Averaging neural network weights sampled by a backbone stochastic gradient descent (SGD) is a simple yet effective approach to assist the backbone SGD in finding better optima, in terms of generalization. From a statistical perspective, weight averaging (WA) contributes to variance reduction. Recently, a well-established stochastic weight averaging (SWA) method is proposed, which is featured by the application of a cyclical or high constant (CHC) learning rate schedule (LRS) in generating weight samples for WA. Then a new insight on WA appears, which states that WA helps to discover wider optima and then leads to better generalization. We conduct extensive experimental studies for SWA, involving a dozen modern DNN model structures and a dozen benchmark open-source image, graph, and text datasets. We disentangle contributions of the WA operation and the CHC LRS for SWA, showing that the WA operation in SWA still contributes to variance reduction but does not always lead to wide optima. The experimental results indicate that there are global scale geometric structures in the DNN loss landscape. We then present an algorithm termed periodic SWA (PSWA) which makes use of a series of WA operations to discover the global geometric structures. PSWA outperforms its backbone SGD remarkably, providing experimental evidences for the existence of global geometric structures. Codes for reproducing the experimental results are available at https://github.com/ZJLAB-AMMI/PSWA.
Hierarchical Weight Averaging for Deep Neural Networks
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Pengcheng Laboratory（鹏城实验室）；Institute of High Performance Computing, Agency for Science, Technology and Research（新加坡科技研究局高性能计算研究所）
Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative solutions into a single solution, is still under-explored. While some increasingly weighted averaging schemes have been considered in the literature, existing works are mostly restricted to strongly convex objective functions and the convergence of optimization error. It remains unclear how these averaging schemes affect the convergence of {\it both optimiza…
SeWA: Selective Weight Average via Probabilistic Masking
Huazhong University of Science and Technology（华中科技大学）；Shanghai Jiao Tong University（上海交通大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Baidu Inc.（百度公司）；Sun Yat-sen University（中山大学）；Nanyang Technological University（南洋理工大学）
ETH Zürich（苏黎世联邦理工学院）；University of Cambridge（剑桥大学）；Google AI Berlin（谷歌柏林人工智能研究院）；Imperial College London（伦敦帝国理工学院）；University of Bristol（布里斯托尔大学）
Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using stochastic gradient descent (SGD). We find that convolutional neural network (CNN) and ResNet weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. We show that building these observatio…
University of Science and Technology of China（中国科学技术大学）；Zhejiang Cainiao Supply Chain Management Co. Ltd（浙江菜鸟供应链管理有限公司）；Advanced Digital Sciences Center（先进数字科学中心）
Adaptive learning rate methods have been successfully applied in many fields, especially in training deep neural networks. Recent results have shown that adaptive methods with exponential increasing weights on squared past gradients (i.e., ADAM, RMSPROP) may fail to converge to the optimal solution. Though many algorithms, such as AMSGRAD and ADAMNC, have been proposed to fix the non-convergence issues, achieving a data-dependent regret bound similar to or better than ADAGRAD is still a challenge to these methods. In this paper, we propose a novel adaptive method weighted adaptive algorithm (W…
Universitat Pompeu Fabra（庞培法布拉大学）；Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利理工学院）；Università degli Studi di Genova（热那亚大学）
We propose and analyze a variant of the classic Polyak-Ruppert averaging scheme, broadly used in stochastic gradient methods. Rather than a uniform average of the iterates, we consider a weighted average, with weights decaying in a geometric fashion. In the context of linear least squares regression, we show that this averaging scheme has a the same regularizing effect, and indeed is asymptotically equivalent, to ridge regression. In particular, we derive finite-sample bounds for the proposed approach that match the best known results for regularized stochastic gradient methods.
Vrije Universiteit Amsterdam（阿姆斯特丹自由大学）；University of Amsterdam（阿姆斯特丹大学）；Eindhoven University of Technology（埃因霍温理工大学）
Despite their success, modern language models are fragile. Even small changes in their training pipeline can lead to unexpected results. We study this phenomenon by examining the robustness of ALBERT (arXiv:1909.11942) in combination with Stochastic Weight Averaging (SWA) (arXiv:1803.05407) -- a cheap way of ensembling -- on a sentiment analysis task (SST-2). In particular, we analyze SWA's stability via CheckList criteria (arXiv:2005.04118), examining the agreement on errors made by models differing only in their random seed. We hypothesize that SWA is more stable because it ensembles model s…
Cornell University（康奈尔大学）；Higher School of Economics（高等经济学院）；Samsung-HSE Laboratory（三星-高等经济学院实验室）；Samsung AI Center in Moscow（莫斯科三星人工智能中心）；Lomonosov Moscow State University（莫斯科国立大学（罗蒙诺索夫莫斯科国立大学））
Deep neural networks are typically trained by optimizing a loss function with an SGD variant, in conjunction with a decaying learning rate, until convergence. We show that simple averaging of multiple points along the trajectory of SGD, with a cyclical or constant learning rate, leads to better generalization than conventional training. We also show that this Stochastic Weight Averaging (SWA) procedure finds much flatter solutions than SGD, and approximates the recent Fast Geometric Ensembling (FGE) approach with a single model. Using SWA we achieve notable improvement in test accuracy over co…
School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院）；School of Computer and Data Science, Nanyang Technological University（南洋理工大学计算机与数据科学学院）；School of Cyber Science & Technology, Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区网络空间科学与技术学院）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Faculty of Engineering, the University of Sydney（悉尼大学工程学院）
Trainable Weight Averaging: Accelerating Training and Improving Generalization
Shanghai Jiao Tong University（上海交通大学）；KU Leuven（鲁汶大学）；National Taiwan University（台湾大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Naver；AITRICS
Ensembles of deep neural networks have demonstrated superior performance, but their heavy computational cost hinders applying them for resource-limited environments. It motivates distilling knowledge from the ensemble teacher into a smaller student network, and there are two important design choices for this ensemble distillation: 1) how to construct the student network, and 2) what data should be shown during training. In this paper, we propose a weight averaging technique where a student with multiple subnetworks is trained to absorb the functional diversity of ensemble teachers, but then th…
We propose Stochastic Weight Averaging in Parallel (SWAP), an algorithm to accelerate DNN training. Our algorithm uses large mini-batches to compute an approximate solution quickly and then refines it by averaging the weights of multiple models computed independently and in parallel. The resulting models generalize equally well as those trained with small mini-batches but are produced in a substantially shorter time. We demonstrate the reduction in training time and the good generalization performance of the resulting models on the computer vision datasets CIFAR10, CIFAR100, and ImageNet.
Adversarial reprogramming, introduced by Elsayed, Goodfellow, and Sohl-Dickstein, seeks to repurpose a neural network to perform a different task, by manipulating its input without modifying its weights. We prove that two-layer ReLU neural networks with random weights can be adversarially reprogrammed to achieve arbitrarily high accuracy on Bernoulli data models over hypercube vertices, provided the network width is no greater than its input dimension. We also substantially strengthen a recent result of Phuong and Lampert on directional convergence of gradient flow, and obtain as a corollary t…
Designing a deep neural network (DNN) with good generalization capability is a complex process especially when the weights are severely quantized. Model averaging is a promising approach for achieving the good generalization capability of DNNs, especially when the loss surface for training contains many sharp minima. We present a new quantized neural network optimization approach, stochastic quantized weight averaging (SQWA), to design low-precision DNNs with good generalization capability using model averaging. The proposed approach includes (1) floating-point model training, (2) direct quant…
Centre for Artificial Intelligence（人工智能中心）；University College London（伦敦大学学院）
Training vision or language models on large datasets can take days, if not weeks. We show that averaging the weights of the k latest checkpoints, each collected at the end of an epoch, can speed up the training progression in terms of loss and accuracy by dozens of epochs, corresponding to time savings up to ~68 and ~30 GPU hours when training a ResNet50 on ImageNet and RoBERTa-Base model on WikiText-103, respectively. We also provide the code and model checkpoint trajectory to reproduce the results and facilitate research on reusing historical weights for faster convergence.
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Criteo AI Lab（Criteo人工智能实验室）；Université de Rouen（鲁昂大学）
Standard neural networks struggle to generalize under distribution shifts in computer vision. Fortunately, combining multiple networks can consistently improve out-of-distribution generalization. In particular, weight averaging (WA) strategies were shown to perform best on the competitive DomainBed benchmark; they directly average the weights of multiple networks despite their nonlinearities. In this paper, we propose Diverse Weight Averaging (DiWA), a new WA strategy whose main motivation is to increase the functional diversity across averaged models. To this end, DiWA averages weights obtain…
Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Université de Montréal（蒙特利尔大学）；University of Waterloo（滑铁卢大学）
Knowledge Distillation (KD) is a commonly used technique for improving the generalization of compact Pre-trained Language Models (PLMs) on downstream tasks. However, such methods impose the additional burden of training a separate teacher model for every new dataset. Alternatively, one may directly work on the improvement of the optimization procedure of the compact model toward better generalization. Recent works observe that the flatness of the local minimum correlates well with better generalization. In this work, we adapt Stochastic Weight Averaging (SWA), a method encouraging convergence …
Low precision operations can provide scalability, memory savings, portability, and energy efficiency. This paper proposes SWALP, an approach to low precision training that averages low-precision SGD iterates with a modified learning rate schedule. SWALP is easy to implement and can match the performance of full-precision SGD even with all numbers quantized down to 8 bits, including the gradient accumulators. Additionally, we show that SWALP converges arbitrarily close to the optimal solution for quadratic objectives, and to a noise ball asymptotically smaller than low precision SGD in strongly…
Recent studies on few-shot classification using transfer learning pose challenges to the effectiveness and efficiency of episodic meta-learning algorithms. Transfer learning approaches are a natural alternative, but they are restricted to few-shot classification. Moreover, little attention has been on the development of probabilistic models with well-calibrated uncertainty from few-shot samples, except for some Bayesian episodic learning algorithms. To tackle the aforementioned issues, we propose a new transfer learning method to obtain accurate and reliable models for few-shot regression and …
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the iterative algorithm into a trainable network that facilitates learning the sparsity prior. We also consider quantization of the network weights. Quantization makes neural networks efficient both in terms of memory and computation during inference, and also renders them compatible for low-precision hardware deployment. Our learning algorithm is based on a varia…
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）；University of Chicago（芝加哥大学）
We propose methods for distributed graph-based multi-task learning that are based on weighted averaging of messages from other machines. Uniform averaging or diminishing stepsize in these methods would yield consensus (single task) learning. We show how simply skewing the averaging weights or controlling the stepsize allows learning different, but related, tasks on the different machines.
CWI；Leiden University（莱顿大学）；University of Helsinki（赫尔辛基大学）
This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL was originally based on data compression ideas, this introduction can be read without any knowledge thereof. It takes into account all major developments since 2007, the last time an extensive overview was written. These include new methods for model selection and averaging and hypothesis testing, as well as the first completely general definition of {\em M…
WASH: Train your Ensemble with Communication-Efficient Weight Shuffling, then Average
ISIR - Sorbonne Université（ISIR - 索邦大学）；Mila（米拉研究所）；Concordia University（康考迪亚大学）；École de technologie supérieure（高等技术学院）；Center for Computational Mathematics（计算数学中心）；Flatiron Institute（弗拉特iron研究所）
