地亚哥分校）；Princeton University（普林斯顿大学）；Carnegie Mellon University（卡内基梅隆大学）
A number of competing hypotheses have been proposed to explain why small-batch Stochastic Gradient Descent (SGD)leads to improved generalization over the full-batch regime, with recent work crediting the implicit regularization of various quantities throughout training. However, to date, empirical evidence assessing the explanatory power of these hypotheses is lacking. In this paper, we conduct an extensive empirical evaluation, focusing on the ability of various theorized mechanisms to close the small-to-large batch generalization gap. Additionally, we characterize how the quantities that SGD…
Batch Normalization (BN) is a commonly used technique to accelerate and stabilize training of deep neural networks. Despite its empirical success, a full theoretical understanding of BN is yet to be developed. In this work, we analyze BN through the lens of convex optimization. We introduce an analytic framework based on convex duality to obtain exact convex representations of weight-decay regularized ReLU networks with BN, which can be trained in polynomial-time. Our analyses also show that optimal layer weights can be obtained as simple closed-form formulas in the high-dimensional and/or ove…
High-dimensional online learning via asynchronous decomposition: Non-divergent results, dynamic regularization, and beyond
School of Statistics, Renmin University of China（中国人民大学统计学院）；School of Statistics and Mathematics, Zhongnan University of Economics and Law（中南财经政法大学统计学与数学学院）；Institute of Statistics and Big Data, Renmin University of China（中国人民大学统计与大数据研究院）；Center for Applied Statistics, Renmin University of China（中国人民大学应用统计中心）
In this paper, a new adaptive multi-batch experience replay scheme is proposed for proximal policy optimization (PPO) for continuous action control. On the contrary to original PPO, the proposed scheme uses the batch samples of past policies as well as the current policy for the update for the next policy, where the number of the used past batches is adaptively determined based on the oldness of the past batches measured by the average importance sampling (IS) weight. The new algorithm constructed by combining PPO with the proposed multi-batch experience replay scheme maintains the advantages …
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究院）
The accuracy of deep neural networks is significantly affected by how well mini-batches are constructed during the training step. In this paper, we propose a novel adaptive batch selection algorithm called Recency Bias that exploits the uncertain samples predicted inconsistently in recent iterations. The historical label predictions of each training sample are used to evaluate its predictive uncertainty within a sliding window. Then, the sampling probability for the next mini-batch is assigned to each training sample in proportion to its predictive uncertainty. By taking advantage of this desi…
Facebook AI Research（脸书人工智能研究院）；Deepmind（深度思维）；Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利理工学院）；University of Genova（热那亚大学）
Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch. In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP opt…
Recent advances in the theoretical understanding of SGD led to a formula for the optimal batch size minimizing the number of effective data passes, i.e., the number of iterations times the batch size. However, this formula is of no practical value as it depends on the knowledge of the variance of the stochastic gradients evaluated at the optimum. In this paper we design a practical SGD method capable of learning the optimal batch size adaptively throughout its iterations for strongly convex and smooth functions. Our method does this provably, and in our experiments with synthetic and real data…
For infinitesimal learning rates, stochastic gradient descent (SGD) follows the path of gradient flow on the full batch loss function. However moderately large learning rates can achieve higher test accuracies, and this generalization benefit is not explained by convergence bounds, since the learning rate which maximizes test accuracy is often larger than the learning rate which minimizes training loss. To interpret this phenomenon we prove that for SGD with random shuffling, the mean SGD iterate also stays close to the path of gradient flow if the learning rate is small and finite, but on a m…
State-of-the-art computer vision models are rapidly increasing in capacity, where the number of parameters far exceeds the number required to fit the training set. This results in better optimization and generalization performance. However, the huge size of contemporary models results in large inference costs and limits their use on resource-limited devices. In order to reduce inference costs, convolutional filters in trained neural networks could be pruned to reduce the run-time memory and computational requirements during inference. However, severe post-training pruning results in degraded p…
While nowadays most gradient-based optimization methods focus on exploring the high-dimensional geometric features, the random error accumulated in a stochastic version of any algorithm implementation has not been stressed yet. In this work, we propose a universal principle which reduces the random error accumulation by exploiting statistic information hidden in mini-batch gradients. This is achieved by regularizing the learning-rate according to mini-batch variances. Due to the complementarity of our perspective, this regularization could provide a further improvement for stochastic implement…
General-purpose embedding is highly desirable for few-shot even zero-shot learning in many application scenarios, including audio tasks. In order to understand representations better, we conducted a thorough error analysis and visualization of HEAR 2021 submission results. Inspired by the analysis, this work experiments with different front-end audio preprocessing methods, including Constant-Q Transform (CQT) and Short-time Fourier transform (STFT), and proposes a Batch Embedding Covariance Regularization (BECR) term to uncover a more holistic simulation of the frequency information received b…
College of Biomedical Engineering & Instrument Science（生物医学工程与仪器科学学院）；Zhejiang University（浙江大学）
Data-free quantization is a task that compresses the neural network to low bit-width without access to original training data. Most existing data-free quantization methods cause severe performance degradation due to inaccurate activation clipping range and quantization error, especially for low bit-width. In this paper, we present a simple yet effective data-free quantization method with accurate activation clipping and adaptive batch normalization. Accurate activation clipping (AAC) improves the model accuracy by exploiting accurate activation information from the full-precision model. Adapti…
Weight decay is often used to ensure good generalization in the training practice of deep neural networks with batch normalization (BN-DNNs), where some convolution layers are invariant to weight rescaling due to the normalization. In this paper, we demonstrate that the practical usage of weight decay still has some unsolved problems in spite of existing theoretical work on explaining the effect of weight decay in BN-DNNs. On the one hand, when the non-adaptive learning rate e.g. SGD with momentum is used, the effective learning rate continues to increase even after the initial training stage,…
Communication-Efficient Adaptive Batch Size Strategies for Distributed Local Gradient Methods
Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；The University of Chicago Booth School of Business（芝加哥大学布斯商学院）；Northwestern University（西北大学）；University of Southern California Marshall School of Business（南加州大学马歇尔商学院）
Multi-epoch, small-batch, Stochastic Gradient Descent (SGD) has been the method of choice for learning with large over-parameterized models. A popular theory for explaining why SGD works well in practice is that the algorithm has an implicit regularization that biases its output towards a good solution. Perhaps the theoretically most well understood learning setting for SGD is that of Stochastic Convex Optimization (SCO), where it is well known that SGD learns at a rate of $O(1/\sqrt{n})$, where $n$ is the number of samples. In this paper, we consider the problem of SCO and explore the role of…
Purdue University（普渡大学）；The University of Chicago（芝加哥大学）；National University of Singapore（新加坡国立大学）
Overfitting frequently occurs in deep learning. In this paper, we propose a novel regularization method called Drop-Activation to reduce overfitting and improve generalization. The key idea is to drop nonlinear activation functions by setting them to be identity functions randomly during training time. During testing, we use a deterministic network with a new activation function to encode the average effect of dropping activations randomly. Our theoretical analyses support the regularization effect of Drop-Activation as implicit parameter reduction and verify its capability to be used together…
National University of Defense Technology（国防科技大学）；University of Utah（犹他大学）
The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another issue is that the fixed explicit regularization limits the applicability to broad images since different images favor different features captured by different explicit regularizations. As such, this paper proposes a new adaptive and implicit low-rank regularization that captures the low-rank prior dynamically from the training data. The core of our new adapt…
Adaptive Batch Size Schedules for Distributed Training of Language Models with Data and Model Parallelism
Perelman School of Medicine, University of Pennsylvania（宾夕法尼亚大学佩雷尔曼医学院）；The University of Chicago Booth School of Business（芝加哥大学布斯商学院）；Northwestern University（西北大学）；University of Southern California Marshall School of Business（南加州大学马歇尔商学院）
Lehigh University（利哈伊大学）；Industrial and Systems Engineering（工业与系统工程（注：此处为系别，按规则不提取））
In this paper we develop dual free mini-batch SDCA with adaptive probabilities for regularized empirical risk minimization. This work is motivated by recent work of Shai Shalev-Shwartz on dual free SDCA method, however, we allow a non-uniform selection of "dual" coordinates in SDCA. Moreover, the probability can change over time, making it more efficient than fix uniform or non-uniform selection. We also propose an efficient procedure to generate a random non-uniform mini-batch through iterative process. The work is concluded with multiple numerical experiments to show the efficiency of propos…
CERMICS, Ecole des Ponts（巴黎桥路学校 CERMICS 实验室）；Inria Paris（法国国家信息与自动化研究所巴黎中心）
Bayesian inference allows to obtain useful information on the parameters of models, either in computational statistics or more recently in the context of Bayesian Neural Networks. The computational cost of usual Monte Carlo methods for sampling posterior laws in Bayesian inference scales linearly with the number of data points. One option to reduce it to a fraction of this cost is to resort to mini-batching in conjunction with unadjusted discretizations of Langevin dynamics, in which case only a random fraction of the data is used to estimate the gradient. However, this leads to an additional …
University of California Merced（加州大学默塞德分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Motivated by extreme multi-label classification applications, we consider training deep learning models over sparse data in multi-GPU servers. The variance in the number of non-zero features across training batches and the intrinsic GPU heterogeneity combine to limit accuracy and increase the time to convergence. We address these challenges with Adaptive SGD, an adaptive elastic model averaging stochastic gradient descent algorithm for heterogeneous multi-GPUs that is characterized by dynamic scheduling, adaptive batch size scaling, and normalized model merging. Instead of statically partition…
University of Chinese Academy of Sciences（中国科学院大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Microsoft Research Asia（微软亚洲研究院）；Pengcheng Laboratory（鹏城实验室）；Zhejiang University（浙江大学）；Microsoft Research（微软研究院）
There is a growing interest in applying machine learning techniques to healthcare. Recently, federated learning (FL) is gaining popularity since it allows researchers to train powerful models without compromising data privacy and security. However, the performance of existing FL approaches often deteriorates when encountering non-iid situations where there exist distribution gaps among clients, and few previous efforts focus on personalization in healthcare. In this article, we propose FedAP to tackle domain shifts and then obtain personalized models for local clients. FedAP learns the similar…
Multi-Label Adaptive Batch Selection by Highlighting Hard and Imbalanced Samples
Key Laboratory of Data Engineering and Visual Computing, Chongqing University of Posts and Telecommunications（重庆邮电大学数据工程与视觉计算重点实验室）；School of Informatics, Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学信息学院）
Batch Normalization (BN) is an important preprocessing step to many deep learning applications. Since it is a data-dependent process, for some homogeneous datasets it is a redundant or even a performance-degrading process. In this paper, we propose an early-stage feasibility assessment method for estimating the benefits of applying BN on the given data batches. The proposed method uses a novel threshold-based approach to classify the training data batches into two sets according to their need for normalization. The need for normalization is decided based on the feature heterogeneity of the con…
AdaBatchGrad: Combining Adaptive Batch Size and Adaptive Step Size
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Institute for Information Transmission Problems RAS（俄罗斯科学院信息传输问题研究所）；Innopolis University（因诺波利斯大学）；Skoltech（斯科尔科沃科学技术研究院）
Batch Normalization (BatchNorm) is commonly used in Convolutional Neural Networks (CNNs) to improve training speed and stability. However, there is still limited consensus on why this technique is effective. This paper uses concepts from the traditional adaptive filter domain to provide insight into the dynamics and inner workings of BatchNorm. First, we show that the convolution weight updates have natural modes whose stability and convergence speed are tied to the eigenvalues of the input autocorrelation matrices, which are controlled by BatchNorm through the convolution layers' channel-wise…
Michigan State University（密歇根州立大学）；NEC Laboratories America（NEC美国实验室）
Distance metric learning (DML) is an important task that has found applications in many domains. The high computational cost of DML arises from the large number of variables to be determined and the constraint that a distance metric has to be a positive semi-definite (PSD) matrix. Although stochastic gradient descent (SGD) has been successfully applied to improve the efficiency of DML, it can still be computationally expensive because in order to ensure that the solution is a PSD matrix, it has to, at every iteration, project the updated distance metric onto the PSD cone, an expensive operatio…
Laboratory for Computational and Statistical Learning（计算与统计学习实验室）；Istituto Italiano di Tecnologia（意大利理工学院）；Massachusetts Institute of Technology（麻省理工学院）；DIBRIS, Università di Genova（热那亚大学DIBRIS（信息学、生物信息学与系统生物学系））；Università di Genova（热那亚大学）
We analyze the learning properties of the stochastic gradient method when multiple passes over the data and mini-batches are allowed. We study how regularization properties are controlled by the step-size, the number of passes and the mini-batch size. In particular, we consider the square loss and show that for a universal step-size choice, the number of passes acts as a regularization parameter, and optimal finite sample bounds can be achieved by early-stopping. Moreover, we show that larger step-sizes are allowed when considering mini-batches. Our analysis is based on a unifying approach, en…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Washington（华盛顿大学）
We describe a graph-based semi-supervised learning framework in the context of deep neural networks that uses a graph-based entropic regularizer to favor smooth solutions over a graph induced by the data. The main contribution of this work is a computationally efficient, stochastic graph-regularization technique that uses mini-batches that are consistent with the graph structure, but also provides enough stochasticity (in terms of mini-batch data diversity) for convergence of stochastic gradient descent methods to good solutions. For this work, we focus on results of frame-level phone classifi…
