Convolutional neural networks are very popular nowadays. Training neural networks is not an easy task. Each convolution corresponds to a structured transformation matrix. In order to help avoid the exploding/vanishing gradient problem, it is desirable that the singular values of each transformation matrix are not large/small in the training process. We propose three new regularization terms for a convolutional kernel tensor to constrain the singular values of each transformation matrix. We show how to carry out the gradient type methods, which provides new insight about the training of convolutional neural networks.
Convolutional neural network is a very important model of deep learning. It can help avoid the exploding/vanishing gradient problem and improve the generalizability of a neural network if the singular values of the Jacobian of a layer are bounded around $1$ in the training process. We propose a new penalty function for a convolutional kernel to let the singular values of the corresponding transformation matrix are bounded around $1$. We show how to carry out the gradient type methods. The penalty is about the structured transformation matrix corresponding to a convolutional kernel. This provid…
Stabilizing PINNs: A regularization scheme for PINN training to avoid unstable fixed points of dynamical systems
Know Center Research GmbH；Christian Doppler Laboratory for Physics-driven Machine Learning in Industrial Applications；Institute of Thermodynamics and Sustainable Propulsion Systems（热力学与可持续推进系统研究所）；Signal Processing and Speech Communication Laboratory（信号处理与语音通信实验室）
We demonstrate the ability of hybrid regularization methods to automatically avoid the double descent phenomenon arising in the training of random feature models (RFM). The hallmark feature of the double descent phenomenon is a spike in the regularization gap at the interpolation threshold, i.e. when the number of features in the RFM equals the number of training samples. To close this gap, the hybrid method considered in our paper combines the respective strengths of the two most common forms of regularization: early stopping and weight decay. The scheme does not require hyperparameter tuning…
Overfitting is one of the most common problems when training deep neural networks on comparatively small datasets. Here, we demonstrate that neural network activation sparsity is a reliable indicator for overfitting which we utilize to propose novel targeted sparsity visualization and regularization strategies. Based on these strategies we are able to understand and counteract overfitting caused by activation sparsity and filter correlation in a targeted layer-by-layer manner. Our results demonstrate that targeted sparsity regularization can efficiently be used to regularize well-known dataset…
University of Waterloo（滑铁卢大学）；Ruhr-University Bochum（波鸿鲁尔大学）
Deep learning requires several design choices, such as the nodes' activation functions and the widths, types, and arrangements of the layers. One consideration when making these choices is the vanishing-gradient problem, which is the phenomenon of algorithms getting stuck at suboptimal points due to small gradients. In this paper, we revisit the vanishing-gradient problem in the context of sigmoid-type activation. We use mathematical arguments to highlight two different sources of the phenomenon, namely large individual parameters and effects across layers, and to illustrate two simple remedie…
Federal Institute of São Carlos - UFSCar（圣卡洛斯联邦学院）；São Paulo State University - UNESP（圣保罗州立大学）
Several image processing tasks, such as image classification and object detection, have been significantly improved using Convolutional Neural Networks (CNN). Like ResNet and EfficientNet, many architectures have achieved outstanding results in at least one dataset by the time of their creation. A critical factor in training concerns the network's regularization, which prevents the structure from overfitting. This work analyzes several regularization methods developed in the last few years, showing significant improvements for different CNN models. The works are classified into three main area…
Technical University of Denmark（丹麦技术大学）；Virginia Tech（弗吉尼亚理工大学）
In this work, we describe a new approach that uses deep neural networks (DNN) to obtain regularization parameters for solving inverse problems. We consider a supervised learning approach, where a network is trained to approximate the mapping from observation data to regularization parameters. Once the network is trained, regularization parameters for newly obtained data can be computed by efficient forward propagation of the DNN. We show that a wide variety of regularization functionals, forward models, and noise models may be considered. The network-obtained regularization parameters can be c…
Facebook AI Research（脸书人工智能研究院）；Inria, École normale supérieure, CNRS, PSL Research University（法国国家信息与自动化研究所、巴黎高等师范学院、法国国家科学研究中心、巴黎文理研究大学）；Courant Institute, New York University（纽约大学库朗数学科学研究所）；Center for Data Science, New York University（纽约大学数据科学中心）
Recent self-supervised methods for image representation learning are based on maximizing the agreement between embedding vectors from different views of the same image. A trivial solution is obtained when the encoder outputs constant vectors. This collapse problem is often avoided through implicit biases in the learning architecture, that often lack a clear justification or interpretation. In this paper, we introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with a simple regularization term on the variance of the embeddings al…
China University of Geosciences（中国地质大学）；University of Kentucky（肯塔基大学）
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresponding to a convolutional kernel bounded around $1$. We propose a penalty function that can be used in the optimization of a convolutional neural network to constrain the singular values of the transformation matrix around $1$. We derive an algorithm to carry out the gradient des…
In this work we revisit gradient regularization for adversarial robustness with some new ingredients. First, we derive new per-image theoretical robustness bounds based on local gradient information. These bounds strongly motivate input gradient regularization. Second, we implement a scaleable version of input gradient regularization which avoids double backpropagation: adversarially robust ImageNet models are trained in 33 hours on four consumer grade GPUs. Finally, we show experimentally and through theoretical certification that input gradient regularization is competitive with adversarial …
Università degli Studi di Genova（热那亚大学）；Machine Learning Genoa Center（热那亚机器学习中心）；Massachusetts Institute of Technology（麻省理工学院）；Istituto Italiano di Tecnologia（意大利技术研究院）
We study learning properties of accelerated gradient descent methods for linear least-squares in Hilbert spaces. We analyze the implicit regularization properties of Nesterov acceleration and a variant of heavy-ball in terms of corresponding learning error bounds. Our results show that acceleration can provides faster bias decay than gradient descent, but also suffers of a more unstable behavior. As a result acceleration cannot be in general expected to improve learning accuracy with respect to gradient descent, but rather to achieve the same accuracy with reduced computations. Our theoretical…
The outcome of Jacobian singular values regularization was studied for supervised learning problems. It also was shown that Jacobian conditioning regularization can help to avoid the ``mode-collapse'' problem in Generative Adversarial Networks. In this paper, we try to answer the following question: Can information about policy conditioning help to shape a more stable and general policy of reinforcement learning agents? To answer this question, we conduct a study of Jacobian conditioning behavior during policy optimization. To the best of our knowledge, this is the first work that research con…
This paper proposes weight regularization for a faster neural vocoder. Pruning time-consuming DNN modules is a promising way to realize a real-time vocoder on a CPU (e.g. WaveRNN, LPCNet). Regularization that encourages sparsity is also effective in avoiding the quality degradation created by pruning. However, the orders of weight matrices must be contiguous in SIMD size for fast vocoding. To ensure this order, we propose explicit SIMD size aware regularization. Our proposed method reshapes a weight matrix into a tensor so that the weights are aligned by group size in advance, and then compute…
Beyond Limits Inc（Beyond Limits公司）；University of Southern California（南加州大学）
Long Short-Term Memory (LSTM) neural networks have been widely used for time series forecasting problems. However, LSTMs are prone to overfitting and performance reduction during test phases. Several different regularization techniques have been shown in literature to prevent overfitting problems in neural networks. In this paper, first, we introduce application of kernel flow methods for time series forecasting in general. Afterward, we examine the effectiveness of applying kernel flow regularization on LSTM layers to avoid overfitting problems. We describe a regularization method by applying…
Linköping University（林雪平大学）；University of Cambridge（剑桥大学）
Convolutional neural networks (CNNs) can model complicated non-linear relations between images. However, they are notoriously sensitive to small changes in the input. Most CNNs trained to describe image-to-image mappings generate temporally unstable results when applied to video sequences, leading to flickering artifacts and other inconsistencies over time. In order to use CNNs for video material, previous methods have relied on estimating dense frame-to-frame motion information (optical flow) in the training and/or the inference phase, or by exploring recurrent learning structures. We take a …
We propose a novel regularizer to improve the training of Generative Adversarial Networks (GANs). The motivation is that when the discriminator D spreads out its model capacity in the right way, the learning signals given to the generator G are more informative and diverse. These in turn help G to explore better and discover the real data manifold while avoiding large unstable jumps due to the erroneous extrapolation made by D. Our regularizer guides the rectifier discriminator D to better allocate its model capacity, by encouraging the binary activation patterns on selected internal layers of…
Chung-Ang University（中央大学）；University of Copenhagen（哥本哈根大学）
Regularization is essential for avoiding over-fitting to training data in network optimization, leading to better generalization of the trained networks. The label noise provides a strong implicit regularization by replacing the target ground truth labels of training examples by uniform random labels. However, it can cause undesirable misleading gradients due to the large loss associated with incorrect labels. We propose a first-order optimization method (Label-Noised Trim-SGD) that uses the label noise with the example trimming in order to remove the outliers based on the loss. The proposed a…
Policy-based reinforcement learning methods suffer from the policy collapse problem. We find valued-based reinforcement learning methods with ε-greedy mechanism are capable of enjoying three characteristics, Closed-form Diversity, Objective-invariant Exploration and Adaptive Trade-off, which help value-based methods avoid the policy collapse problem. However, there does not exist a parallel mechanism for policy-based methods that achieves all three characteristics. In this paper, we propose an entropy regularization free mechanism that is designed for policy-based methods, which achieves Close…
School of Computer Science Reichman University（Reichman大学计算机学院）；Data Science Institute Reichman University（Reichman大学数据科学研究所）
The weight decay regularization term is widely used during training to constrain expressivity, avoid overfitting, and improve generalization. Historically, this concept was borrowed from the SVM maximum margin principle and extended to multi-class deep networks. Carefully inspecting this principle reveals that it is not optimal for multi-class classification in general, and in particular when using deep neural networks. In this paper, we explain why this commonly used principle is not optimal and propose a new regularization scheme, called {\em Pairwise Margin Maximization} (PMM), which measur…
Johns Hopkins University（约翰霍普金斯大学）；University of California, Los Angeles（加州大学洛杉矶分校）
Regularization for optimization is a crucial technique to avoid overfitting in machine learning. In order to obtain the best performance, we usually train a model by tuning the regularization parameters. It becomes costly, however, when a single round of training takes significant amount of time. Very recently, Neu and Rosasco show that if we run stochastic gradient descent (SGD) on linear regression problems, then by averaging the SGD iterates properly, we obtain a regularized solution. It left open whether the same phenomenon can be achieved for other optimization problems and algorithms. In…
In this paper, we study the Temporal Difference (TD) learning with linear value function approximation. It is well known that most TD learning algorithms are unstable with linear function approximation and off-policy learning. Recent development of Gradient TD (GTD) algorithms has addressed this problem successfully. However, the success of GTD algorithms requires a set of well chosen features, which are not always available. When the number of features is huge, the GTD algorithms might face the problem of overfitting and being computationally expensive. To cope with this difficulty, regulariz…
In recent years, hyper-complex deep networks (such as complex-valued and quaternion-valued neural networks) have received a renewed interest in the literature. They find applications in multiple fields, ranging from image reconstruction to 3D audio processing. Similar to their real-valued counterparts, quaternion neural networks (QVNNs) require custom regularization strategies to avoid overfitting. In addition, for many real-world applications and embedded implementations, there is the need of designing sufficiently compact networks, with few weights and neurons. However, the problem of regula…
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Deep neural networks with remarkably strong generalization performances are usually over-parameterized. Despite explicit regularization strategies are used for practitioners to avoid over-fitting, the impacts are often small. Some theoretical studies have analyzed the implicit regularization effect of stochastic gradient descent (SGD) on simple machine learning models with certain assumptions. However, how it behaves practically in state-of-the-art models and real-world datasets is still unknown. To bridge this gap, we study the role of SGD implicit regularization in deep learning systems. We …
Center for Cognitive Ubiquitous Computing (CUbiC), Arizona State University（认知普适计算中心（CUbiC），亚利桑那州立大学）
Recently, Generative Adversarial Networks (GANs) have been applied to the problem of Cold-Start Recommendation, but the training performance of these models is hampered by the extreme sparsity in warm user purchase behavior. In this paper we introduce a novel representation for user-vectors by combining user demographics and user preferences, making the model a hybrid system which uses Collaborative Filtering and Content Based Recommendation. Our system models user purchase behavior using weighted user-product preferences (explicit feedback) rather than binary user-product interactions (implic…
Bridging the Gap Between Target Networks and Functional Regularization
ServiceNow Research（ServiceNow研究院）；Mila（米拉人工智能研究所）；Université de Montréal（蒙特利尔大学）；DeepMind（深度思维）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Polytechnique Montréal（蒙特利尔理工学院）
UiT The Arctic University of Norway（挪威北极大学UiT）；NORCE Norwegian Research Centre（NORCE挪威研究中心）
Full characterization of the spectral behavior of generative models based on neural networks remains an open issue. Recent research has focused heavily on generative adversarial networks and the high-frequency discrepancies between real and generated images. The current solution to avoid this is to either replace transposed convolutions with bilinear up-sampling or add a spectral regularization term in the generator. It is well known that Variational Autoencoders (VAEs) also suffer from these issues. In this work, we propose a simple 2D Fourier transform-based spectral regularization loss for …
University of Maryland（马里兰大学）；Aunalytics；Hillsdale College（希尔斯代尔学院）；Potomac Research LLC（波托马克研究有限责任公司）
Recent work has shown that machine learning (ML) models can be trained to accurately forecast the dynamics of unknown chaotic dynamical systems. Short-term predictions of the state evolution and long-term predictions of the statistical patterns of the dynamics (``climate'') can be produced by employing a feedback loop, whereby the model is trained to predict forward one time step, then the model output is used as input for multiple time steps. In the absence of mitigating techniques, however, this technique can result in artificially rapid error growth. In this article, we systematically exami…
Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two methods for approximating the Koopman operator, are reformulated as convex optimization problems with linear matrix inequality constraints. Asymptotic stability constraints and system norm regularizers are then incorporated as methods to improve the numerical conditioning of the Koopman op…
Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a nonconvex extension of the overlapped nuclear norm regularizer. Based on the proximal average algorithm, the proposed algorithm can avoid expensive tensor folding/unfolding operations. A special "sparse plus low-rank" structure is maintained throughout the iterations, and allows fast computation of the individual proximal steps. Empirical convergence is further …
Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features statistics/ranking, or additional optimization designs in the training process. In this paper, we propose a simple and effective regularization strategy from a new perspective of evolution of features, which we call feature flow regularization (FFR), for improving structured sparsity and filter pruning in DNNs. Specifically, FFR imposes controls on the gradient and …
Istituto Italiano di Tecnologia（意大利技术研究院）；University of Genova（热那亚大学）
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric model, hence avoiding linear or additive models. The key idea is to measure the importance of each variable in the model by making use of partial derivatives. Based on this intuition we propose a new notion of nonparametric sparsity and a corresponding least squares regularization scheme. Using concepts and results from the theory of reproducing kernel Hilbe…
Texas State University（德克萨斯州立大学）；Yale University（耶鲁大学）
Neural networks have attracted a lot of attention due to its success in applications such as natural language processing and computer vision. For large scale data, due to the tremendous number of parameters in neural networks, overfitting is an issue in training neural networks. To avoid overfitting, one common approach is to penalize the parameters especially the weights in neural networks. Although neural networks has demonstrated its advantages in many applications, the theoretical foundation of penalized neural networks has not been well-established. Our goal of this paper is to propose th…
Representing shapes as level sets of neural networks has been recently proved to be useful for different shape analysis and reconstruction tasks. So far, such representations were computed using either: (i) pre-computed implicit shape representations; or (ii) loss functions explicitly defined over the neural level sets. In this paper we offer a new paradigm for computing high fidelity implicit neural representations directly from raw data (i.e., point clouds, with or without normal information). We observe that a rather simple loss function, encouraging the neural network to vanish on the inpu…
