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 two truth labels while further soften that between the truth labels and the other targets, resulting in models producing much less confident predictions than the LS strategy. Also, unlike current LS methods, which typically require to find a global smoothing distribution mass through cross-validation search, PLS automatically learns the distribution mass for each input pair during training. We empirically show that PLS significantly outperforms LS and the baseline models, achieving up to 30% of relative classification error reduction. We also visually show that when achieving such accuracy gains the PLS tends to produce very low winning softmax scores.
We present a meta-method for initializing (seeding) the $k$-means clustering algorithm called PNN-smoothing. It consists in splitting a given dataset into $J$ random subsets, clustering each of them individually, and merging the resulting clusterings with the pairwise-nearest-neighbor (PNN) method. It is a meta-method in the sense that when clustering the individual subsets any seeding algorithm can be used. If the computational complexity of that seeding algorithm is linear in the size of the data $N$ and the number of clusters $k$, PNN-smoothing is also almost linear with an appropriate choi…
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 regio…
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））
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…
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…
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…
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…
Transfer learning methods address the situation where little labeled training data from the "target" problem exists, but much training data from a related "source" domain is available. However, the overwhelming majority of transfer learning methods are designed for simple settings where the source and target predictive functions are almost identical, limiting the applicability of transfer learning methods to real world data. We propose a novel, weaker, property of the source domain that can be transferred even when the source and target predictive functions diverge. Our method assumes the sour…
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）
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…
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…
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…
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）
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…
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）
We propose local distributional smoothness (LDS), a new notion of smoothness for statistical model that can be used as a regularization term to promote the smoothness of the model distribution. We named the LDS based regularization as virtual adversarial training (VAT). The LDS of a model at an input datapoint is defined as the KL-divergence based robustness of the model distribution against local perturbation around the datapoint. VAT resembles adversarial training, but distinguishes itself in that it determines the adversarial direction from the model distribution alone without using the lab…
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…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Oversmoothing has been assumed to be the major cause of performance drop in deep graph convolutional networks (GCNs). In this paper, we propose a new view that deep GCNs can actually learn to anti-oversmooth during training. This work interprets a standard GCN architecture as layerwise integration of a Multi-layer Perceptron (MLP) and graph regularization. We analyze and conclude that before training, the final representation of a deep GCN does over-smooth, however, it learns anti-oversmoothing during training. Based on the conclusion, the paper further designs a cheap but effective trick to i…
Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via $L_2$ regularization. Multiple GAMs allow finer statistical inference by incorporating explanatory information in any or all of the parameters of the distribution. Owing to their nonlinearity, flexibility and interpretability, GAMs are widely used, but reliable and fast methods for automatic smoothing in large datasets are still lacking, despite recent advances. We develo…
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…
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…
MIT Computer Science & Artificial Intelligence Lab（麻省理工学院计算机科学与人工智能实验室）
Adversarial training methods typically align distributions by solving two-player games. However, in most current formulations, even if the generator aligns perfectly with data, a sub-optimal discriminator can still drive the two apart. Absent additional regularization, the instability can manifest itself as a never-ending game. In this paper, we introduce a family of objectives by leveraging pairwise discriminators, and show that only the generator needs to converge. The alignment, if achieved, would be preserved with any discriminator. We provide sufficient conditions for local convergence; c…
Label Smoothing (LS) improves model generalization through penalizing models from generating overconfident output distributions. 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. We extend this technique by considering example pairs, coined PLS. PLS first creates midpoint samples by averaging random sample pairs and then learns a smoothing distribution during training for each of these midpoint samples, resulting in midpoints with high uncertainty labels for training. We empirically show…
Texas A&M University（德克萨斯A&M大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning them as model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. …
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…
LABO: Towards Learning Optimal Label Regularization via Bi-level Optimization
Department of Computer Science and Operations Research, Université de Montréal（蒙特利尔大学计算机科学与运筹学系）；Huawei Noah’s Ark Lab, Canada（华为诺亚实验室，加拿大）；Department of Statistics and Actuarial Science, University of Waterloo（滑铁卢大学统计与精算科学系）
Department of Genetics, Stanford University, CA, USA（遗传学系，斯坦福大学，加州，美国）；Department of Computer Science, Texas A\&M University, TX, USA（计算机科学系，德克萨斯A&M大学，德克萨斯州，美国）
MaxSup: Overcoming Representation Collapse in Label Smoothing
University of Mannheim（曼海姆大学）；University of Washington（华盛顿大学）；Meta AI；CISPA Helmholtz Center for Information Security（信息安全霍普夫研究所）；Max Planck Institute for Informatics（马克斯·普朗克信息研究所）
Simon Fraser University（西蒙弗雷泽大学）；Borealis AI（Borealis人工智能研究院）
Data imbalance, in which a plurality of the data samples come from a small proportion of labels, poses a challenge in training deep neural networks. Unlike classification, in regression the labels are continuous, potentially boundless, and form a natural ordering. These distinct features of regression call for new techniques that leverage the additional information encoded in label-space relationships. This paper presents the RankSim (ranking similarity) regularizer for deep imbalanced regression, which encodes an inductive bias that samples that are closer in label space should also be closer…
Label noise presents a real challenge for supervised learning algorithms. Consequently, mitigating label noise has attracted immense research in recent years. Noise robust losses is one of the more promising approaches for dealing with label noise, as these methods only require changing the loss function and do not require changing the design of the classifier itself, which can be expensive in terms of development time. In this work we focus on losses that use output regularization (such as label smoothing and entropy). Although these losses perform well in practice, their ability to mitigate …
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）
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…
