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 and update the optimal label representation online. On the other hand, compared with knowledge distillation, which learns the correlation of categories using teacher network, our proposed method requires only a minuscule increase in parameters without cumbersome teacher network. Furthermore, we evaluate our method on CIFAR-10/CIFAR-100/ImageNet datasets for image recognition tasks and AGNews/Yahoo/Yelp-Full datasets for text classification tasks. The empirical results show significant improvement under all experimental settings.
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…
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…
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…
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…
Among the most successful methods for sparsifying deep (neural) networks are those that adaptively mask the network weights throughout training. By examining this masking, or dropout, in the linear case, we uncover a duality between such adaptive methods and regularization through the so-called "$η$-trick" that casts both as iteratively reweighted optimizations. We show that any dropout strategy that adapts to the weights in a monotonic way corresponds to an effective subquadratic regularization penalty, and therefore leads to sparse solutions. We obtain the effective penalties for several pop…
We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient is a system intrinsic data-adaptive (SIDA) RKHS, whose norm restricts the learning to take place in the function space of identifiability. DARTR utilizes this norm and selects the regularization parameter by the L-curve method. We illustrate its performance in examples including integral operators, nonlinear operators and nonlocal operators with discrete synthetic data. Numerical results show that DARTR leads to an …
Consistency regularization on label predictions becomes a fundamental technique in semi-supervised learning, but it still requires a large number of training iterations for high performance. In this study, we analyze that the consistency regularization restricts the propagation of labeling information due to the exclusion of samples with unconfident pseudo-labels in the model updates. Then, we propose contrastive regularization to improve both efficiency and accuracy of the consistency regularization by well-clustered features of unlabeled data. In specific, after strongly augmented samples ar…
Deep neural networks (DNNs) exhibit great success on many tasks with the help of large-scale well annotated datasets. However, labeling large-scale data can be very costly and error-prone so that it is difficult to guarantee the annotation quality (i.e., having noisy labels). Training on these noisy labeled datasets may adversely deteriorate their generalization performance. Existing methods either rely on complex training stage division or bring too much computation for marginal performance improvement. In this paper, we propose a Temporal Calibrated Regularization (TCR), in which we utilize …
Laval University（拉瓦尔大学）；INRIA（法国国家信息与自动化研究所）；McGill University（麦吉尔大学）
We consider the problem of streaming kernel regression, when the observations arrive sequentially and the goal is to recover the underlying mean function, assumed to belong to an RKHS. The variance of the noise is not assumed to be known. In this context, we tackle the problem of tuning the regularization parameter adaptively at each time step, while maintaining tight confidence bounds estimates on the value of the mean function at each point. To this end, we first generalize existing results for finite-dimensional linear regression with fixed regularization and known variance to the kernel se…
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…
Academy for Advanced Interdisciplinary Studies, Peking University（北京大学前沿交叉学科研究院）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）
Regularized MDPs serve as a smooth version of original MDPs. However, biased optimal policy always exists for regularized MDPs. Instead of making the coefficientλof regularized term sufficiently small, we propose an adaptive reduction scheme for λ to approximate optimal policy of the original MDP. It is shown that the iteration complexity for obtaining anε-optimal policy could be reduced in comparison with setting sufficiently smallλ. In addition, there exists strong duality connection between the reduction method and solving the original MDP directly, from which we can derive more adaptive re…
On Regularization and Inference with Label Constraints
University of Pennsylvania（宾夕法尼亚大学）；University of Rochester（罗切斯特大学）；Massachusetts Institute of Technology（麻省理工学院）；Systems and Technology Research（系统与技术研究公司）
We propose a novel regularization-based continual learning method, dubbed as Adaptive Group Sparsity based Continual Learning (AGS-CL), using two group sparsity-based penalties. Our method selectively employs the two penalties when learning each node based its the importance, which is adaptively updated after learning each new task. By utilizing the proximal gradient descent method for learning, the exact sparsity and freezing of the model is guaranteed, and thus, the learner can explicitly control the model capacity as the learning continues. Furthermore, as a critical detail, we re-initializ…
Stony Brook University（石溪大学）；Tencent AI Lab（腾讯人工智能实验室）
Multi-task learning (MTL) is a common paradigm that seeks to improve the generalization performance of task learning by training related tasks simultaneously. However, it is still a challenging problem to search the flexible and accurate architecture that can be shared among multiple tasks. In this paper, we propose a novel deep learning model called Task Adaptive Activation Network (TAAN) that can automatically learn the optimal network architecture for MTL. The main principle of TAAN is to derive flexible activation functions for different tasks from the data with other parameters of the net…
U.S. Naval Academy（美国海军学院）；Naval Research Laboratory（海军研究实验室）
Many classification problems involve data instances that are interlinked with each other, such as webpages connected by hyperlinks. Techniques for "collective classification" (CC) often increase accuracy for such data graphs, but usually require a fully-labeled training graph. In contrast, we examine how to improve the semi-supervised learning of CC models when given only a sparsely-labeled graph, a common situation. We first describe how to use novel combinations of classifiers to exploit the different characteristics of the relational features vs. the non-relational features. We also extend …
Stanford University（斯坦福大学）；Harvard University（哈佛大学）；Toyota Research Institute（丰田研究所）
Real-world large-scale datasets are heteroskedastic and imbalanced -- labels have varying levels of uncertainty and label distributions are long-tailed. Heteroskedasticity and imbalance challenge deep learning algorithms due to the difficulty of distinguishing among mislabeled, ambiguous, and rare examples. Addressing heteroskedasticity and imbalance simultaneously is under-explored. We propose a data-dependent regularization technique for heteroskedastic datasets that regularizes different regions of the input space differently. Inspired by the theoretical derivation of the optimal regulariza…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）
Many weakly supervised classification methods employ a noise transition matrix to capture the class-conditional label corruption. To estimate the transition matrix from noisy data, existing methods often need to estimate the noisy class-posterior, which could be unreliable due to the overconfidence of neural networks. In this work, we propose a theoretically grounded method that can estimate the noise transition matrix and learn a classifier simultaneously, without relying on the error-prone noisy class-posterior estimation. Concretely, inspired by the characteristics of the stochastic label c…
Gatsby Computational Neuroscience Unit, UCL（伦敦大学学院盖茨比计算神经科学单元）；Department of Mathematics, Imperial College London（伦敦帝国理工学院数学系）；WMG, University of Warwick（华威大学制造工程学院）
Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning $\ell_1$ regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parameter when data arrives sequentially and the underlying distribution is non-stationary (implying the choice of optimal regularization parameter is itself time-varying). We propose a framework through…
University Bretagne Sud（布列塔尼南部大学）；CNRS（法国国家科学研究中心）；INRIA（法国国家信息与自动化研究所）；IRISA（法国信息与自动化系统研究所）；InterDigital R&D（InterDigital研发中心）；Université de Paris（巴黎大学）；Wageningen University（瓦赫宁根大学）；École Polytechnique（巴黎综合理工学院）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Noisy labels often occur in vision datasets, especially when they are obtained from crowdsourcing or Web scraping. We propose a new regularization method, which enables learning robust classifiers in presence of noisy data. To achieve this goal, we propose a new adversarial regularization scheme based on the Wasserstein distance. Using this distance allows taking into account specific relations between classes by leveraging the geometric properties of the labels space. Our Wasserstein Adversarial Regularization (WAR) encodes a selective regularization, which promotes smoothness of the classifi…
Carnegie Mellon University（卡内基梅隆大学）；Microsoft Research Montreal（蒙特利尔微软研究院）
Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing an adaptive and data-dependent regularization motivated by the empirical Bayes method. Specifically, we propose to construct a matrix-variate normal prior (on weights) whose covariance matrix has a Kronecker product structure. This structure is designed to capture the correlations in neurons through backpropagation. Under the assumption of this Kronecker fac…
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…
The main goal of this work is equipping convex and nonconvex problems with Barzilai-Borwein (BB) step size. With the adaptivity of BB step sizes granted, they can fail when the objective function is not strongly convex. To overcome this challenge, the key idea here is to bridge (non)convex problems and strongly convex ones via regularization. The proposed regularization schemes are \textit{simple} yet effective. Wedding the BB step size with a variance reduction method, known as SARAH, offers a free lunch compared with vanilla SARAH in convex problems. The convergence of BB step sizes in nonco…
Partial Label Learning (PLL) aims to learn from the data where each training instance is associated with a set of candidate labels, among which only one is correct. Most existing methods deal with such problem by either treating each candidate label equally or identifying the ground-truth label iteratively. In this paper, we propose a novel PLL approach called HERA, which simultaneously incorporates the HeterogEneous Loss and the SpaRse and Low-rAnk procedure to estimate the labeling confidence for each instance while training the model. Specifically, the heterogeneous loss integrates the stre…
Google AI Princeton（谷歌AI普林斯顿）；Toyota Technological Institute at Chicago（丰田工业大学芝加哥分校）；Princeton University（普林斯顿大学）；Microsoft Research（微软研究院）
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how to modify full-matrix adaptive regularization in order to make it practical and effective. We also provide a novel theoretical analysis for adaptive regularization in non-convex optimization settings. The core of our algorithm, termed GGT, consists of the efficient computation of the inverse square root of a low-rank matrix. Our preliminary experiments show i…
Hangzhou Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Beihang University（北京航空航天大学）；University of Ottawa（渥太华大学）
Recent researches have suggested that the predictive accuracy of neural network may contend with its adversarial robustness. This presents challenges in designing effective regularization schemes that also provide strong adversarial robustness. Revisiting Vicinal Risk Minimization (VRM) as a unifying regularization principle, we propose Adversarial Labelling of Perturbed Samples (ALPS) as a regularization scheme that aims at improving the generalization ability and adversarial robustness of the trained model. ALPS trains neural networks with synthetic samples formed by perturbing each authenti…
We describe a framework for deriving and analyzing online optimization algorithms that incorporate adaptive, data-dependent regularization, also termed preconditioning. Such algorithms have been proven useful in stochastic optimization by reshaping the gradients according to the geometry of the data. Our framework captures and unifies much of the existing literature on adaptive online methods, including the AdaGrad and Online Newton Step algorithms as well as their diagonal versions. As a result, we obtain new convergence proofs for these algorithms that are substantially simpler than previous…
Sichuan University（四川大学）；Rutgers University – New Brunswick（罗格斯大学新不伦瑞克分校）；Zhejiang University（浙江大学）；Tennessee State University（田纳西州立大学）
The dynamic ensemble selection of classifiers is an effective approach for processing label-imbalanced data classifications. However, such a technique is prone to overfitting, owing to the lack of regularization methods and the dependence of the aforementioned technique on local geometry. In this study, focusing on binary imbalanced data classification, a novel dynamic ensemble method, namely adaptive ensemble of classifiers with regularization (AER), is proposed, to overcome the stated limitations. The method solves the overfitting problem through implicit regularization. Specifically, it lev…
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…
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 …
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…
Over-parameterized deep neural networks trained by simple first-order methods are known to be able to fit any labeling of data. Such over-fitting ability hinders generalization when mislabeled training examples are present. On the other hand, simple regularization methods like early-stopping can often achieve highly nontrivial performance on clean test data in these scenarios, a phenomenon not theoretically understood. This paper proposes and analyzes two simple and intuitive regularization methods: (i) regularization by the distance between the network parameters to initialization, and (ii) a…
Dropout and other feature noising schemes control overfitting by artificially corrupting the training data. For generalized linear models, dropout performs a form of adaptive regularization. Using this viewpoint, we show that the dropout regularizer is first-order equivalent to an L2 regularizer applied after scaling the features by an estimate of the inverse diagonal Fisher information matrix. We also establish a connection to AdaGrad, an online learning algorithm, and find that a close relative of AdaGrad operates by repeatedly solving linear dropout-regularized problems. By casting dropout …
We propose an AdaPtive Noise Augmentation (PANDA) technique to regularize the estimation and construction of undirected graphical models. PANDA iteratively optimizes the objective function given the noise augmented data until convergence to achieve regularization on model parameters. The augmented noises can be designed to achieve various regularization effects on graph estimation, such as the bridge (including lasso and ridge), elastic net, adaptive lasso, and SCAD penalization; it also realizes the group lasso and fused ridge. We examine the tail bound of the noise-augmented loss function an…
Consistency regularization is a commonly-used technique for semi-supervised and self-supervised learning. It is an auxiliary objective function that encourages the prediction of the network to be similar in the vicinity of the observed training samples. Hendrycks et al. (2020) have recently shown such regularization naturally brings test-time robustness to corrupted data and helps with calibration. This paper empirically studies the relevance of consistency regularization for training-time robustness to noisy labels. First, we make two interesting and useful observations regarding the consiste…
We introduce a new neural network-based continual learning algorithm, dubbed as Uncertainty-regularized Continual Learning (UCL), which builds on traditional Bayesian online learning framework with variational inference. We focus on two significant drawbacks of the recently proposed regularization-based methods: a) considerable additional memory cost for determining the per-weight regularization strengths and b) the absence of gracefully forgetting scheme, which can prevent performance degradation in learning new tasks. In this paper, we show UCL can solve these two problems by introducing a f…
School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）；NLPR, Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所模式识别国家重点实验室）
Partial-label learning (PLL) is an important branch of weakly supervised learning where the single ground truth resides in a set of candidate labels, while the research rarely considers the label imbalance. A recent study for imbalanced partial-Label learning proposed that the combinatorial challenge of partial-label learning and long-tail learning lies in matching between a decent marginal prior distribution with drawing the pseudo labels. However, we believe that even if the pseudo label matches the prior distribution, the tail classes will still be difficult to learn because the total weigh…
Partial label learning (PLL) aims to solve the problem where each training instance is associated with a set of candidate labels, one of which is the correct label. Most PLL algorithms try to disambiguate the candidate label set, by either simply treating each candidate label equally or iteratively identifying the true label. Nonetheless, existing algorithms usually treat all labels and instances equally, and the complexities of both labels and instances are not taken into consideration during the learning stage. Inspired by the successful application of self-paced learning strategy in machine…
Chung-Ang University（中央大学）；University of California Los Angeles（加州大学洛杉矶分校）
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 emp…
Large datasets often have unreliable labels-such as those obtained from Amazon's Mechanical Turk or social media platforms-and classifiers trained on mislabeled datasets often exhibit poor performance. We present a simple, effective technique for accounting for label noise when training deep neural networks. We augment a standard deep network with a softmax layer that models the label noise statistics. Then, we train the deep network and noise model jointly via end-to-end stochastic gradient descent on the (perhaps mislabeled) dataset. The augmented model is overdetermined, so in order to enco…
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；McGill University（麦吉尔大学）；Université de Montréal（蒙特利尔大学）
It is common in computer vision to be confronted with domain shift: images which have the same class but different acquisition conditions. In domain adaptation (DA), one wants to classify unlabeled target images using source labeled images. Unfortunately, deep neural networks trained on a source training set perform poorly on target images which do not belong to the training domain. One strategy to improve these performances is to align the source and target image distributions in an embedded space using optimal transport (OT). However OT can cause negative transfer, i.e. aligning samples with…
This paper addresses image classification through learning a compact and discriminative dictionary efficiently. Given a structured dictionary with each atom (columns in the dictionary matrix) related to some label, we propose cross-label suppression constraint to enlarge the difference among representations for different classes. Meanwhile, we introduce group regularization to enforce representations to preserve label properties of original samples, meaning the representations for the same class are encouraged to be similar. Upon the cross-label suppression, we don't resort to frequently-used …
New York University（纽约大学）；NYU School of Medicine（纽约大学医学院）
We propose a novel framework to perform classification via deep learning in the presence of noisy annotations. When trained on noisy labels, deep neural networks have been observed to first fit the training data with clean labels during an "early learning" phase, before eventually memorizing the examples with false labels. We prove that early learning and memorization are fundamental phenomena in high-dimensional classification tasks, even in simple linear models, and give a theoretical explanation in this setting. Motivated by these findings, we develop a new technique for noisy classificatio…
We propose \textit{Meta-Regularization}, a novel approach for the adaptive choice of the learning rate in first-order gradient descent methods. Our approach modifies the objective function by adding a regularization term on the learning rate, and casts the joint updating process of parameters and learning rates into a maxmin problem. Given any regularization term, our approach facilitates the generation of practical algorithms. When \textit{Meta-Regularization} takes the $φ$-divergence as a regularizer, the resulting algorithms exhibit comparable theoretical convergence performance with other …
Peking University（北京大学）；University of Technology, Sydney（悉尼科技大学）；Nanyang Technological University（南洋理工大学）
In computer vision, image datasets used for classification are naturally associated with multiple labels and comprised of multiple views, because each image may contain several objects (e.g. pedestrian, bicycle and tree) and is properly characterized by multiple visual features (e.g. color, texture and shape). Currently available tools ignore either the label relationship or the view complementary. Motivated by the success of the vector-valued function that constructs matrix-valued kernels to explore the multi-label structure in the output space, we introduce multi-view vector-valued manifold …
Deep Learning with noisy labels is a practically challenging problem in weakly supervised learning. The state-of-the-art approaches "Decoupling" and "Co-teaching+" claim that the "disagreement" strategy is crucial for alleviating the problem of learning with noisy labels. In this paper, we start from a different perspective and propose a robust learning paradigm called JoCoR, which aims to reduce the diversity of two networks during training. Specifically, we first use two networks to make predictions on the same mini-batch data and calculate a joint loss with Co-Regularization for each traini…
Stanford University（斯坦福大学）；Meituan-Dianping Group（美团点评集团）；Hong Kong Polytechnic University（香港理工大学）
Knowledge graphs capture structured information and relations between a set of entities or items. As such knowledge graphs represent an attractive source of information that could help improve recommender systems. However, existing approaches in this domain rely on manual feature engineering and do not allow for an end-to-end training. Here we propose Knowledge-aware Graph Neural Networks with Label Smoothness regularization (KGNN-LS) to provide better recommendations. Conceptually, our approach computes user-specific item embeddings by first applying a trainable function that identifies impor…
Institute of Computer Science（计算机科学研究所）；University of Hildesheim（希尔德斯海姆大学）
Diverse regularization techniques have been developed such as L2 regularization, Dropout, DisturbLabel (DL) to prevent overfitting. DL, a newcomer on the scene, regularizes the loss layer by flipping a small share of the target labels at random and training the neural network on this distorted data so as to not learn the training data. It is observed that high confidence labels during training cause the overfitting problem and DL selects disturb labels at random regardless of the confidence of labels. To solve this shortcoming of DL, we propose Directional DisturbLabel (DDL) a novel regulariza…
Pennsylvania State University（宾夕法尼亚州立大学）；Sant’Anna School of Advanced Studies（圣安娜高等研究院）
In this paper we propose $ε$-Consistent Mixup ($ε$mu). $ε$mu is a data-based structural regularization technique that combines Mixup's linear interpolation with consistency regularization in the Mixup direction, by compelling a simple adaptive tradeoff between the two. This learnable combination of consistency and interpolation induces a more flexible structure on the evolution of the response across the feature space and is shown to improve semi-supervised classification accuracy on the SVHN and CIFAR10 benchmark datasets, yielding the largest gains in the most challenging low label-availabil…
