Open-set Label Noise Can Improve Robustness Against Inherent Label Noise

1 Introduction . The success of deep neural networks ( DNNs ) heavily relies on a large number of training instances with fully accurate labels [ 16 ] . In real-world applications , it is expensive and time-consuming to collect such large-scale datasets . To alleviate this problem , some surrogate methods are commonly used to improve labelling efficiency , such as online queries [ 3 ] and crowdsourcing [ 74 ] . These cheap but imperfect methods usually suffer from unavoidable noisy labels that can be easily memorized by Deep Neural Networks ( DNNs ) , leading to poor generalization performance [ 2 , 79 ] . Therefore , designing robust algorithms against noisy labels is of great practical importance . Label noise can be separated into two categories : 1 ) closed-set noise , where instances with noisy labels have true class labels within the noisy label set [ 15 , 24 , 50 , 51 , 60 , 63 ] . 2 ) open-set noise , where instances with noisy labels have some true class labels outside the noisy label set [ 30 , 54 , 61 , 67 ] . In the existing literature , open-set noises are always considered to be harmful to the training of DNNs like closed-set noises [ 30 , 61 , 54 , 67 ] . For example , ILON [ 61 ] reduces the effect of open-set noises by using noisy label detector and contrastive loss to pull away noisy samples from clean samples . Extended T [ 67 ] uses an extended transition matrix to mitigate the impacts of open-set noises and EvidentialMix [ 54 ] filters out the open-set examples by modelling the loss distribution . Therefore , there arises a question to be answered : Do open-set noises always play a negative role in the training ? ∗Corresponding author . 35th Conference on Neural Information Processing Systems ( NeurIPS 2021 ) . In this work , we answer this question by experiments with an open-set auxiliary dataset . We empirically show that additional open-set noises can be harmless to generalization if the number of open-set noises is sufficiently large . More surprisingly , we observe that the open-set noises can even benefit the robustness of neural networks against noisy labels from the original training dataset , while the closed-set counterpart could not . Based on the “ insufficient capacity ” hypothesis [ 2 ] , an intuitive explanation for this phenomenon is that increasing the number of open-set auxiliary samples slows down the fitting of inherent noises . In other words , fitting open-set label noises consumes extra capacity of the network , thereby reducing the memorization of inherent noisy labels . The details of experimental results are presented in Subsection 2.2 . Inspired by the above observations , we propose an effective and complementary method to improve robustness against noisy labels . The high-level idea is to introduce Open-set samples with Dynamic Noisy Labels ( ODNL ) into training . In each epoch , we assign random labels to instances of open-set auxiliary dataset by uniformly sampling from the label set . In other words , the label of each open-set sample is independently random and is constantly changing over training epochs . In this manner , ODNL consistently produce “ benign hard examples ” to consume the extra representation capacity of neural networks , thereby preventing the neural network from overfitting inherent noisy labels . To further understand the effect of ODNL , we provide an analysis from the lens of SGD noise [ 7 , 65 ] , and formalize the differences and connections between our regularization and related methods . From the analysis , we show that the SGD noises induced by our method are 1 ) random-direction , helping the model converge to a flat minimum ; 2 ) conflict-free , leading to good stability for the training ; 3 ) biased , enforcing the model to produce more conservative predictions on OOD examples . In this manner , our method not only improves the robustness against noisy labels , but also provides benefits for OOD detection performance , which is also essential for the deployment of deep learning in safety-critical applications . To the best of our knowledge , we are the first to explore the benefits of open-set auxiliary dataset in learning with noisy labels . To verify the efficacy of our regularization , we conduct extensive experiments on both simulated and real-world noisy datasets , including CIFAR-10 , CIFAR-100 and Clothing1M datasets . In summary , the proposed method can be easily adapted for a wide range of existing algorithms to prevent overfitting noisy labels . Furthermore , experimental results validate that our regularization could also achieve impressive performance for detecting OOD examples , even if the labels of training dataset are noisy . 2 Problem setting and motivation . In this section , we first briefly introduce the problem setting of learning from training data with noisy labels . Then we start in Subsection 2.2 with an observational study highlighting the effect of open-set noisy examples from the auxiliary dataset on generalization and robustness against noisy labels . 2.1 Preliminaries : learning with inherent noisy labels . In this work , we consider multi-class classification with k classes . Let X ⊂ Rd be the feature space and Y = { 1 , . . . , k } be the label space , we suppose the training dataset with N samples is given as { xi , yi } Ni=1 , where xi ∈ X is the i-th instance sampled from a certain data-generating distribution Dtrain in an i.i.d . manner and yi ∈ { 1 , . . . , k } represents its observed label that might be different from the ground truth . To prevent confusion , the noisy labels in the training dataset are referred to as inherent noisy labels . A classifier is a function that maps the feature space to the label space f : X → Rk with trainable parameter θ ∈ Rp . In this paper , we consider the common case where the function f is a DNN with the softmax output layer . The objective function of standard training can be represented as a cross-entropy loss : LCCE = EDtrain [ ` ( f ( x ; θ ) , y ) ] ' − 1 N N∑ i=1 eyi log f ( xi ; θ ) , ( 1 ) where f ( xi ; θ ) denotes the output of the classifier f with θ for xi and eyi : = ( 0 , . . . , 1 , . . . , 0 ) > ∈ { 0 , 1 } k is a one-hot vector and only the yi-th entry of eyi is 1 . In addition to the training data , we consider there is an unlabelled auxiliary dataset consisting of open-set instances { x̃i } Mi=1 . Specifically , open-set instances are sampled from Dout , disjoint from 50 100 150 200 250 300 . Dtrain . Therefore , they are also called Out-of-Distribution ( OOD ) instances . In real applications , it is easy to get such an auxiliary dataset , which is commonly used in OOD detection tasks [ 20 , 48 ] . 2.2 Motivation : the role of open-set label noise in generalization and robustness . To analyze the effects of open-set noisy labels , we build an open-set noisy dataset with the unlabelled auxiliary dataset . For each open-set instance , we assign a fixed random label ỹi uniformly sampled from the label set { 1 , . . . , k } . In each iteration , we concatenate the two batches that are sampled from the training dataset and the open-set noisy dataset respectively , then perform standard training . In addition , we conduct controlled experiments by replacing the open-set dataset with a closed-set dataset to verify the effectiveness of open-set noisy dataset during the training . To demonstrate the importance of the sample size of the given auxiliary dataset , we compare the performance of training with different-sized auxiliary datasets , built by randomly sampling from the original auxiliary dataset . Throughout this subsection , we perform training with WRN-40-2 [ 77 ] on CIFAR-10 [ 27 ] using standard cross-entropy loss . For experiments under inherent label noise , we use symmetric noise with 40 % noisy rate . For auxiliary dataset , we use 300K Random Images2 [ 20 ] as the open-set auxiliary dataset and CIFAR-5m3 [ 21 , 43 ] as the closed-set auxiliary dataset . Specifically , all images that belong to CIFAR classes are removed in 300K Random Images so that Dtrain and Dout are disjoint . More training details can be found in Appendix B . Learning with clean labels . Fig . 1a presents the results on clean training set of CIFAR-10 , training with the open/closed-set noisy auxiliary dataset . The results show that open-set noisy labels from the auxiliary dataset become harmless gradually with the increase of the sample size of the auxiliary dataset , while closed-set noisy labels consistently deteriorate the generalization performance . Furthermore , we observe that closed-set noisy labels result in unstable training shown by the large standard deviations in the figure . It is worthy to note that open-set noisy labels do not encounter this issue . Learning with inherent noisy labels . Fig . 1b presents the results on CIFAR-10 with inherent noisy labels , training with the open/closed-set noisy auxiliary dataset . Surprisingly , we can observe that as we increase the sample size of the open-set noisy dataset , the open-set noises can even improve the generalization performance beyond standard training without the noisy auxiliary dataset . In this case , closed-set noisy auxiliary dataset still plays a negative role in the training . An intuitive interpretation . From the results , one can hypothesize that open-set noisy labels in the auxiliary dataset would be harmless and can even benefit the robustness against inherent noisy labels , if the sample size of the auxiliary dataset is large enough . This phenomenon is somewhat counter-intuitive since one would expect that open-set noisy labels should have been “ poison ” to the training of network , like closed-set noises [ 30 , 54 , 61 , 67 ] . Here we provide an intuitive interpretation from “ insufficient capacity ” [ 2 ] : increasing the number of examples while keeping representation capacity fixed would increase the time needed to memorize the data set . Hence , the larger the size of auxiliary dataset is , the more time it needs to memorize the open-set noises in the auxiliary dataset as 2The dataset is published on https : //github.com/hendrycks/outlier-exposure . 3The dataset is published on https : //github.com/preetum/cifar5m . well as the inherent noises in the training set , relative to clean data . This interpretation is supported by our plot of training losses of inherent noises with different-sized auxiliary datasets in Fig . 1c , where increasing the number of open-set auxiliary samples slows down the fitting of inherent noises . 3 Method : Open-set regularization with Dynamic Noisy Labels . Motivated by the previous observations , we propose to utilize open-set auxiliary dataset to further improve the robustness against inherent noisy labels . This approach can be considered as an auxiliary task that continuously consumes the extra capacity of neural networks but does not interfere with learning patterns from clean data . Such auxiliary tasks will prevent deep networks from overfitting noisy data . Dynamic Noisy Labels . To maintain the effectiveness of the auxiliary task during training , an ideal method is to use an auxiliary dataset with unlimited instances based on “ insufficient capacity ” [ 2 ] . In this way , the network would always try to fit a stream of new instances sequentially in an online learning setting . However , it is unrealistic to provide such an auxiliary dataset in real scenarios . To relieve the requirement on sample size , we propose an alternative approach called Dynamic Noisy Labels . For each open-set instance x̃i , a noisy label ỹi is uniformly sampled from the label set { 1 , . . . , k } independently , regardless of the instance x̃i . More importantly , the generated labels are not fixed and would be changed dynamically over training epochs . In this way , the auxiliary task becomes an “ impossible mission '' , continuously consuming the extra capacity of network . Without Dynamic Noisy Labels , the effectiveness of the auxiliary task would be degraded gradually during training , because deep network can easily memorize the finite open-set samples , even though the labels of those samples are randomly generated [ 2 , 79 ] . Training Objective . For the original training dataset , we use the standard cross entropy as the training objective function : L1 = EDtrain [ ` ( f ( x ; θ ) , y ) ] = EDtrain [ −ey log f ( x ; θ ) ] , ( 2 ) For the auxiliary dataset , we enforce the outputs to be consistent with dynamic noise labels , uniformly sampled from the label set in each epoch . Therefore , the training objective function is as follows : L2 = EDout [ ` ( f ( x̃ ; θ ) , ỹ ) ] = EDout [ −eỹ log f ( x̃ ; θ ) ] , where ỹ ∼ Uk ( 3 ) where Uk represents a discrete uniform distribution on the label set { 1 , . . . , k } . Combining the original training dataset and the auxiliary dataset in the training , now we can formalize ODNL as minimizing the final objective : Ltotal = L1 + η · L2 = EDtrain [ ` ( f ( x ; θ ) , y ) ] + η · EDout [ ` ( f ( x̃ ; θ ) , ỹ ) ] ( 4 ) where η denotes the trade-off hyperparameter . The details of ODNL are provided in Algorithm 1 . Extensions to Other Robust Training Algorithms . It is worthy to note that our regularization is a general method and can be easily incorporated into existing robust training algorithms , including sample selection [ 15 , 63 ] , loss correction [ 50 ] , robust loss function [ 80 , 62 ] , etc . Given the original learning objective Lrobust of the robust methods and the hyperparameter η , we can formalize the final objective as : Ltotal = Lrobust + η · L2 ( 5 )

Summary: This paper empirically shows that open-set noisy labels can benefit the robustness against inherent noisy labels in the training data, and proposes a simple but effective regularization method through introducing open-set data with Dynamic Noisy Labels (ODNL) into the training process. Specifically, the ODNL utilizes the open-set data with randomly generated labels in training, to exploit the extra capacity of neural networks, and thus makes the network avoid the memorization of noises in training data. The model trained with ODNL can achieve a better capability on Out-of-Distribution detection tasks. Extensive experiments show the effectiveness of the proposed method.