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 proposed a training method for improving the robustness of deep neural networks against inherent label noise. Specifically, the authors first found that the open-set noise is helpful for the generalization and robustness of a deep neural network, and then proposed the strategy that use an additional training set with open-set noise as the regularization in the training objective. Experiments showed improved performance by the proposed method against inherent label noise.