Regularization is an effective way to promote the generalization performance of machine learning models. In this paper, we focus on label smoothing, a form of output distribution regularization that prevents overfitting of a neural network by softening the ground-truth labels in the training data in an attempt to penalize overconfident outputs. Existing approaches typically use cross-validation to impose this smoothing, which is uniform across all training data. In this paper, we show that such label smoothing imposes a quantifiable bias in the Bayes error rate of the training data, with regions of the feature space with high overlap and low marginal likelihood having a lower bias and regions of low overlap and high marginal likelihood having a higher bias. These theoretical results motivate a simple objective function for data-dependent smoothing to mitigate the potential negative consequences of the operation while maintaining its desirable properties as a regularizer. We call this approach Structural Label Smoothing (SLS). We implement SLS and empirically validate on synthetic, Higgs, SVHN, CIFAR-10, and CIFAR-100 datasets. The results confirm our theoretical insights and demonstrate the effectiveness of the proposed method in comparison to traditional label smoothing.
Label smoothing is commonly used in training deep learning models, wherein one-hot training labels are mixed with uniform label vectors. Empirically, smoothing has been shown to improve both predictive performance and model calibration. In this paper, we study whether label smoothing is also effective as a means of coping with label noise. While label smoothing apparently amplifies this problem --- being equivalent to injecting symmetric noise to the labels --- we show how it relates to a general family of loss-correction techniques from the label noise literature. Building on this connection,…
Random Smoothing Regularization in Kernel Gradient Descent Learning
Fudan University（复旦大学）；Purdue University（普渡大学）；The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Label Smoothing (LS) is an effective regularizer to improve the generalization of state-of-the-art deep models. For each training sample the LS strategy smooths the one-hot encoded training signal by distributing its distribution mass over the non ground-truth classes, aiming to penalize the networks from generating overconfident output distributions. This paper introduces a novel label smoothing technique called Pairwise Label Smoothing (PLS). The PLS takes a pair of samples as input. Smoothing with a pair of ground-truth labels enables the PLS to preserve the relative distance between the tw…
Carnegie Mellon University（卡内基梅隆大学）；University of Tokyo（东京大学）
It has been hypothesized that label smoothing can reduce overfitting and improve generalization, and current empirical evidence seems to corroborate these effects. However, there is a lack of mathematical understanding of when and why such empirical improvements occur. In this paper, as a step towards understanding why label smoothing is effective, we propose a theoretical framework to show how label smoothing provides in controlling the generalization loss. In particular, we show that this benefit can be precisely formulated and identified in the label noise setting, where the training is par…
Due to diverse architectures in deep neural networks (DNNs) with severe overparameterization, regularization techniques are critical for finding optimal solutions in the huge hypothesis space. In this paper, we propose an effective regularization technique, called Neighborhood Region Smoothing (NRS). NRS leverages the finding that models would benefit from converging to flat minima, and tries to regularize the neighborhood region in weight space to yield approximate outputs. Specifically, gap between outputs of models in the neighborhood region is gauged by a defined metric based on Kullback-L…
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cases with multiple nonsmooth terms, in which standard conditional gradient methods may be difficult to apply. The HCGS algorithm borrows techniques from smoothing proximal methods and requires first-order computations (subgradients and proximity operations). Unlike proximal methods…
The generalization and learning speed of a multi-class neural network can often be significantly improved by using soft targets that are a weighted average of the hard targets and the uniform distribution over labels. Smoothing the labels in this way prevents the network from becoming over-confident and label smoothing has been used in many state-of-the-art models, including image classification, language translation and speech recognition. Despite its widespread use, label smoothing is still poorly understood. Here we show empirically that in addition to improving generalization, label smooth…
Seoul National University（首尔国立大学）；Chung-Ang University（中央大学）
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model in the determination of regularity to achieve better generalization. The degree of regularization at each element in the target space of the neural network architecture is determined based on the residual at each optimization iteration in an adaptive way. Our adaptive regularization algorithm is designed to apply a diffusion process driven by the heat equat…
South China University of Technology（华南理工大学）；Northwestern Polytechnical University（西北工业大学）
Inspired by the strong correlation between the Label Smoothing Regularization(LSR) and Knowledge distillation(KD), we propose an algorithm LsrKD for training boost by extending the LSR method to the KD regime and applying a softer temperature. Then we improve the LsrKD by a Teacher Correction(TC) method, which manually sets a constant larger proportion for the right class in the uniform distribution teacher. To further improve the performance of LsrKD, we develop a self-distillation method named Memory-replay Knowledge Distillation (MrKD) that provides a knowledgeable teacher to replace the un…
Adversarial training is one of the strongest defenses against adversarial attacks, but it requires adversarial examples to be generated for every mini-batch during optimization. The expense of producing these examples during training often precludes adversarial training from use on complex image datasets. In this study, we explore the mechanisms by which adversarial training improves classifier robustness, and show that these mechanisms can be effectively mimicked using simple regularization methods, including label smoothing and logit squeezing. Remarkably, using these simple regularization m…
Generating confidence calibrated outputs is of utmost importance for the applications of deep neural networks in safety-critical decision-making systems. The output of a neural network is a probability distribution where the scores are estimated confidences of the input belonging to the corresponding classes, and hence they represent a complete estimate of the output likelihood relative to all classes. In this paper, we propose a novel form of label smoothing to improve confidence calibration. Since different classes are of different intrinsic similarities, more similar classes should result i…
It has been recently demonstrated that multi-generational self-distillation can improve generalization. Despite this intriguing observation, reasons for the enhancement remain poorly understood. In this paper, we first demonstrate experimentally that the improved performance of multi-generational self-distillation is in part associated with the increasing diversity in teacher predictions. With this in mind, we offer a new interpretation for teacher-student training as amortized MAP estimation, such that teacher predictions enable instance-specific regularization. Our framework allows us to the…
ETH Zürich（苏黎世联邦理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）；University of Cambridge（剑桥大学）
Prior work has explored directly regularizing the output distributions of probabilistic models to alleviate peaky (i.e. over-confident) predictions, a common sign of overfitting. This class of techniques, of which label smoothing is one, has a connection to entropy regularization. Despite the consistent success of label smoothing across architectures and data sets in language generation tasks, two problems remain open: (1) there is little understanding of the underlying effects entropy regularizers have on models, and (2) the full space of entropy regularization techniques is largely unexplore…
We study Label-Smoothing as a means for improving adversarial robustness of supervised deep-learning models. After establishing a thorough and unified framework, we propose several variations to this general method: adversarial, Boltzmann and second-best Label-Smoothing methods, and we explain how to construct your own one. On various datasets (MNIST, CIFAR10, SVHN) and models (linear models, MLPs, LeNet, ResNet), we show that Label-Smoothing in general improves adversarial robustness against a variety of attacks (FGSM, BIM, DeepFool, Carlini-Wagner) by better taking account of the dataset geo…
Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
A recent technique of randomized smoothing has shown that the worst-case (adversarial) $\ell_2$-robustness can be transformed into the average-case Gaussian-robustness by "smoothing" a classifier, i.e., by considering the averaged prediction over Gaussian noise. In this paradigm, one should rethink the notion of adversarial robustness in terms of generalization ability of a classifier under noisy observations. We found that the trade-off between accuracy and certified robustness of smoothed classifiers can be greatly controlled by simply regularizing the prediction consistency over noise. This…
National University of Singapore（新加坡国立大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）
Knowledge Distillation (KD) aims to distill the knowledge of a cumbersome teacher model into a lightweight student model. Its success is generally attributed to the privileged information on similarities among categories provided by the teacher model, and in this sense, only strong teacher models are deployed to teach weaker students in practice. In this work, we challenge this common belief by following experimental observations: 1) beyond the acknowledgment that the teacher can improve the student, the student can also enhance the teacher significantly by reversing the KD procedure; 2) a poo…
Training deep neural networks (DNNs) in the presence of noisy labels is an important and challenging task. Probabilistic modeling, which consists of a classifier and a transition matrix, depicts the transformation from true labels to noisy labels and is a promising approach. However, recent probabilistic methods directly apply transition matrix to DNN, neglect DNN's susceptibility to overfitting, and achieve unsatisfactory performance, especially under the uniform noise. In this paper, inspired by label smoothing, we proposed a novel method, in which a smoothed transition matrix is used for up…
In this article, we mathematically study several GAN related topics, including Inception score, label smoothing, gradient vanishing and the -log(D(x)) alternative. --- An advanced version is included in arXiv:1703.02000 "Activation Maximization Generative Adversarial Nets". Please refer Section 6 in 1703.02000 for detailed analysis on Inception Score, and refer its appendix for the discussions on Label Smoothing, Gradient Vanishing and -log(D(x)) Alternative.
Kim Jaechul Graduate School of AI, KAIST（韩国科学技术院金宰澈人工智能研究生院）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）
As deep neural networks can easily overfit noisy labels, robust training in the presence of noisy labels is becoming an important challenge in modern deep learning. While existing methods address this problem in various directions, they still produce unpredictable sub-optimal results since they rely on the posterior information estimated by the feature extractor corrupted by noisy labels. Lipschitz regularization successfully alleviates this problem by training a robust feature extractor, but it requires longer training time and expensive computations. Motivated by this, we propose a simple ye…
Label smoothing is widely used in deep neural networks for multi-class classification. While it enhances model generalization and reduces overconfidence by aiming to lower the probability for the predicted class, it distorts the predicted probabilities of other classes resulting in poor class-wise calibration. Another method for enhancing model generalization is self-distillation where the predictions of a teacher network trained with one-hot labels are used as the target for training a student network. We take inspiration from both label smoothing and self-distillation and propose two novel i…
Smoothing the Edges: Smooth Optimization for Sparse Regularization using Hadamard Overparametrization
Department of Statistics, LMU Munich（慕尼黑大学统计系）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；Institute of Computational Biology, Helmholtz Munich（亥姆霍兹慕尼黑计算生物学研究所）；Center for Computational Mathematics, Flatiron Institute（熨斗研究所计算数学中心）
Label smoothing regularization (LSR) has a great success in training deep neural networks by stochastic algorithms such as stochastic gradient descent and its variants. However, the theoretical understanding of its power from the view of optimization is still rare. This study opens the door to a deep understanding of LSR by initiating the analysis. In this paper, we analyze the convergence behaviors of stochastic gradient descent with label smoothing regularization for solving non-convex problems and show that an appropriate LSR can help to speed up the convergence by reducing the variance. Mo…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；Brown University（布朗大学）；The University of Sydney（悉尼大学）；RIKEN AIP（理化学研究所人工智能研究中心）；University of Tokyo（东京大学）
Label smoothing (LS) is an arising learning paradigm that uses the positively weighted average of both the hard training labels and uniformly distributed soft labels. It was shown that LS serves as a regularizer for training data with hard labels and therefore improves the generalization of the model. Later it was reported LS even helps with improving robustness when learning with noisy labels. However, we observed that the advantage of LS vanishes when we operate in a high label noise regime. Intuitively speaking, this is due to the increased entropy of $\mathbb{P}(\text{noisy label}|X)$ when…
Robust Classification by Coupling Data Mollification with Label Smoothing
Department of Computer Science（计算机科学系）；Mathematical and Algorithmic Sciences Lab（数学与算法科学实验室）；Huawei Paris Research Center（华为巴黎研发中心）；Department of Physics and Technology（物理与技术系）；UiT The Arctic University of Norway（北极大学挪威分校）；Statistics Program（统计学项目）；KAUST（卡塔尔大学）
Overconfidence has been shown to impair generalization and calibration of a neural network. Previous studies remedy this issue by adding a regularization term to a loss function, preventing a model from making a peaked distribution. Label smoothing smoothes target labels with a pre-defined prior label distribution; as a result, a model is learned to maximize the likelihood of predicting the soft label. Nonetheless, the amount of smoothing is the same in all samples and remains fixed in training. In other words, label smoothing does not reflect the change in probability distribution mapped by a…
Tsinghua University（清华大学）；Chinese University of Hong Kong（香港中文大学）；PengCheng Laboratory（鹏城实验室）
Recently, a variety of regularization techniques have been widely applied in deep neural networks, such as dropout, batch normalization, data augmentation, and so on. These methods mainly focus on the regularization of weight parameters to prevent overfitting effectively. In addition, label regularization techniques such as label smoothing and label disturbance have also been proposed with the motivation of adding a stochastic perturbation to labels. In this paper, we propose a novel adaptive label regularization method, which enables the neural network to learn from the erroneous experience a…
Label smoothing has been shown to be an effective regularization strategy in classification, that prevents overfitting and helps in label de-noising. However, extending such methods directly to seq2seq settings, such as Machine Translation, is challenging: the large target output space of such problems makes it intractable to apply label smoothing over all possible outputs. Most existing approaches for seq2seq settings either do token level smoothing, or smooth over sequences generated by randomly substituting tokens in the target sequence. Unlike these works, in this paper, we propose a techn…
Training modern neural networks is an inherently noisy process that can lead to high \emph{prediction churn} -- disagreements between re-trainings of the same model due to factors such as randomization in the parameter initialization and mini-batches -- even when the trained models all attain similar accuracies. Such prediction churn can be very undesirable in practice. In this paper, we present several baselines for reducing churn and show that training on soft labels obtained by adaptively smoothing each example's label based on the example's neighboring labels often outperforms the baseline…
Graph convolutional neural networks (GCNNs) have received much attention recently, owing to their capability in handling graph-structured data. Among the existing GCNNs, many methods can be viewed as instances of a neural message passing motif; features of nodes are passed around their neighbors, aggregated and transformed to produce better nodes' representations. Nevertheless, these methods seldom use node transition probabilities, a measure that has been found useful in exploring graphs. Furthermore, when the transition probabilities are used, their transition direction is often improperly c…
Institute of Automation（自动化研究所）；University of Chinese Academy of Sciences (UCAS)（中国科学院大学）；Alibaba Group（阿里巴巴集团）；Twitter（推特）
A fundamental challenge for machine learning models is how to generalize learned models for out-of-distribution (OOD) data. Among various approaches, exploiting invariant features by Domain Adversarial Training (DAT) received widespread attention. Despite its success, we observe training instability from DAT, mostly due to over-confident domain discriminator and environment label noise. To address this issue, we proposed Environment Label Smoothing (ELS), which encourages the discriminator to output soft probability, which thus reduces the confidence of the discriminator and alleviates the imp…
Multi-label learning is usually used to mine the correlation between features and labels, and feature selection can retain as much information as possible through a small number of features. $\ell_{2,1}$ regularization method can get sparse coefficient matrix, but it can not solve multicollinearity problem effectively. The model proposed in this paper can obtain the most relevant few features by solving the joint constrained optimization problems of $\ell_{2,1}$ and $\ell_{F}$ regularization.In manifold regularization, we implement random walk strategy based on joint information matrix, and ge…
SGD method for entropy error function with smoothing l0 regularization for neural networks
VNPT AI；Viettel High Technology Industries Corporation（越南电信高科技产业公司）；Università degli studi dell’Aquila（拉奎拉大学）；Thai Nguyen University of Education（太原师范大学）
The problem of learning from label proportions (LLP) involves training classifiers with weak labels on bags of instances, rather than strong labels on individual instances. The weak labels only contain the label proportion of each bag. The LLP problem is important for many practical applications that only allow label proportions to be collected because of data privacy or annotation cost, and has recently received lots of research attention. Most existing works focus on extending supervised learning models to solve the LLP problem, but the weak learning nature makes it hard to further improve L…
This work aims to empirically clarify a recently discovered perspective that label smoothing is incompatible with knowledge distillation. We begin by introducing the motivation behind on how this incompatibility is raised, i.e., label smoothing erases relative information between teacher logits. We provide a novel connection on how label smoothing affects distributions of semantically similar and dissimilar classes. Then we propose a metric to quantitatively measure the degree of erased information in sample's representation. After that, we study its one-sidedness and imperfection of the incom…
Raymond and Beverly Sackler School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv 69978, Israel（雷蒙德与贝弗利·萨克勒物理与天文学学院，特拉维夫大学）；École Polytechnique Fédérale de Lausanne (EPFL), Switzerland（洛桑联邦理工学院（EPFL），瑞士）；Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem 9190401, Israel（拉卡姆物理研究所，耶路撒冷希伯来大学）；Selim Benin School of Computer Science and Engineering, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Jerusalem 9190401, Israel（塞利姆·本因计算机科学与工程学院，耶路撒冷希伯来大学）
Recent works reveal that feature or label smoothing lies at the core of Graph Neural Networks (GNNs). Concretely, they show feature smoothing combined with simple linear regression achieves comparable performance with the carefully designed GNNs, and a simple MLP model with label smoothing of its prediction can outperform the vanilla GCN. Though an interesting finding, smoothing has not been well understood, especially regarding how to control the extent of smoothness. Intuitively, too small or too large smoothing iterations may cause under-smoothing or over-smoothing and can lead to sub-optim…
Be Careful What You Smooth For: Label Smoothing Can Be a Privacy Shield but Also a Catalyst for Model Inversion Attacks
Technical University of Darmstadt（达姆施塔特工业大学）；German Research Center for AI (DFKI)（德国人工智能研究中心）；Centre for Cognitive Science of TU Darmstadt（达姆施塔特工业大学认知科学中心）；Hessian Center for AI (hessian.AI)（黑森州人工智能中心）
Carnegie Mellon University（卡内基梅隆大学）；Bosch Center for AI（博世人工智能中心）
Machine learning algorithms are known to be susceptible to data poisoning attacks, where an adversary manipulates the training data to degrade performance of the resulting classifier. In this work, we present a unifying view of randomized smoothing over arbitrary functions, and we leverage this novel characterization to propose a new strategy for building classifiers that are pointwise-certifiably robust to general data poisoning attacks. As a specific instantiation, we utilize our framework to build linear classifiers that are robust to a strong variant of label flipping, where each test exam…
National University of Singapore（新加坡国立大学）；Nanyang Technological University（南洋理工大学）；USC（南加州大学）；The Hong Kong University of Science and Technology（香港科技大学）
Representing a label distribution as a one-hot vector is a common practice in training node classification models. However, the one-hot representation may not adequately reflect the semantic characteristics of a node in different classes, as some nodes may be semantically close to their neighbors in other classes. It would cause over-confidence since the models are encouraged to assign full probabilities when classifying every node. While training models with label smoothing can ease this problem to some degree, it still fails to capture the nodes' semantic characteristics implied by the graph…
University of Padova（帕多瓦大学）；University of Catania（卡塔尼亚大学）
Human capability to anticipate near future from visual observations and non-verbal cues is essential for developing intelligent systems that need to interact with people. Several research areas, such as human-robot interaction (HRI), assisted living or autonomous driving need to foresee future events to avoid crashes or help people. Egocentric scenarios are classic examples where action anticipation is applied due to their numerous applications. Such challenging task demands to capture and model domain's hidden structure to reduce prediction uncertainty. Since multiple actions may equally occu…
ETH Zürich（苏黎世联邦理工学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；ETH AI Center（苏黎世联邦理工学院人工智能中心）
Models that can predict the occurrence of events ahead of time with low false-alarm rates are critical to the acceptance of decision support systems in the medical community. This challenging task is typically treated as a simple binary classification, ignoring temporal dependencies between samples, whereas we propose to exploit this structure. We first introduce a common theoretical framework unifying dynamic survival analysis and early event prediction. Following an analysis of objectives from both fields, we propose Temporal Label Smoothing (TLS), a simpler, yet best-performing method that …
We study Label Smoothing (LS), a widely used regularization technique, in the context of neural learning to rank (L2R) models. LS combines the ground-truth labels with a uniform distribution, encouraging the model to be less confident in its predictions. We analyze the relationship between the non-relevant documents-specifically how they are sampled-and the effectiveness of LS, discussing how LS can be capturing "hidden similarity knowledge" between the relevantand non-relevant document classes. We further analyze LS by testing if a curriculum-learning approach, i.e., starting with LS and afte…
Rice University（莱斯大学）；University of Georgia（佐治亚大学）；Samsung Research America（三星美国研究院）；Samsung Electronics（三星电子）
Graph neural networks (GNNs), which learn the node representations by recursively aggregating information from its neighbors, have become a predominant computational tool in many domains. To handle large-scale graphs, most of the existing methods partition the input graph into multiple sub-graphs (e.g., through node clustering) and apply batch training to save memory cost. However, such batch training will lead to label bias within each batch, and then result in over-confidence in model predictions. Since the connected nodes with positively related labels tend to be assigned together, the trad…
