L2B: Learning to Bootstrap for Combating Label Noise
Authors: Yuyin Zhou
Xianhang Li
Fengze Liu
Xuxi Chen
Lequan Yu
Cihang Xie
Matthew P. Lungren
Lei Xing
Venue: Submitted to ICLR 2023 (2023)
Keywords: learning with noisy labels
bootstrapping
meta-learning
medical image analysis

Abstract: Deep neural networks are powerful tools for representation learning, but can easily overfit to noisy labels which are prevalent in many real-world scenarios. Generally, noisy supervision could stem from variation among labelers, label corruption by adversaries, etc. To combat such label noises, one popular line of approach is to apply customized weights to the training instances, so that the corrupted examples contribute less to the model learning. However, such learning mechanisms potentially erase important information about the data distribution and therefore yield suboptimal results. To leverage useful information from the corrupted instances, an alternative is the bootstrapping loss, which reconstructs new training targets on-the-fly by reweighting the real labels and the network's own predictions (i.e., pseudo labels).
In this paper, we propose a more generic learnable loss objective which enables a joint reweighting of instances and labels at once. Specifically, our method dynamically adjusts the $\textit{per-sample importance weight}$ between the real observed labels and pseudo-labels, where the weights are efficiently determined in a meta process. Compared to the previous instance reweighting methods, our approach concurrently conducts implicit relabeling, and thereby yields substantial improvements with almost no extra cost. Extensive experimental results demonstrated the strengths of our approach over existing methods on multiple natural and medical image benchmark datasets, including CIFAR-10, CIFAR-100, ISIC2019 and Clothing 1M. Code will be made publicly available.

Under review as a conference paper at ICLR 2023
L2B: LEARNING TO BOOTSTRAP FOR COMBATING LABEL NOISE
Anonymous authors Paper under double-blind review
ABSTRACT
Deep neural networks are powerful tools for representation learning, but can easily overfit noisy labels which are prevalent in many real-world scenarios. Gener- ally, noisy supervision could stem from variation among labelers, label corruption by adversaries, etc. To combat such label noises, one popular line of approach apply customized weights to the training instances, so that the corrupted examples contribute less to the model learning. However, such learning mechanisms poten- tially erase important information about the data distribution and therefore yield suboptimal results. To leverage useful information from the corrupted instances, alternative is the bootstrapping loss, which reconstructs new training targets on-the-fly by incorporating the network's own predictions (i.e, pseudo-labels).
In this paper, we propose a more generic learnable loss objective which enables joint reweighting of instances and labels at once. Specifically, our method dy- namically adjusts the per-sample importance weight between the real observed labels and pseudo-labels, where the weights are efficiently determined in a meta process. Compared to the previous instance reweighting methods, our approach concurrently conducts implicit relabeling, and thereby yield substantial improve- ments with almost no extra cost. Extensive experimental results demonstrated the strengths of our approach over existing methods on multiple natural and medi- cal image benchmark datasets, including CIFAR-10, CIFAR-100, ISIC2019 and Clothing IM. Code will be made publicly available.
INTRODUCTION
Recent advances in deep learning have achieved great success on various computer vision appli- cations, where large-scale clean datasets are available. However, noisy labels or intentional label corruption by adversarial rival could easily cause dramatic performance drop (Nettleton et al.) 2010). This problem even more crucial in the medical field, given that the annotation quality requires great expertise. Therefore, understanding. modeling, and learning with noisy labels has gained great momentum in recent research efforts (Frénay & Verleysen 2013 Natarajan et al. 2013
Han al. 2019 Li et al. [2099]]]] Liu et al. 22200: Jiang et 2018 Ren al. 2018 Xue al.
2019
Li et al. 2020; Wang et al., 2020: Zheng et al. 2021 Yao et al. 202 Zhu et al. 202
Wu et al.
202
Zhou
(021).
Existing methods of learning with noisy labels primarily take a loss correction strategy. One popu- lar direction is first estimate the noise corruption matrix and then use it correct the loss func- tion PPttrin et al. 2017 Goldberger & Reuven 2017). However, correctly estimating the noise corruption matrix is usually challenging and often involves assumptions about the noise generation process (Xia et al.] 2019 Liu & Tao, 2015 Hendrycks et al. 2018). Other research efforts focus
on selecting clean samples from the noisy data (Jiang et al.] 2018 Han et al., 2018 Yu et al. 2019 Fang et al.) 2020) by treating samples with small loss as clean ones (Arpit al. 2017). Instead of directly discarding those "unclean" examples, an extension of this idea is focusing on assigning leamable weights to each example in the noisy training set (Ren al., 2018 Shu et al. 2019). where noisy samples have low weights. However, discarding or attending less to a subset of the training data (e.g., noisy samples) can erase important information about the data distribution.
To fully exploit the corrupted training samples, another direction is to leverage the network predic- tions (i.e., laeudo (Lee al. (013)) correct reweight the original labels (Reed et al.

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2014 Tanaka et al. 2018), that the holistic data distribution information could be preserved during network training. One representative work is the bootstrapping loss (Reed et al.) 2014). which introduces perceptual consistency term in the learning objective that assigns weight to the pseudo-labels to compensate for the erroneous guiding of noisy samples. While in this strategy, the weight for the pseudo-labels is manually selected and remains the same for all training sam- ples, which does not prevent fitting the noisy ones and can even lead to low-quality label correction (Arazo al., 2019). To tackle this challenge, Arazo et al. (Arazo al. 2019) designed dynamic bootstrapping strategy to adjusts the label weight by fitting a mixture model. Instead of separately reweighting labels or instances, in this paper, we propose more generic learning strategy to enable joint instance and label reweighting. We term our method as Learning to Bootstrap (L2B), where we aim to leverage the learner's own predictions to bootstrap itself up for combating label noise from meta-learning perspective.
During each training iteration, L,2B learns to dynamically re-balance the importance between the real observed labels and pseudo-labels, where the per-sample weights are determined by the validation performance on a separated clean set in a meta network. Unlike the bootstrapping loss used in (Reed et al. 2014; Arazo et al. 2019; Zhang al. 2020) which explicitly conducts relabeling by taking a weighted sum of the pseudo- and the real label, L2B reweights the two losses associated with the pseudo- and the real label instead (where the weights need not be summed as 1). In addition, we theoretically prove that our formulation, which reweights different loss terms, can be reduced to the original bootstrapping loss and therefore conducts an implicit relabeling instead. By learning these weights in meta-process, our L2B yields substantial improvement (c.g..+8.99 % improvement on CIFAR-I00 with 50% noise) compared with the instance reweighting baseline with almost no extra cost. We conduct extensive experiments CIFAR- 100, and Clothing 1M) and medical image dataset (i.e., ISIC2019), under different types of simulated noise and real-world noise. Our method outperforms various existing explicit label correction and instance reweighting works, demonstrating the strengths our approach.
+8.9
public natural image datasets (i.e., CIFAR-10,
Our main contributions are as follows:
We propose a generic learnable loss objective which enables a joint instance and label reweighting, for combating label noise in deep learning models.
We prove that our new objective is, in fact, a more general form of the bootstrapping loss, and propose L2B to efficiently solve for the weights in meta-learning framework.
Compared with previous instance re-weighting methods, L2B exploits noisy examples more effectively without discarding them by jointly re- b-balnncing the contribution of real and pseudo labels.
We show the theoretical convergence guarantees for L2B, and superior results natural and medical image recognition tasks under both synthetic and real-world noise.
2 RELATED WORKS
Learning through explicit relabeling. To effectively handle noisy supervision, many works pro- pose to directly correct the training labels through estimating the noise transition matrix (Xia et al.) 2019 Yao et al. 2020 Goldberger & Ben- Reuven
2017| Patrini et al.) (017) modeling noise by graph models or neural networks (Xiao et al. 2015 Vahdat 2017 Veit et al. 2017] Lee et al.) 2018). Patrini et al. (Patrini et al. 2017) estimate the label corruption matrix directly correct the loss func- tion. Hendrycks et al. (Hendrycks et al. 2018) further propose to improve the corruption matrix by using a clean set of data, which then enables training a corrected classifier. However, these meth- ods usually require assumptions about noise modeling. For instance, Hendrycks et al. (Hendrycks) jet al.,, 2018) assume that the noisy label is only dependent on the true label and independent of the data. Another line of approaches proposes to leverage the network prediction for explicit relabeling. Some methods (Tanaka et al., 2018 Yi & Wu 2019) relabel the samples by directly using pseudo- labels in an iterative manner. Han et al. use generated prototypes pseudo-labels to be more noise tolerant (Han et al. 2019). Instead of assigning the pseudo-labed as supervision, Reed et al. (Reed et al. 2014) propose to generate new training targets by convex combination of the real and pseudo labels. In a recent study, Ortego et al. (Ortego et al.) (00T)) directly apply this strategy for classifica- tion refinement, and combine with contrastive learning for training noise-robust models. However,
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using fixed weight for all samples does not prevent fitting the noisy ones could even limit the label correction. To tackle this challenge, Arazo et al. propose a dynamic bootstrapping strategy, which calculates sample weights by modeling per-sample loss with beta mixture model (Arazo et al. 2019). Zhang et al. further propose to learn this weight in a meta step, and combine semi-supervised learning for furthering the performance (Zhang et al. 2020).
Instance reweighting, To reduce the negative effect of corrupted examples, many research ef- forts have also been dedicated to selecting or reweighting training instances so that noisy samples contribute less to the loss (Jiang et al. 2018 Ren et al. 2018 Fang et al. 2020). Based on the observation deep neural networks tend to learn simple patterns first before fitting label noise (Arpit et al. (017), many methods treat samples with small loss as clean ones (Jiang al. 2018 Shen & Sanghavi 2019; Han et al. 2018 Yu et al., 2019] Wei et al. 2020). Among those methods, Co-teaching (Han et al. 2018) and Co-teaching- (Yu et al. 2019) train two networks where each network selects loall-loss samples in a mini-batch to train the other. Li et al. (Li et al., 2020) further propose incorporate semi-supervised learning techniques to better leverage the noisy amples. Jiang et al. (Jiang et al.) 2018) propose to use curriculum learning to improve convergence and generalization by ordering instances. Rather than directly selecting clean examples for training. meta-Icarning based instance reweighting methods are also gaining momentum recently (Ren et al., 2018 Shu et al.) 2019 Xu et al.) 2021). In these methods, the example weights and the network parameters are updated in a bi-level optimization to determine the contribution of each training sam- ple. This line of approach has also been successfully applied for robust medical image analysis (Xue
et al. 2019 Mirikharaji et al. (019)).
Different from the aforementioned approaches which separately handle instance reweighting and label reweighting, we propose a new general learning objective to simultaneously adjust the per- sample loss weight while implicitly relabeling the training samples.
METHODOLOGY
3.1 PRELIMINARY
Given set of N training samples, i.c., Dira- [II, M)li I.... N). where 2; E RWxH denotes the i-th image and y, is the observed noisy label. In this work, we also assume that there a small unbiased and clean validation set Deat {xx vi denote the neural network model parameterized by A. Given input-target pair (I, y). we consider the loss function of L(F(x, f), y) (e.g.. cross- entropy loss) to minimize during the training process. Our goal, in this paper, is to properly utilize the small validation set Drat guide the model training on Drras for reducing the negative effects brought by the noisy annotation.
M) and M < N, where the
superscript v denotes the validation set. Let
To establish a more robust training procedure, Reed et al. proposed the bootstrapping loss (Reed) et al., (2014) to enable the learner to "disagree" with the original training label, and effectively re- label the data during the training- Specifically, the training targets will be generated using a convex combination of training labels and predictions of the current model (i.e., pseudo-labele (Lee et al.) 2)13)), for purifying the training labels. Therefore, for L-class classification problem, the loss function for optimizing 0 can be derived as follows:
U peeddo arg max P(x;,
I=,...,.
0" = arg min Σ C(F(s,))), + +(1 B)
(2)
where B is used for balancing the weight between the real labels and the pseudo-labels. P(x;, 0)
is the model output. ya and peuddo denote the observed label and the pseudo-label respectively. However, in this method, 3 is manually selected and fixed for all training samples, which does not prevent fitting the noisy ones and can even lead to low-quality label correction (Arazo et al. 2019). Moreover, observe that this method is quite sensitive to the selection of the hyper-parameter 3. For instance, as shown in Figure Ia), even a similar 3 selection (i.e., 3 = 0.6/3 = 0.8) behaves differently under disparate noise levels, making the selection of even more intractable. Another
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CIFAR-10
CIFAR-100
Schematic of
84.5
62
Accuracy
63.5
84
48
Validating exemples
(x/hn
TC.o)
Eff
Forward
Backward
88
46
Mela-process: weights a
62.6
42
Training examples (xch
#)
S f/ use
fn
fu. Per-sample loss w.r. and labels training data
ft" Per-sample loss on validation dera
NF 40%
NF- 90%
(a)
(b)
Figure I: (a) The original bootstrapping loss (Reed et al. 2014) sensitive to the reweighting hyper- parameter 3. Under different noise levels, the optimal 3 is different (NF stands for noise fraction). (b) Schematic de- scription of our Learning to Bootstrap (i.e., I.2B) method. The reweighting hyper-parameters are learned in meta-process.
limitation lies in that Eq. equation treats all examples as equally important during training, which could easily cause overfitting for blased training data.
3.2 LEARNING TO BOOTSTRAP THROUGHI META LEARNING
To address these above challenges, in this paper, aim to learn to bootstrap the model by ducting joint label reweighting and instance reweighting. To achieve this, we propose to generate meta-learned weights for guiding our main learning objective:
0" (a, arg min
CuL(F(ri, 0),0
(3)
+B,C(F (x,, 0), y/ poeudo).
with {as, 3.) being the balance weights. Here we note that this new learning objective can be regarded as a general form of the original bootstrapping loss, as Eq. equation 3 can be reduced to given that L(-) is the cross-entropy loss (see details in Appendix B.I). By relaxing this constraint such that a. 3 2 O, we can see that the optimization of Eq. equa- tion 3 not only allows the main learner explore the optimal combination between the two loss terms but also concurrently adjust the contribution of different training samples. In addition, com- pared with Eq. equation 2 the optimization of Eq. equation 3 does not rely on explicitly generating new training targets (i.c.. By,ea + (1 3) (eeddo, but rather conducts implicit relabeling during training by reweighting different loss terms. We note that the key to I.2B is that the sum of o; and (3; need not be which results in +8.9 % improvement on CIFAR 100 with 50% noise (Section 4.2)
Eq. equation when + 3,
Note that this form is also similar to self-distillation in (Li et al. 2017). But different from (Li et al.) 2017) where the weights are determined by heuristics, our weights ax B are meta-learned based on its performance on the validation set Daat that is
1 M
a a² arg min a,320 M
Σ
C(F(2)
It is necessary to constrain 0; B3 2 0 for all to avoid potential unstable training (Ren et al. 2018 Both the meta learner (i.e., Eq. equation 4 and the main learner (i.e., Eq. equation (3) are optimized concurrently, which allows the model to maximize the performance on the clean validation set D by adjusting the importance weights of the observed and the pseudo-labels in a differentiable man- ner.
Online Approximation. For each step at training, mini-batch of training examples {( 34), 1 S n) with n < N is sampled estimate temporary adjustment the parameters based on the descent direction of the loss function. For simplicity. let fc(0) denote L(F(s;, (z., 0), yf
and (0) denote C(F(x;, 0), v,,
pseulo, in the following sections. Given any a. B, we use
0 = 0, - Σ as f(( + B g: g))
AV
(5)
B 8=8:
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Algorithm Learning to Bootstrap
Require: 0o. Dira. D L
Ensure: Or
1: for trrt- = 0 T - 1 do
2: {Iy M +- SumpleMimiBatch(D n))
3: {" + SumpleMimiBatch(DD.. m)
4: For the i-th sample of Dira, compute uf ypreudo arg max,= P(rx, 82)
5: Learnable weights ox, ,
6: Compute training loss I f- Ei=1 (sSe(0:) + Begi
7: O.+1 0, SVIs
0=0,
Compute validation loss 1 - #h 2 f. (0(+1)
8:
9:
(at,, 31) + V7
a=0,3=0
10:
i f max (a,,, 0), 6rd
Be, + max (3,,5, 0)
11:
0t,i f- Σ? &e,
Be,
B
Σ &
Apply learned weights a, reweight the training loss as is E (r..f((0))+
13:
0.+1 + 0g - --Vi
6=8.
14:
end for
to approach the solution of Eq. equation ing optimal a. as
3 Here the step size. We then estimate the correspond-
05 B = arg min
(((0++1).
(6)
0,920 M 2=1
However, directly solving for Eq. equation 6 at every training step requires too much computation cost. To reduce the computational complexity, apply step gradient descent of au 3 mini-batch validation set ((x), v²), < $ m) with m I M as an approximation. Specifically,
(0 Be,s)
v
((++1)))
=.=00
where 7) the step size for updating or, B. To ensure that the weights are non-negative, we apply the following rectified function:
مt = max(or, 0), Br,,
0).
To stabilize the training process, we also normalize the weights in single training batch so that they sum up to one:
Hi, 8c. =
B
,,, Σ. āi, B
Σ, âi, + B
Finally, we estimate o++1 based on the updated ot, Gr so that 0.41 can consider the meta information included in az Br:
T2
0++1= = AV
on, fi(0) + Br, (1))
(10)
0=0,"
See Appendix B.2 for detailed calculation of the gradient in Eq. equation 10 A schematic descrip- tion of our Learning to Bootstrap algorithm is illustrated in Figure Tbb) and the overall optimization procedure can be found in Algorithm] I
3.3 CONVERGENCE ANALYSIS
In proposing Eq. equation 3, we show that with the first-order approximation of a, 3 in Eq. equa- tion and some mild assumptions, our method guarantees to convergence to local minimum point
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of the validation loss, which yields the best combination of a. B. Details of the proof are provided in Appendix B.3.
Theorem 1. Suppose that the training loss function f.g have o-bounded gradients and the valida- tion loss f is Lipschitz smooth with conslant L. With small enough learning rale X, the validation loss monotonically decreases for any training batch B, namely,
G(0++1) G(Oe).
(11)
where u is obtained using Eq. equation 10 and G is the validation loss
M
G(
12)
(12)
M
Furthermore, Eq. equation 77 holds for all possible training batches only when the gradient of validation loss function becomes 0 at step t, namely, G(f++1) = G((,) AB VG((,)
4 EXPERIMENTS
4.1 DATASETS
CIFAR-10 & CIFAR-100. Both CIFAR-IO and CIFAR-100 contain 50K training images and 10K
test images of size 32 x 32. Following previous works (Tanaka al., 2018 Kim et al.) 2019 Li
cet al. 2020), we experimented with both symmetric and asymmetric label noise. In our method, we
used 1,000 clean images in the validation set Deal following (Jiang et al. 2018 Ren et al. 2018
Shu et al. 2019 Hendrycks et al. 2018 Zheng et al.) (021).
ISIC2019, Following (uee et al. 2019), we also evaluated our algorithm on a medical image dataset, i... skin lesion classification data, under different symmetric noise levels. Our experiments were conducted on the 25,331 dermoscopic images of the 2019 ISIC Challenge where we used 20400 images as the training set Diras 640 images the validation set Deat, and lested on 4291 images. Clothing 1M. We evaluate on real-world noisy dataset, Clothing 1M (Xiao et al. 2015), which has million training images collected from online shopping websites with labels generated from surrounding texts. In addition, the Clothing 1M also provides an official validation set of 14,313 images and test set of 10,526 images. Implementation details be found in Appendix A.1.
4.2 PERFORMANCE COMPARISONS
Experiments on CIFAR-10 & CIFAR-100. We compare our method with different baselines: 1) Bootstrapping, which modifies the training loss by generating new training targets 2) Dis- tillation (Li et al. 2017). which transfers the knowledge distilled from the small clean dataset; 3) L2RW (Ren et al. 2018), which reweights different instances through meta-learning: 4) GLC (Hendrycks et al. 2018), which uses the trusted clean data to correct losses; and 5) Cross- Entropy (the standard training) under different levels symmetric labels noise ranging from 20% ~ 50%. To ensure fair comparison, we report the best epoch for all comparison approaches. All results are summarized in Table [ and Table 3 which shows L2B significantly outperforms all other competing methods by a large margin across all noise fractions. It is also observed that compared with previous meta-learning-base improvement substantial especially under larger noise fraction, which suggests the advantages of jointly reweighting different loss terms. For example, on CIFAR-100 100, the accuracy improvement of our proposed L.BB reaches 7.6% and 8.9% under 40% and 50% noise fraction, respectively.
instance reweighting method 1.2RW, the performance
We also test our model with asymmetric noise labels (i.e., 40% noise fractions) and summarize the testing accuracy in Table Among all compared methods, we re-implement L2RW under the same setting and report the performance of all other competitors from previous papers (Kim et al.) 2019) instance reweighting methods (i.c.. LR2W (Ren et al., 2018)), MW-Net (Shu et al.) 2019)). dynamic bootstrapping method (M- correction (Arazo et al., 2019)) and other explicit relabeling methods (i.c., F-correction (Patrini
2021
Li et al. 2020). Compared with previous metaalearning-basee
ct al. 7). Tanaka et al. (Tanaka et al. 2018 ), our L2B achieves superior performance with 40%
https://chal1 http://cchalllee2111111
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Table 1: Comparison of different methods in test accuracy (%)
Table 2: Comparison with asymmet- ric noise.
CIFAR-10 with symmetric noise. NF stands for the noise fraction.
CIFAR-10 10
Wettod
CIEAK
Method
20% NF
30% NF
40% NF
30% NP
Cloga Ealnney
K5.0
Ecomessin
Deriet at
2017
87.2
Cmsse Entropy
86.9
81.3
Vecurmezion
87.3
Bootstrapping (Reed et
2014
85.2
84.8
82.9
79.2
Chme
83.6
Distillation (L) ace 201
88.0
86.8
85.5
80.0
Ti
Prasnaction
2119
83.5
83.9
GLC (Hendrycks
91.4
90.3
86.4
L2RW (Rea er al.
2016
90.6
89.0
86.6
85.3
L2B (Ours)
92.2
90.7
89.9
88.5
Table 3: Comparison with different methods in test accuracy (%) on Figure Test accuracy v.s. number of CIFAR-100 with symmetric noise. NF stands for the noise fraction. epochs on CIFAR- 100 under the noise fraction of 20% and 40%.
CIFAR-100
Method
40% NF
Cross-Eatropy
59.6
52.2
49.2
44.4
Bootstrapping [Reed et 2014
61.8
54.2
50.2
45.8
Distillation (La 2017
62.7
57.3
53.7
45.7
GLC (Hendrycks al. 2018
68.8
65.9
62.1
57.9
L2RW (Ken
67.8
63.8
59.7
L2B (Ours)
71.8
69.5
67.3
64.5
Pach
asymmetric noise. Note that we mainly compare with methods which do not use any augmentation techniques, as our L2B does not rely on those. However, we do notice that our method outperforms M-correction which is built on top of mixup augmentation (Zhang et al., 2018). demonstrating the benefits of our joint instance and label reweighting mechanisms for tackling asymmetric noise.
Alleviate potential overfitting to noisy examples. We also plot the testing accuracy curve under different noise fractions in Figure 2 which shows that our proposed L.2B would help preventing potential overfitting to noisy samples compared with standard training. Meanwhile, compared to simply sample reweighting (L2RW), our L2B introduces pseudo-labels for bootstrapping the learner and is able to converge to a better optimum.
Generalization to real-world noisy labels. We test L2B Clothing 1M (Xiao al. 2015
large-scale dataset with real-world noisy labels. To further illustrate the effectiveness of our ap- proach, compare with: 1) Tanaka et al. (Tanaka al. 2018), 2) MINT (Li et al. 2019). 3) MW-Net (Shu et al. 2019). 4) GLC (Hendrycks et al. [2018), and 5) MLC (Zheng et al. 202 using the same validation and testing splits provided by the benchmark. The results all competitors are reported from (Zheng et al. (202T). As shown in Table 4 our L2B achieves an average perfor- mance of 77.5% accuracy from 3 independent runs with different random seeds, outperforming all competing methods on the Clothing 1M benchmark.
Table Comparison with state-of-ther methods test accuracy (%) under real-works noise on Clothing 1M. Our results are reported from independent runs with different random seeds. All other results are reported from Zheng et al. 2021).
Method
Tanaka
MENT
MW-Ner
GLC Hendrycks 2018
MLC Zheng et
2019
Accuracy
722
23.5
15.7
73.7
75.8
77.5 1 1.2
Generalization to medical image analysis. Table shows the generalizability of our proposed L2B medical image analysis (Xue al. 2019). Compared with 1) L2RW (Ren al. 2018), which has also been applied to skin lesion clssification/semmenattioo (Xue et 2019 kharaji
al. 2019) with noisy supervision; 2) Distillation (Li et al.] 2017); 3) Mixup (Zhang et al. (018);;
and 4) Bootsrapping (Reed et al.) 2014), our method achieves better results under all different noise levels.
Stability of experimental results. We repeated the experiments times with different random seeds for network initialization and label noise generation, and report mean + standard deviation under different experimental settings. As can be seen from Table 6 with different noise fractions and datasets, the standard deviation among the 5 runs consistently less that 0.5%.

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Table 5: Comparison with different methods in test accuracy (%) Table 6: Multiple-runs experiments under noise fraction of 20% NF and 40% NF.
ISIC with symmetric noise.
Mechod
2020 NY
30% NY
40%
50%
Boetstrapping
Crow Fstrum
Reed al 2014
50.8
75.4
77.7
77.5
73.7
75.1
74.8
75.7
Datasets
20% KF
40
Distilation
76.8
74.4
CIFAR-IO 10
91.99 0.10
89.3941 0.22
CIFAR-100
67.23 + 0.33
Min
77.7
76.3
74.1
ISIC 2019
81.16 0.29
78.26 + 0.45
Led (OBI))
81.1
80.3
75.6
76.8
4.3 ABLATION STUDY
On the importance of az f. To understand why our proposed new learning objective can outper- form previous meta-learning-haas ysis to understand the importance of hyper-parameter a and 3 in our method. Specifically, we set and 0 respectively to investigate the importance of each loss term in Eq. equation 3 In addition, we also show how the restriction of a + A3 (Eq. equation would deteriorate our model performance as follows.
instance reweighting methods,
conduct the following anal-
CIFAR-100, 40%
Table 7: Ablation study under the noise frac- tion of 20% and 40%. L2B (a., B 0) consistently achieves superior results to L2B (a + 3 1) under diffcrent noise levels on CIFAR-100.
Tea Aecave
Toll Acoureo
5 8
Eacch
20
100
Epoch
200
300
Method
20% NF
40% NF
Normalization in Ren et S-gmoo Sootmax
Cross- Entropy
59.6
49.2
Figure 3: Comparison among different normalization functions (l.e. Eq. equation [ Sigmoid function and Softmax function). Testing accuracy curv: (a) with dif- ferent normalization functions under 40% symmetric noise label on the ISIC dataset, (b) with different normalization under 40% symmetric label noise on CIFAR-100.
a 0
55.7
47.1
= 0 a + 3 =
63.2
57.5
64.8
59.1
a, 2 0
71.8
67.3
a = O. As shown in Table 7 in this case, the performance even decreases compared with the baseline approach. This due to that when only pscudo-labels are included in the loss computation, the error which occurs in the initial pscudo-label will be reinforced by the network during the following iterations.
, = O. From Eq. equation 3 we can see that setting / as 0 is essentially equivalent to the baseline meta-learming-basee instance reweighting method L2RW (Ren et al.. (0118). In this case, the performance is largely improved compared to the baseline, but still inferior to our method, which jointly optimizes a and [3.
B 1. We also investigate whether the restriction of 3 is required for obtaining optimal weights during the meta-update, as in (Zhang et al. 2020). As shown in Table L2B (a. 2 0) consistently achieves superior results than L2B (a 3 1) under different noise levels on CIFAR- 100. The reason may be the latter is only reweighting different loss terms, whereas the former not only explores the optimal combination between the two loss terms but also jointly adjusts the contribution of different training samples.
Parameter normalization. We note that the normalization of and B is key component for accelerating the training process. However, we observe that different normalization methods of and B behave quite differently for different datasets. To further investigate this, we apply the following normalization functions to each as and 8 on ISIC2019, CIFAR-106 and Clothing 1M: 1) Eq. equation as in (Ren et al. 2018). 2) Sigmoid function,
Ct Ite a+e-
B
(13)
1 e
and 3) Softmax function,
01 Σ. cossT + 8//T 31
(14)
Σn eaalT + ePo.s/T
where t stands for the training iteration and denotes the temperature parameter for scaling the weight distribution. 7 is set as 10.0 when using the Softmax function for normalization. The com- parison among these three different normalization methods is summarized in Figure 3 on ISIC2019
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Under review as a conference paper at ICLR 2023
and 110 datasets with 40% symmetric noise. We that while Eq. equation 9 achieves the best result on CIFAR-100, it yields large training instability on the ISIC2019 dataset. Changing the normalization function Sigmoid and Softmax can make the training procedure much more stable on the ISIC2019 dataset.
In addition, notice that Softmax (e.g., using the Softmax function with a temperature scaling of 10.0 instead of Eq. equation 9 to normalize a and (3) slightly outperforms Sigmoid for ISIC2019. Future research should address how to develop a unified normalization function which can be gen- eralizable for different learning tasks.
Comparison with meta-learning-baat based label correction. One recent study (Zheng et al. 2021 has proposed meta label correction to explicitly relabel the noisy examples via a meta-network. Unlike our L2B which conducts implicit relabeling via reweighting different loss components, this method uses a meta-model for explicit label correction. We re-implement the results with the public code by using Nre as the backbone network and the comparison results on CIFAR- 10 are show in Table 8 We can see that our method consistently outperforms MLC for noise ratios
ranging from 10% to 50% on CIFAR-10.
Table 8: Comparison with MLC
(Zheng et al.
2021 on CIFAR- 10 with symmetric noise.
Method
10% NF
20% NF
30% NF
40% NF
50% NF
MLC
90.1
90.1
88.3
87.2
86.0
L,B (Ours)
93.6
92.2
90.7
89.9
88.5
Training cost. We report our training time on CIFAR-10 compared with the previous meta- learning based instance reweighting methods, i.e., MLNT (Li al.) 2019). L2RW (Ren al. 2018). in Table The training times are reported based on NreActResNee--16 on single VIOO GPU card. Our method L.B is directly built on top of L2RW, and our method (which applies joint instance reweighting and label reweighting) incurs almost no extra training cost when using the same archi- tecture and hardware conditions.
Table 9: Training time comparison of MLNT (Li et al. 2019) L2RW (Ren et al. 2018 and L2B (Ours). Our L.2 incurs almost no additional training cost when using the same architecture and hardware conditions.
MINT (Li et al. 2019
I.RWW (Ren et al. 2018)
I.2B (Ours)
8.6 h
6.5h
6.5h
4.4 DISCUSSION & LIMITATION
L.B is designed for building robust representation models, which is crucial for many real-world applications in healthcare, vision, etc. For example, high intra- and inter-physician variations well-known in medical diagnostic tasks, which lead to erroneous labels that could derail our learning algorithms. L2B can help rectify such noisy data distributions and prevent potential overfitting during training and thus reduce the risking of medical errors.
This paper specifically focuses on the situation where small clean validation set is accessible (e.g., Clothing 1M (Xiao et al., 2015)). However, we do note that the extra validation dataset is not requirement in meta-learmin
as we can use a subset of pscudo-labeled training data as the validation data (Xu et al., (021). How to properly select high-quality pseudo-labeled set and how it affects the algorithm compared to the external validation set should be investigated in the future. Future study should also analyze the role of L2B in conjunction with other meta-learning- based instance reweighting methods such as MW-Net (Shu et al., 2019), and semi-superrised/ssfff
supervised learning methods (Li et al. 2020 202 for furthering the performance.
5 CONCLUSION
In this paper, we present L2B, simple and effective method for training noise-robust models. Con- cretely, we propose novel and generic learning objective enable joint reweighting of instances and labels for combating the label noise in deep representation learning. A meta process is em- ployed dynamically adjust the per-sample importance weight between real observed labels and lseudo-labels. Our L2B outperforms prior instance reweighting or label reweighting works under both synthetic and real-world noise with almost no extra cost.

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Under review as a conference paper at ICLR 2023
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A APPENDIX
A.1 IMPLEMENTATION DETAILS
For all CIFAR-10 and CIFAR-100 100 comparison experiments, we used an 18-layer PreActResNet (He et al. 2016) as the baseline network following the setups in (Li et al. 2020), unless otherwise specified. The model was trained using SGD with momentum of 0.9, weight decay of 0.0005, and a batch size of 256 for CIFAR-100 and 512 for CIFAR-10. The network was trained from scratch for 300 epochs. We the learning rate as 0.15 initially with cosine annealing decay. Following (Li et al., 2020), we set the warm up period as 10 epochs for both CIFAR-10 10 & CIFAR- 100. The optimizer and the learning rate schedule remained the same for both the main and the meta model. Gradient clipping is applied to stabilize training. All experiments were conducted with one V100 GPU, except for the experiments on Clothing 1M which were conducted with one RTX A6000 GPU.
For ISIC2019 experiments, we used ResNet-50 with ImageNet pretrained weights. A batch size of 64 was used for training with an initial learning rate of 0.01. The network was trained for 30 epochs in total with the warmup period as epoch. All other implementation details remained the same as above. For Clothing 1M experiments, we used an ImageNet pre-trained 18-layer ResNet (He al.) 2016) as our baseline. We finetuned the network with a learning rate of 0.005 for 300 epochs. The model was trained using SGD with momentum of 0.9, weight decay of 0.0005, and a batch size of 256. Following (Li et al., 2020), to ensure the labels (noisy) were balanced, for each epoch, we sampled 250 mini-batches from the training data.
A.2 QUALITATIVE RESULTS
We also demonstrate a set of qualitative examples to illustrate how our proposed L,B benefits from the joint instance and label reweighting paradigm. In Figure we can see that when the estimated pseudo label is of high-quality, i.e., the pseudo label is different from the noisy label but equal to the clean label, our model will automatically assign a much higher weight to 3 for corrupted training samples. On the contrary, can be near zero in this case. This indicates that our L2B algorithm will pay more attention to the pseudo label than the real noisy label when computing the losses. In addition, we also show several cases where the pseudo label is equal to the noisy label, where can see that a and B are almost identical under this circumstance since the two losses are of the same value. Note that the relatively small values of and B are due to that size (i.e., 512) for CIFAR-10 experiments. By normalizing the weights in each training batch (see Eq. equation 9), the value of a and B can be the scale of 10
large batch
Cless Label: Mlo! Treadd Label 'ing'
Claa Labdt "srphand Toog" Pheilo Label 'seppee""
Clean Labet 'rndk" Poeao "rook"
Clers Label 'oa' Poodd Label
Label 'uasneble"" Nisty 102r
Case Lakel Nitt" Pizaoo Label 'lngg
6e-4
2e-2
B α
B
B
a
B
B
Figure 4: Examples of a and 3 on CIFAR-I0 with asymmetric noise fraction of 20%. When the estimated pseudo label is of high-quality, i.... the pseudo label is different from the noisy label but equal to the clean label, our model will automatically assign much higher weight to 3 than to for corrupted training samples. When the pseudo label equal the noisy label (i.c., the two loss terms are equal each other), and 3 are almost identical.
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B THEORETICAL ANALYSIS
B.I EQUIVALENCE OF THE TWO LEARNING OBJECTIVES
We show that Eq. equation 3 is equivalent with Eq. equation
2 when vi ai For convenience,
we denote y!taa, 1/
pocado F(,,,)) 8) using sl vh p; respectively.
Σ
ag + 3,C(Pr.
aiyi log
(15)
+ Pey log Pr. Pi,1
Cawti B.V(.,) log
(16)
Due to that ((-) is the cross-entropy loss, we have E/=1 Vi,1 Et' Uh. = 1. Then Σ/= a.vl, +
Beyf. = a, + Rz. So if a; + B, = 1, we have
Σ (asyl, + B. log C(ps, a.y + B.y?))
(17)
C(p,, (1 Bo)dk B,y)))
(18)
B.2 GRADIENT USED FOR UPDATING
We derivative the update rule for a, G in Eq. equation T0
m
01, = 11 Day
fJ (0(+1))
(19)
j=1
00c+1
=
(0 T
(20)
8cxi
10.=0
(21)
00, XV ak [x) - Ba (o)
10-0
(22)
Sas
a,=0
m
n7>
(8)
(23)
j=1
B= = -1 03
1 ((+++1))
(24)
13=00
j
000+1
-
V VJ (0. 1)
(25)
03,
A.=0
(0,1)
(26)
0(0 AV x as (0) + Bk (o))
18=8
(27)
03,
3,=0
(28)
Then O++1 can be calculated by Eq. equation 10 using the updated or,i, ,1,1
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B.3 CONVERGENCE
This section provides the proof for covergence (Theorem
Theorem. Suppose that the training loss function J.9 9 have a-bounded gradients and the validation loss f is Lipschitz smooth with constant L. With small enough learning rate X, the validation loss monotonically decreases for any training batch B, namely.
G(O++1) S G(Oz):
(29)
where 1,+1 is obtained using Eq. equation 10 G is the validation loss
1 M G(0)
Σ f0)).
(30)
Furthermore, Eq. equation 29 holds for all possible training batches only when the gradient of validation loss function becomes at some step t, namely, G(O++1) = G(O.) VB a VG(O,) =
Proof. At each training step pick mini-batch B from the union of training and validation data with B = n. From section B we can derivative de+1 as follows:
Oc+1 =0 A
aa, (f.)0)) 3r.
(31)
t=1
= 1 M
VV
(32)
We omit O, after every function for briefness and set m in section equals to M. Since G(0) Lipschitz-smooth, we have
((044)) S VG AB + T. 1110011.
(33)
Then we show VG AO + 1 || 1 S with a small enough X. Specifically,
VG AO m E(vG"VA)++ Vg.
(34)
Then since fi, have a-bounded gradients, we have
1 |1 - 2
22
Σ IVV
(35)
(V
V 1
(36)
Ln L
VV (VG Vg.)
(37)
Then if X2 < ML
L VG A0 + - 11100112 <
LO"X0M002 - 12
(38)
2
EVV (VG 0.
(39)
If VG = 0. from section B we have O1, = 3r, = 0, then 0,t1 = 8/ and thus G(0(+1) = G(B,) BB. Otherwise, if VG(A,) * 0, we have
Finally we prove G(f,-1) G(O,) VB
VG(A.) VB
1 M
2| = VG = M Σ VG
(40)
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which means there exists ls such that VG VG 0. So for the mini-batch Bg that contains this example, we have
S VG AO + マ 1|
(41)
Lnj² o 7)
(42)
2
VG f1)² + (V)"
(43)
(44)
2
0.
(45)
16


Reviews:
[{"review_id": "sM6nqs_nXT", "reviewer": "Reviewer_LnzH", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a more generic learnable loss objective which enables a joint reweighting of instances and labels at once, in order to mitigate the effect of noise labels on the model generalization. Specifically, their method dynamically adjusts the per-sample importance weight between the real observed labels and pseudo-labels, where the weights are efficiently determined in a meta process.", "summary_of_the_review": "The paper meta-learns two weighting parameters for the real label and the pseudo label for combating the label noise problem. There are some vague explanations/experiments in the paper that need to be clarified. Will consider changing my score after I see some of the other reviewers' opinions and the authors' responses.", "strength_and_weaknesses": "strength:\n1. the motivation of this paper is valid to me, i.e., simultaneously adjust the per-sample loss weight while implicitly relabeling the training samples\n2. the results seem to be effective from the main tables on main benchmarks.\n3. the paper is written clearly and is easy to understand.\n\nweakness:\n1. A small unbiased and clean validation set is required in this method. Is it a strong assumption made in the current framework?\n2. One of the popular and relevant baselines is Dividemix[1], which also involves reweighting mechanism in their approach. Have the authors ever compared their method with this baseline?\n3. From fig 4, the weight before the samples is very small. It is interesting to explain why this phenomenon happens. Does that affect the learning procedure? Also, if that is indeed the case, why the authors can claim the data distribution is protected since a lot of samples seem to be ``discarded\" as well?\n\n[1] Junnan Li, Richard Socher, and Steven CH Hoi. Dividemix: Learning with noisy labels as semisupervised learning. In ICLR, 2020.\n\n\n-----post rebuttal\n\nThank the authors for the detailed response! I would like to raise my score.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "etAYv1akhYY", "reviewer": "Reviewer_7ks8", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "L2B is a learnable loss objective that enables a joint reweighting of instances and labels at once.  L2B dynamically adjusts the per-sample importance weight between the given labels and pseudo-labels in a meta way.", "summary_of_the_review": "The parameters of the loss terms are adjusted by meta-learning. However, the novelty seems not that good in this work. Further analysis should be made to give a deeper understanding.", "strength_and_weaknesses": "Strengths:\n1)  L2B dynamically adjusts the per-sample importance weight between the given labels and pseudo-labels.\n2) The results are somehow higher than some reweighting methods but not other noisy methods.\n3) The experiments are done on different datasets.\n4) The convergence is analyzed in the paper.\n\nWeakness:\n1) should the \\alpha_{t,i} and \\beta_{t,i} in Eq.10 and algorithm line 12 be \\tilde{\\alpha_{t,i}} and \\tilde{\\beta_{t,i}}?\n2) Here is a suggestion: an ablation should be made: \\mathcal{L}( \\mathcal{F}(x_i,\\theta), \\alpha y_i^{real}+\\beta y_i^{psudo})  \\alpha and \\beta is learned as in your algorithm. This ablation can better analyze whether the re-weighting between the samples is useful or the re-weighting between the label and psuedo-label is useful.\n3) comparison of experiments results: maybe previous works [1][2][3] should be compared. Is there any analysis that the results of L2B are not higher compared to [1][2][3]? Since this work is based on the loss design, can L2B be applicable to the current SOTA noisy methods? Can you please show more results based on these works to better illustrate the effectiveness?\n4) typo: 'Eq. equation' \n\n[1] Li, Junnan, Richard Socher, and Steven CH Hoi. \"DivideMix: Learning with Noisy Labels as Semi-supervised Learning.\" International Conference on Learning Representations. 2019.\n[2] Bai, Yingbin, et al. \"Understanding and improving early stopping for learning with noisy labels.\" Advances in Neural Information Processing Systems 34 (2021): 24392-24403.\n[3] Liu, Sheng, et al. \"Early-learning regularization prevents memorization of noisy labels.\" Advances in neural information processing systems 33 (2020): 20331-20342.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "DXXSx3bT-U", "reviewer": "Reviewer_vvhR", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes to meta-learn an instance-level weight for real labels and pseudo-labels when learning with noisy labels. ", "summary_of_the_review": "Overall, considering the clarity, novelty, and quality, the current version of the paper is slightly below the acceptance bar. \n\n===\n\nAfter rebuttal, the author shows that the proposed method can improve the performance of the current SOTA. Thus I raise my score from 5 to 6. ", "strength_and_weaknesses": "Pros\n\n1. The paper is well-written and easy to follow. \n\n2. Theoretical guarantee of the convergence of the proposed method is provided. \n\nCons\n\nMy major concern is that the proposed method is not comparable or compatible with the current SOTA of the methods (of combating noisy labels) which leverage self-supervised learning algorithms and data augmentation [1,2]. \n\nThe author is trying to rule those works out of the scope of this work. In the related work, [1] is categorized as \"approaches which separately handle instance reweighting and label reweighting\" In Section 4.2, the author validates themselves by saying \"Note that we mainly compare with methods which do not use any augmentation techniques, as our L2B does not rely on those.\"\n\nHowever, the methods proposed in [1,2,3] have much better performance than the method in this paper. For example, in the setting of CIFAR-10 50% symmetric noise. The proposed method L2B has an accuracy of 88.5 while the method of [1] has an accuracy of 94.5±0.1\n\nI am concerned about the usefulness of L2B in real practice since it does not help improve the SOTA method. \n\n\n\n[1] Junnan Li, Richard Socher, and Steven CH Hoi. Dividemix: Learning with noisy labels as semisupervised learning. In ICLR, 2020.\n[2] Junnan Li, Caiming Xiong, and Steven C.H. Hoi. Learning from noisy data with robust representation learning. In Proceedings of the IEEE/CVF International Conference on Computer Vision\n(ICCV), pp. 9485–9494, October 2021.\n[3] Wang, Zhaoqing, et al. \"Exploring set similarity for dense self-supervised representation learning.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "Not applicable"}, "extra_text": {}}]

Author rebuttal:

Decision: Reject