The Dynamic of Consensus in Deep Networks and the Identification of Noisy Labels
Authors: Daniel Shwartz
Uri Stern
Daphna Weinshall
Venue: Submitted to ICLR 2023 (2023)
Keywords: Noisy Labels
Training Dynamics
Label Noise

Abstract: Deep neural networks have incredible capacity and expressibility, and can seemingly memorize any training set. This introduces a problem when training in the presence of noisy labels, as the noisy examples cannot be distinguished from clean examples by the end of training. Recent research has dealt with this challenge by utilizing the fact that deep networks seem to memorize clean examples much earlier than noisy examples. Here we report a new empirical result: for each example, when looking at the time it has been memorized by each model in an ensemble of networks, the diversity seen in noisy examples is much larger than the clean examples. We use this observation to develop a new method for noisy labels filtration. The method is based on a statistics of the data, which captures the differences in ensemble learning dynamics between clean and noisy data. We test our method on three tasks: (i) noise amount estimation; (ii) noise filtration; (iii) supervised classification. We show that our method improves over existing baselines in all three tasks using a variety of datasets, noise models, and noise levels. Aside from its improved performance, our method has two other advantages. (i) Simplicity, which implies that no additional hyperparameters are introduced. (ii) Our method is modular: it does not work in an end-to-end fashion, and can therefore be used to clean a dataset for any other future usage.

Under review as a conference paper at ICLR 2023
THE DYNAMIC OF CONSENSUS IN DEEP NETWORKS AND THE IDENTIFICTIION OF NOISY LABELS
Anonymous authors Paper under double-blind review
ABSTRACT
Deep neural networks have incredible capacity and expressibility. and can seem- ingly memorize any training set. This introduces a problem when training in the presence of noisy labels, as the noisy examples cannot be distinguished from clean examples by the end of training. Recent research has dealt with this challenge by utilizing the fact that deep networks seem to memorize clean examples much earlier than noisy examples. Here we report a new empirical result: for each example, when looking at the time it has been memorized by each model in an ensemble of networks, the diversity seen in noisy examples is much larger than the clean examples. We this observation develop new method for noisy labels filtration. The method is based on a statistics of the data, which captures the differences in ensemble learning dynamies between clean and noisy data. We test our method on three tasks: (i) noise amount estimation; (ii) noise filtration; (iii) supervised classification. We show that our method improves over existing baselines in all three tasks using a variety of datasets, noise models, and noise levels. Aside from its improved performance, our method has two other advantages. (i) Simplicity, which implies that no additional hyperparameters are introduced. (ii) Our method is modular: it does not work in an end-to-end fashion, and can therefore be used to clean dataset for any other future usage.
INTRODUCTION
Deep neural networks dominate the state of the art in an ever increasing list of application domains, but for the most part, this incredible success relies on very large datasets of annotated examples available for training. Unfortunately, large amounts of high-quality annotated data are hard and expensive to acquire. whereas cheap alternatives (obtained by way of crowd-sourcing or automatic labeling, for example) often introduce noisy labels into the training set. By now there is much empirical evidence that neural networks can memorize almost every training set, including ones with noisy and even random labels (Zhang et al., 2017), which in turn increases the generalization error of the model. As a result, the problems of identifying the existence of label noise and the separation of noisy labels from clean ones, are becoming more urgent and therefore attract increasing attention.
Henceforth, we will call the set of examples in the training data whose labels are correct "clean data", and the set of examples whose labels are incorrect "noisy data". While all labels can be eventually learned by deep models, it has been empirically shown that most noisy datapoints are learned by deep models late, after most of the clean data has already been learned (Arpit et al., 2017). Therefore many methods focus on the learning time of an example in order to classify it as noisy or clean, by looking at its loss (Pleiss et al., 2020; Arazo et al., 2019) or loss per epoch (Li et al., 2020) in single model. However, these methods struggle to classify correctly clean and noisy datapoints that are learned at the same time, or worse noisy datapoints that are learned early. Additionally, many of these methods work in end-to-end manner, and thus neither provide noise level estimation nor do they deliver separate sets of clean and noisy data for novel future usages.
Our first contribution is new empirical results regarding the learning dynamics of an ensemble of deep networks, showing that the dynamics is different when training with clean data vs. noisy data. The dynamics of clean data has been studied in (Hacohen et al., 2020; Pliushch et al., 2021), where it reported that different deep models learn examples in the same order and pace. This means that when training a few models and comparing their predictions, binary occurrence (approximately)

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is seen at each epoch e: either all the networks correctly predict the example's label, or none of them does. This further implies that for the most part, the distribution of predictions across points is bimodal. Additionally, variety of studies showed that the bias and variance of deep networks decrease as the networks complexity grow (Nakkiran et al., 2021; Neal et al., 2018), providing additional evidence that different deep networks learn data at the same time simultaneously.
In Section 3 we describe a new em- pirical result: when training an en- semble of deep models with noisy data, and in contrast to what happens when using clean data, different mod- els learn different datapoints at differ- ent times (see Fig. 1). This empirical finding tells us that in an ensemble of networks, the learning dynamics of clean data and noisy data can be distinguished. When training such an ensemble with a mixture of clean and noisy data, the emerging dynamics reflects this observation, as well as the tendency of clean data to be learned faster as previously observed.
Labe: Car
Labet "Tee (nd
Epech
Epach
Ending
Epech u-1
Epoch e
Ending
Figure I: With noisy labels models show higher disagreement. The noisy examples are not only learned at a later stage, but each model learns the example at its own different time.
In our second contribution, we use this result to develop a new algorithm for noise level estimation and noise filtration, which we call DisagreeNer (see Section 4). Importantly, unlike most alternative methods, our algorithm is simple (it does not introduce any new hyperparameters), parallelizable, easy integrate with any supervised or semi-supervised learning method and any loss function, and does not rely on prior knowledge of the noise amount. When used for noise filtration, our empirical study (see Section 5) shows the superiority of DisagreeNer as compared the state of the art, using different datasets, different noise models and different noise levels. When used for supervised classification by way of pre-processing the training set prior to training deep model, provides a significant boost in performance, more so than alternative methods.
Relation to prior art
Work on the dynamics of learning in deep models has received increased attention in recent years (e.g.. Nguyen et al., 2020; Hacohen et al., 2020; Baldock et al., 2021). Our work adds a new observation to this body of knowledge, which is seemingly unique to an ensemble of deep models (as against an ensemble of other commonly used classifiers). Thus, while there exist other methods that use ensembles to handle label noise (e.g., Sabzevari et al., 2018; Feng et al., 2020; Chai et al., 202 de Moura et al., 2018), for the most part they cannot take advantage of this characteristic of deep models, and result are forced to additional knowledge, typically the availability of a clean validation set and/or prior knowledge of the noise amount.
Work on deep learning with noisy labels (see Song et al. (2022) for recent survey) can be coarsely divided to two categories: general methods that use a modified loss or network's 's architecture, and methods that focus on noise identification. The first group includes methods that aim to estimate the underlying noise transition matrix (Goldberger and Ben- 2016; Patrini et al., 2017), employ noise-robust loss (Ghosh et al., 2017; Zhang and Sabuncu, 2018; Wang al., 2019; Xu al., 2019), or achieve robustness to noise by way of regularization (Tanno et al., 2019; Jenni and Favaro, 2018). Methods in the second group, which is more inline with our approach, focus more directly on noise identification. Some methods assume that clean examples are usually learned faster than noisy examples (e.g. Liu et al., 2020). Others (Arazo et al., 2019; Li et al., 2020) generate soft labels by interpolating the given labels and the model's predictions during training. Yet other methods (Jiang et al., 2018; Han et al., 2018; Malach and Shalev- Shwarr,, 2017; Yu et al., 2019; Lee and Chung, 2019), like our own, inspect an ensemble of networks, usually in order to transfer information between networks and thus avoid agreement bias.
Notably, we also analyze the behavior of ensembles in order to identify the noisy examples, resembling (Pleiss et al., 2020; Nguyen et al., 2019; Lee and Chung, 2019). But unlike these methods, which track the loss of the networks, we track the dynamics of the agreement between multiple networks over epochs. We then show that this statistic is more effective, and achieves superior results. Additionally (and not less importantly), unlike these works, we do not assume prior knowledge of the noise amount or the presence of clean validation set, and do not introduce new hyper- parameters in our algorithm.
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Recently, the emphasis has somewhat shifted the use of semi-superrvsed learning and contrastive learning (Li et al., 2020; Liu et al., 2020; Ortego et al., 2020; Wei et al., 2020; Yao et al., 2021; Zheltonozhskii et al., 2022; Li et al., 2022; Karim et al., 2022). Semi-supervised learning is an effective paradigm for the prediction of missing labels. This paradigm especially useful when the identification of noisy points cannot be done reliably, in which case it is advantageous remove labels whose likelihood to be true is not negligible. The effectiveness of semi-supervised learning in providing reliable pseudo-labels for unlabeled points will compensate for the loss of clean labels.
However, semi-supervised learning is not universally practical as it often relies on the extraction of effective representations based on unsupervised learning tasks, which typically introduces implicit priors (e.g., that contrastive loss is uppropriate). In contrast, our goal is to reliably identify noisy points, be subsequently removed. Thus, our method can be easily incorporated into any SOTA method which uses supervised or semi-supervised learning (with or without contrastive learning), and may provide benefit even when semi-supervised learning is not viable.
2 INTER-NETWORK AGREEMENT: DEFINITION AND SCORES
Measuring the similarity between deep models is not a trivial challenge, modern deep neural networks are complex functions defined by huge number of parameters, which are invariant to transformations hidden in the model's ' architecture. Here measure the similarity between deep models in an ensemble by measuring inter-model prediction agreement at each datapoint. Accordingly, in Section 2.2 describe scores that based on the state of the networks at each epoch c, while in Section 2.3 we describe cumulative scores that integrate these states through many epochs. Practically (see Section 4), our proposed method relies on the cumulative scores, which are shown empirically to provide more accurate results in the noise filtration task. These scores promise added robustness, as it no longer necessary to identify the epoch at which the score is be evaluated.
2.1 PRELIMINARIES
Notations Let f Rd + [0. 1| denote a deep model, trained with Stochastic Gradient Descent M
1s)) where æ; Rd denotes single example and Y: E [C] its corresponding label. Let F (X) " fN denote an ensemble of N such models, where each model /ie[N] initialized and trained independently on X for & epochs.
(SGD) for epochs training set X {2;; 9:)
Noise model We analyze the training dynamics of an ensemble of models in the presence of label noise. Label noise is different from data noise (like image distortion or additive Gaussian noise). Here it is assumed that after the training set X = {( 4)
MT is sampled, the labels (4) are corrupted by
some noise function g [C] - [C]. and the training set becomes X {(x,, v)) : 4/4 = =g(4). The two most common models of label noise are termed symmetric noise and asymmetric noise (Patrini et al., 2017). In both cases it is assumed that some fixed percentage of the labels are corrupted by g()). With symmetric noise, (() assigns any new label from the set [C] {2} with equal probability. With asymmetric noise, g() is the deterministic permutation function (see App. F for details). Note that the asymmetric noise model is considered much harder than the symmetrie noise model.
2.2 PER-EPOCH AGREEMENT SCORE
Following Hacohen et al. (2020), we define the True Positive Agreement (TPA) score of ensemble
FX) at each datapoint (æ. y), where TPA(æ, Fx) = 1 The TPA score measures the average accuracy of the models in the ensemble, when seeing after each model has been trained for exactly e epochs on X. Note that TPA measures the average accuracy of multiple models on one example, as opposed to the generalization enror that measures the average error of one model on multiple examples.
2.3 CUMULATIVE SCORES
When inspecting the dynamics of the TPA score clean data, see that at the beginning the distribution of (TPA(x, y)) } is concentrated around 0, and then quickly shifts to as training proceeds (see side panels in Fig. 2a). This implies that empirically, data is learned in specific order
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by all models in the ensemble. To measure this phenomenon the Ensemble Learning Pace (ELP) score defined below, which essentially integrates the TPA using all training epochs: (1)
FLP(
Σ FF
eE(L....8]
ELP y) captures both the time of learning by a single model, and its consistency across models. For example, if all the models learned the example early, the score would be high. It would be significantly lower if some of them learned it later than others (see pseudo-code in App. C).
In our study we evaluated two additional cumulative scores of inter-model agreement:
1. Cumulative loss:
CumLoss(z. (z,
1
Σ (E), LeE
NE
Above CE denotes the cross entropy function. This score is very similar to ELP, engaging the average of the cross-entropy loss instead of the accuracy indicator 1 (1
Area under the margin: following (Pleiss et al., 2020), the MeanMargin score is defined as follows
1
Mean.Margin(z. v) NE
Σ
(1)())) [f jtn
E.E(E.....)]
The MeanMargin score the mean of the 'margin', the difference between the value of the ground-truth logit (before softmax) and the value of the otherwise maximal logit.
3 THE DYNAMICS OF AGREEMENT: NEW EMPIRICAL OBSERVATION
In this section we analyze, both theoretically and empirically, how measures of inter-network agree- ment may indicate the detrimental phenomenon of Overfit. Overfit is condition that can occur during the training of deep neural networks. error loss and the increase of test error or loss. Recall that train loss is the quantity that is being continuously minimized during the training of deep models, while the test error is the quantity linked to generalization error. When these quantities change in opposite directions, training harms the final performance and thus early stopping is recommended.
characterized by the co-occurring decrease of train
We begin by showing in Section 3.1 that in ensemble of linear regression models, overfit and the agreement between models are negatively correlated. When this is the case, an epoch which the agreement between networks reaches its maximal value is likely to indicate the beginning of overfit.
Our next goal is to examine the relevance of this result to deep learning in practice. Yet inexplicably, least as far image datasets are concerned, overfit rarely occurs in practice when deep learning is used for image recognition. However, when label noise is introduced, significant overfit occurs. Capitalizing on this observation, we report Section 3.3 that when overfit occurs in the independent training of an ensemble of deep networks, the agreement between the networks starts to decrease.
The approach we describe in Section 4 is motivated by these results: Since it has been observed that noisy data are memorized later than clean data, we hypothesize that overfit occurs when the memorization of noisy labels becomes dominant. This suggests that measuring the dynamics of agreement between networks, which is correlated with overfit as shown below, can be effectively used for the identification of label noise.
3.1 OVERFIT AND AGREEMENT: THEORETICAL RESULT
Since deep learning models are not amenable to rigorous theoretical analysis, and in order to gain computational insight into such general phenomena as overfit, simpler models are sometimes analyzed (e.g. Weinshall and Amir, 2020). Accordingly, in App. A analyze the relation between overfit and inter-model agreement in an ensemble of linear regression models. Our analysis culminates in a theorem, which states that the agreement between linear regression models decreases when overfit occurs in all the models, namely, when the generalization error in all the models increases. Here is a brief sketch of the theorem's proof (see Appendix A);
Disagreement measured by the empirical variance over models of the error vector at each test point, averaged over the test examples.
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We prove the intuitive Lemma 1, stating the following: overfit occurs in model iff the gradient step the model, which is computed from the training set, is negatively correlated with vector unknown the learner the gradient step defined by the test set.
Using some asymptotic assumptions and lengthy and technical derivation, we show that the disagreement is approximately the sum of the correlations between each network's gradient step and its "test gradient step". Then, it follows immediately from Lemma 1 that if overfit occurs all the models then the aforementioned disagreement score increases.
3.2 MEASURING THE AGREEMENT BETWEEN MODELS
In order obtain score that captures the level of disagreement between networks, inspect closely the distribution of T PA((,, y; F (X)). defined in Section 2.2, over sample of datapoints, and analyze its dynamics as training proceeds. First, note that if all of the models in ensemble (X) give identical predictions at each point, the TPA score would be either 0 (when all the networks predict false label) or (when all the networks predict the correct label). In this case, the TPA distribution is perfectly bimodal, with only two peaks at O and 1. If the predictions of the models at each point are independent with mean accuracy p, then can be readily shown that TPA is approximately binomial random variable with unimodal distribution around
Empirically, (Hacohen et al., 2020) showed that in ensembles of deep models trained on 'real' datasets here, the TPA distribution is highly bimodal. Since commonly used measures of bimodality, such as the Pearson bimodality score, are ill-fitted for the discrete TPA distribution, we measure bimodality with the following Bimodal Index score:
1
BI(e)
Σ (BP + M
BT(e) measures how many examples are either correctly or incorrectly classified by all the models in the ensemble, rewarding distributions where points (roughly) equally divided between and 1. Here we use this score to measure the agreement between networks at epoch e.
Thst Accuracy
0.3
Na 0.5 85 2 max DI
0.1
0.0
Train BI
0.6
Test Sccurary
3.0
0.3
Phase1
Phase2
57
150
23
Train BI
(a) BT (Y -xxis) vs. epochs (X-axis)
(b)
Figure 2: (a) Main panel: bimodality in an ensemble of 10 DenseNet networks, trained to classify Cifar10 with 20% symmetric noise. Side panels: TPA distribution epochs (blue clean examples, orange noisy ones). (b) Scatter plots of test accuracy vs train bimodality, measured by BI(e) as defined in (2), where changes in color from blue to yellow correspond with advancing epochs.
If we were to draw the Bimodality Index (BI) of the TPA score as function of the epochs (Fig. 2a). we often see two distinct phases. Initially (phase 1), BI monotonically increasing, namely, both test accuracy and agreement are on the rise. We call it the 'learning' phase. Empirically, in this phase most of the clean examples are being learned (or memorized), as can also be seen in the left side panels of Fig. 2a (cf. Li et al., 2015). At some point BI may start to decrease, followed by another possible ascent. This is phase 2, in which empirically the memorization of noisy examples dominates the learning (see the right side panels of Fig. 2a). This fall and rise is explained by another set of empirical observations, that noisy labels are not being learned in the same order by an ensemble of networks (see App. B), which therefore predicts decline in BI when noisy labels are being learned.

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3.3 OVERFIT AND AGREEMENT: EMPIRICAL EVIDENCE
Earlier work, investigating the dynamics of learning in deep networks, suggests that examples with noisy labels are learned later (Krueger et al., 2017; Zhang et al., 2017; Arpit et al., 2017; Arora et al., 2019). Since the learning of noisy labels unlikely to improve the model's test accuracy, we hypothesize that this may be correlated with the occurrence (or increase) of overfit. The theoretical result in Section 3.1 suggests that this may be correlated with decrease in the agreement between networks. Our goal now
test this prediction empirically.
We next outline empirical evidence that this is indeed the case in actual deep models. In order to boost the strength of overfit, we adopt the scenario of recognition with label noise, where the occurrence of overfit is abundant. When overfit indeed occurs, our experiments show that if the test accuracy drops, then the disagreement score also decreases (see example Fig. 2b-bottom). This observation is confirmed with various noise models and different datasets. When overfit does not occur, the prediction is no longer observed (see example Fig. 2b-top).
These results suggest that consistent drop in the BI index of some training set X can be used to estimate the occurrence of overfit, and possibly even the beginning noisy label memorization.
4 DEALING WITH NOISY LABELS: PROPOSED APPROACH
When dealing with noisy labels, there are essentially three intertwined problems that may require separate treatment:
Noise level estimation: estimate the number of noisy examples.
2.
Noise filtration: flag points whose label is to be removed. Classifier construction:
train model without the examples that are flagged as noisy.
4.1 DISAGREENET, FOR NOISE LEVEL ESTIMATION AND NOISE FILTRATION
Guided by Section we propose a method to estimate the noise level in training set denoted DisagreeNet, which is further used to filter out the noisy examples (see pscudo-code below in Alg, I):
Compute the ELP score from (I) each training example.
2. Fit two component BMM to the ELP distribution (see Fig. 3).
Use the intersection between the components of the BMM fit to divide the data to two groups.
4. Call the group with lower ELP "noisy data'. Estimate noise level by counting the number of datapoints in the noisy group
Algorithm 1: DisagreeNet
Input: ELP_arr __rr specifying the ELP score of each point training set X Output: Noise level estimate, and the list of indices of noisy points
(Giow-ELP Ghigh- ELP) <- divide the data to two groups using fit BMM(ELP _ar): noise jodiccs indices of ELP arr assigned to -tow-ELP:
GGoo ELPl.
moise_estiing +
EEL
return moise_estim,
15
Cifar10, Symm.
Cifar100. 20% Asymm.
TinyImagenet, 40% Symm, noise
Figure 3: ELP distribution, shown separately for the clean data in blue and the noisy data orange. Superim- posed, blue orange lines, the bi-modal BMM fit to ELP (not separated) distribution

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4.2 CLASSIFIER CONSTRUCTION
Aiming to achieve modular handling of noisy labels, we propose the following two-step approach:
1. Run DisagreeNet.
Run SOTA supervised learning method using the filtered data.
In step 2 it is possible to invoke semi-supervised SOTA methods, using the noisy group unsuper- vised data. However, given that suni-super learning typically involves additional assumptions (or prior knowledge) well as high computational complexity (that restricts its applicability to smaller datasets), as discussed Section 1, we do not consider this scenario here.
5 EMPIRICAL EVALUATION
We evaluate our method in the following scenarios and tasks:
Noise identification (Section 5.2), with two complementary sub-tasks: (i) estimate the noise level in the given dataset; (ii) identify the noisy examples.
Supervised classification (Section 5.3), after the removal of the noisy examples.
5.1 DATASET AND BASELINES (DETAILS ARE DEFERRED TO APP.
Datasets We evaluate our method on few standard image classification datasets, including Cifarl0 and C0 (Krizhevsky et al., 2009), Tiny imagenet (Le and Yang, 2015), subsets of Imagenet (Deng et al., 2009), Clothing M (Xiao et al., 2015) and Animal (Song al., 2019a), see App. F for details. These datasets were used earlier work to evaluate the success of noise estimation (Pleiss et al., 2020; Arazo et al., 2019; Li et al., 2020; Liu et al., 2020).
Baselines and comparable methods We report results with the following supervised learning methods for learning from noisy data: DY-BMM and DY-GMM (Arazo et al., 2019), INCV (Chen et al., 2019), AUM (Pleiss et al., 2020), Bootstrap (Reed et al., 2014), D2L (Ma et al., 2018), MentorNet (Jiang al., 2018), FINE (Kim et al., 2021). We also report the results of two absolute baselines: (i) Oracle, which trains the model on the clean dataset; (ii) Random, which trains the model after the removal of random fraction of the whole data, equivalent the noise level.
Other methods The following methods use additional prior information, such as clean validation known level of noise: Co-teaching (Han et al., 2018), 02U (Huang al., 2019b), LEC (Lee and Chung, 2019) and SELFIE (Song et al.. 2019b). Direct comparison does injustice to the previous group of methods, and is therefore deferred to App. H. Another group of methods is excluded from the comparison because they invoke semi-supervised or contrastive learning (e.g., Ortego et al., 2020; Li al., 2020; Karim al., 2022; Li et al., 2022; Wei al., 2020; Yao et al., 2021), which is different learning paradigm (see discussion of prior art in Section 1).
Implementation details We used DenseNet (landola et al., 2014), ResNet-18 and ResNet50 (He et al., 2016, 6) when training on CIFAR-10/100 and Tiny imagenet, and ResNet50 for Clothing IM and Animal1ON.
DY-GMM
DY-BMM
AUM
DisagreeNet
GroundTruth
0.0
0.4
3.6
0.5
0.4
0.4
0.4
0.1
(a) Cifar sym
(b) 100 asym
(c) 100 sym
(d) Cifar100 asym
Figure 4: (a)-(b Noise identification: F1 score for noisy label identification task, using different noise levels (X (X-axis), with asymmetric (a) and asymmetric (b) noise models. Results reflect repetitions involving an ensemble 10 Densenets each. (c)-(d) Noise level estimation: different noise levels are evaluated (X-axis) axiss, with asymmetric (c) and asymmetric (d) noise models (the 3 comparison baselines did not report this estimate).

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5.2 RESULTS: NOISE IDENTIFICATION
The performance of DisagreeNel evaluated in two tasks: (i) The detection of noisy examples, shown in Fig. 4a-4b (see also Figs. 7 and 8 in App. D), where DisagreeNet is seen to outperform the three baselines- AUM, DY-GMM and DY-BMM. (ii) Noise level estimation, shown in Fig. 4c-4d, showing good noise level estimation especially in the of symmetric noise. We also compare DisagreeNet to MeanMargin and CumLoss, see Fig.
5.3 RESULT: SUPERVISED CLASSIHICATIONS
Table I: Test accuracy (%). average and standard error, in the best epoch of retraining after filtration. Results of benchmark methods (see Section 5.1) are taken from (Pleiss et al., 2020) except FINE (Kim al., 2021). which was re-implemented by using the official code. The top and middle tables show CIFAR-10, CIFAR-100 and Tiny Imagenet, with simulated noise. bottom table shows three 'real noise' datasets, and includes addition results of noise level estimation (when applicahle). The presumed noise level for these datasets is indicated in the top line following (Huang al., 2019a; Song et al., 2019b).
Sashod/Datasee
CIFAR-10 sym
CIFAR-100 100 sym
Noise level
20%
40%
60%
20%
40%
60%
random
87.18 0.6
81.59
0.4
64.35 1 0.4
65.49 1 0.4
49.1 0.2 0.2
28.7 0.5
Bootstrap
77.6
62.6 0.4
48.0 - 0.2
0.2
5.2
41.1
29.7 = 0.2
MentorNet
8.1
5.2
6..2
5.2
D2L
0.2
0.34
0.6
1.
2..7
INCV
89.5
86.8
81.1 0.3
58.6 0.5
55.4
43.7 0.3
AUM
+..0
87.5 0.1
82.1 + 0.0
6.2
6.13
53.0 + 0.5
FINE
92.7
90.9
81.5
73.2
66.8
52.04
DisagreeNer+SL
0.2
11.10.1
83.9 - 0.08
77.3 0.2
71.8 7
64.7 + 0.3
oracle
95.1 0.2
94.1 1 0.2
92.4 0.1
78.2 0.3
7..40..11
70.3 + 0.2
Seshod/Datasee
CIFAR-10 10 constant asym
CIFAR-100 constant asym
Tiny Imagenct sym
Noise level
20%
40%
20%
40%
20%
40%
random
89.5 0.2
79.3
0.4
65.2 15.2:00 0.1
44.64 0.2
49.8 1 0.4
29.9 1 0.3
Bootstrap
76.2 0.2
55.0
0.6
5.34
38.7 + 0.3
D2L
88.6 0.2
1.5
43.6
1.29
DY-BMM
0.1
0.6
5.0
0.0
4.1
36.3 + 0.2
INCV
88.3 88.3 0.1
0.4
5.1
4.74
4.1
42.6 = 0.1
AUM
89.7 0.1
58.7 1 0.2
0.2
40.2 10.2000 0.1
18.9
4..7 +
FINE
92.3
87.4
73.04
61.03
53.8
50.3
DisagreeNer+SL
94.4 0.1
91.9 + 0.0
73.9 0.5
61.3 - 0.2
64.5
58.5 + 0.2
oracle
95.2 1 0.0
94.33 1 0.0
78.1 1.11000 0.1
75 1 0.1
6.04
60.8 1. 0.2
Method/Datasee
animal10N, 8% noise
ClothingIM, 38% noise
Noise level
noise est
test accuracy
noise est
test accuracy
Cross-Entropy AUM
84.1 + 0.3
69
10.7
70.4
DisagreeNer+SL
7.8
85.1 0.1
70.8
DisagreeNer is used to remove noisy examples, after which we train deep model from scratch using the remaining examples only. We report our main results using the Densenet architecture, and report results with other architectures in the ablation study. Table summarizes the results for simulated symmetric and asymmetric noise on 5 datasets, and 3 repetitions. It also shows results on 2 real datasets, which are assumed (in previous work) to contain significant levels of 'real' label noise. Additional results are reported in App. H, including methods that require additional prior knowledge.
Not surprisingly, dealing with datasets that are presumed include inherent label noise proved more difficult, and quite different, than dealing with synthetic noise. As claimed in (Ortego et al., 2020), non-malicious label noise does less damage to networks' generalization than random label noise: on Clothing M, for example, hardly any overfit is seen during training, even though the data is believed to contain more than 35% noise. Still, here too, DisagreeNet achieves improved accuracy without access to clean validation set or known noise level (see Table 1). In App. H. Table 8 compare Disagreenet to methods that do use such prior knowledge. Surprisingly, we see that DisagreeNer still achieves better results without using any additional prior knowledge.
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5.4
ABLATION STUDY
How many networks are needed? We report in Table. the F1 score for noisy label identification, using DisagreeNet with varying numbers of networks. The main boost in performance provided by the use of additional networks is seen when using DisagreeNel on hard noise scenarios, such as the asymmetric noise, with small amounts of noise.
Table Fl score of DisagreeNet, using different numbers of models.
Dataset
Noise
size of ensemble (number of networks)
Metbod
2
10%
0.605 0.00
0.77 0.0
0.862 + 0.0
0.906 = 0.0
0.941 = 0.0
0.936 0.0
Cifar10 sym
20%
0.861 0.0
0.939
0.95 =
0.919 = 0.0
0.943
0.0
0.941 0.0
40%
0.954 + 0.0
0.953 0.0
0.952 + 0.0
0.952
0.951 = 0.0
0.951 0.0
10%
0.225 1 0.05
0.855 0.0
0.855 1 0.01
0.854 1: 0.0
0.860 0.01
0.864
1 0.01
Cifar100 sym
20%
+:
0.895
0.0
0.897
4 0.0
0.899
40%
0.89 - 0.0
0.917 0.00
0.921 0.0
0.924 0.0
0.924 = 0.0
0.927 0.0
10%
0.355 1: 0.0
0.469 1: 0.01
0.568 1 0.01
0.631 1 0.01
0.748 1: 0.0
0.814 1144:00 0.0
Ci asym
20%
0.553 0.0
0.642 0.01
0.703 0.01
0.734
0.799 0.001
0.829 + 0.01
10%
0.739 + 0.0
0.795 0.0
0.816 + 0.0
0.826 + 0.0
0.824 = 0.0
0.812 0.0
10%
0.703 0.0
0.708
0.712 + 0.0
0.716 0.0
0.718 = 0.0
0.717 0.0
Cifar100 ssym
20%
0.727
0.0
0.732 0.0
0.732 1 0.0
0.735 0.0
0.736 1 0.0
0.737 0.0
40%
0.594 + 0.0
0.606 0.0
0.614 + 0.0
0.614 + 0.0
0.618 + 0.0
0.62 + 0.0
Additional ablation results Results in App. E, Table 3 indicate robustness to architecture, scheduler, and usage of augmentation, although the standard training procedures achieve the best results. Addi- tionally, we see robustness to changing the backbone architecture of DisagreeNet, using ResNet18 and ResNet50, see App. E, Table 6. Finally, Fig. we compare DisagreeNet using ELP to disagreeNet using the MeanMargin and CumLoss scores, defined in Section 2.3. In symmetric noise scenarios all scores perform well, while in asymmetric noise scenarios the ELP score performs much better, as can be seen in Figs. 5b,5d. Additional comparisons of the 3 scores reported in Apps. E and G.
CumLoss
MeanMarcin
ELP
0.8
0.8
0
0.6
0.6
-10
-10
-30
0.1
0.2
0.4
0.6
0.5
0.3
0/2
2.6
-40
0.3
0.2
0.4
0.6
08
0.2
0.22
0.4
Cifar sym
Cifar 100 asym
(c) Cifar100 sym
Cifar (00 asym
Figure 5: (a)-(b): Fl score (Y-axis) for the noisy label identification task, using different noise levels (X-axis), with asymmetric (a) asymmetric (b) noise models. Results with variants of DisagreeNer are shown, based on scores: MeanMargin, ELP and CumLoss. (c)-(d): Error noise level estimation (Y -axis) using different noise levels (X-axis), with asymmetric (c) and asymmetric (d) noise models, As can be seen, ELP very significantly outperforms the other 2 scores when handling asymmetric noise.
SUMMARY AND DISCUSSION
We presented new empirical observation, that the variability in the predictions of an ensemble of deep networks is much larger when labels are noisy, than it is when labels are clean. This observation used as basis for a new method for classification with noisy labels, addressing along the way the tasks of noise level estimation, noisy labels identification, and classifier construction. Our method is easy to implement, and can be readily incorporated into existing methods for deep learning with label noise, including semi-supervised methods, improve the outcome of the methods.
Importantly, our method achieves this improvement without making additional assumptions, which commonly made by alternative methods: (i) Noise level is expected to be unknown. (ii There is no need for a clean validation set, which many other methods require, but which very difficult to acquire when the training is corupted. (iii) Almost additional hyperparameters introduced.

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APPENDIX
A OVERFIT AND INTER-MODEL CORRELATION
In this section formally analyze the relation between two type of scores, which measure either overfit or inter-model agreement. Overfit is a condition that can occur during the training of deep neural networks. It is characterized by the co-occurring decrease of train error loss, which is continuously minimized during the training of a deep model, and the increase test error or loss, which is the ideal measure would have liked to minimize and which determines the network's generalization error. An agreement score measures how similar the models are in their predictions.
We start by introducing the model and some notations in Section A. In Section A.2 prove the main result (Prop. A.2): the occurrence of overfit at time s in all the models of the ensemble implies that the agreement between the models decreases.
A.1 MODEL AND NOTATIONS
Model. We analyze the agreement between an ensemble of Q models, computed by solving the linear regression problem with Gradient Descent (GD) and random initialization. In this problem, the learner estimates a linear function [(x) Rd - IR, where æ E R2 denotes an input vector and y IR the desired output. Given training set of M pairs (a0m Vm Vm JM let X E RdxM denote the training input a matrix whose m column is
E IRd, and let row vector y E RM denote the
output vector whose m th element is ym. Let N denote the size of the test set. When solving linear
regression problem, we seek row vector ib E IR that satisfies
= argmin L(w),
L(w) = w.x- - yl?
(3)
To solve (3) with GD, we perform at each iterative step 8 2 the following computation:
w ++ Aw
w² pAw
0L(X) Ow
(4)
w Exx Eyx
Σxx = XXT, Σyx =x
for some random initialization vector we E Rdd where usually E[woy] = 0, and learning rate μ. Henceforth omit the index when self evident from context.
As a final remark, when we use the notation ||A]] below for some matrix A, differently from |||| denotes the operator norm of the symmetric matrix A, namely, its largest singular value.
Additional notations
Index i [Q] denotes network instance, and & denotes the test data. For simplicity and with some risk of notation abuse, let Q and Q' also denote sets of indices, either training or test. Specifically, Q [1,.... ... Q] and Q' Q'_[1...... ......,Q4))
We use function notation, where {X(1), w(i) is the training set network and (X(t). is the test set. Thus
Σxx(j) =xxx))=x(XX(T
Eyx()) = v0)x())
JEQ'
Similarly, wii) E IRd the model learned by network and Aw( the gradient step of w(i), where
Aw(i) = (i) - (x)(1) iEQ
e(i,j) denotes a function. which maps indices E Q.j E Q' to the cross error of model on data j the classification error vector when using model w(i) to estimate 8(j). Let M M if E Q is training index, and M' = N if (t) .Ten we can write
e(i.j) Q Q' M
e(i.j) = w() 4())
Aw - e())
Note that in this notation, e(i, t) is the classification is trained on data (i), to estimate the desired outcome on the test data y(t). [[e(i, t)ll is the test error, estimate of the generalization error, of classifier i.
vector when using model i, which
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Let (i. denote the cross gradient:
(i.,) e(i, e(i w(()
Eyx
Aw(1) A(i,t)
(5)
After each GD step, the model and the error are updated as follows:
(i) = w(1) ((
e(i.j) ()) v( c(i.)) (1),))
We note that at step and j E Q. (i) )) is a random vector in R and é(t, is random vector in RM í E (t), then é(i,j) )) ē(i, is random vector in RR..
Test error random variable. Using the above notations, {e(i, ()); is set of Q test errors vectors in RN, where the nh component of the 7th vector e(i, tn captures the test error of model on test example n. In effect, it is a sample of size Q from the random variable e(*, t)n. This random variable captures the error over test point of model computed from a random sample of size M. The empirical variance this random variable will be used to estimate the agreement between the models.
Overfit. Overfit occurs at step s if
|iē(i, |e((i,
Measuring inter-model agreement. In classification problems, bi-modality of the ELP score captures the agreement between set of classifiers, all trained on the same training matrix ( = X. Since here we are analyzing regression problem, we need comparable score to measure agreement between the predictions of Q linear functions. This measure is chosen to be the variance of the test error among models. Accordingly, we will measure disagreement by the empirical variance of test eиror random variable ē(*, t)n, average over all test examples [N].
More specifically, consider an ensemble of linear models (w(i)) trained on set X to minimize (3) with gradient steps, where denotes the index of a network instance and Q the number of network instances. Using the each element var(e( (an(e((t)))) and sum over the test examples n E [N]:
vectors of these models e(i, l), we compute the empirical variance of
Σ [e((e>> Σ
le(i,t), c(j.t)ml²
le(i, e(j, +)
2Q
2Q"
Definition (Inter-model DisAgreement.). The disagreement among set of Q linear models (w(1) at step s defined as follows
DisAg(s) = 2Q ==1
Σ
(((i,t))e(jt)lfE
A.2 OVERAIT AND INTER-NETWORK AGREEMENT
We first prove Lemma 1, which has the following intuitive interpretation: overfit occurs in model i iff the gradient step of model i (denoted Aw())) which computed using the training set, negatively correlated with the 'correct' gradient step the one we would have obtained had we known the test set (this unattainable vector is denoted (ii,t))
Lemma 1. Assume that the learning rate μs is small enough so that we can neglect terms that are 01+2). Then in each gradient descent step s, overfit occurs iff the gradient step Aw(i) of network is negatively correlated with the cross gradient Mii,t).
Proof. Starting from (6)
(overfit) > |(( > ||e(i,
|@(i, - |le(i, 1) ||e(i,
||e(i, >0
- (i,A(i))X(()eeef
+(12)>
(8)
A(i,)) A(i,0) <0
Aw(i)- Ali,t) <0
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Lemma claims that if the magnitude of the gradient step I is small enough, then the operator norm of matrix I - xxxxx smaller than The implication is that geometric sum of this matrix converges, technical result which will be used later.
Lemma For any invertible covariance matrix Exx there exists f > 0, such that js is pExxl <1
Proof. Since Exx is positive-definite, we can write Σxx USU for orthogonal matrix U and the
diagonal matrix of singular values 5 diag(s;} s.). J. It follows that / - μーx xx U didigg[1 (1- -18; JU JU" matrix whose largest singular value is pusa- Since by assumption 8d > 0, the lemma follows. L
Our last Lemma claims that eventually, after sufficiently many gradient steps, the expected value of the solution is exactly the closed-fore form solution of the vetor that minimizes the loss.
Lemma 3. Assume that | 5Σxxl < and Exx is invertible. If the number of gradient steps s large enough so that || - p² x 11 can be neglected, then
Elw") R DxxDxxx
Proof. Starting from (4), show that
8-1 w" = w0 = [xxx) WExx
Σ (1
pExx)
k=1
Since B(w²))
E(w") = (T - xxxxx) + p
(1 - pxxx
Σ (1- ---18e -Ixx)xx
k=1
Given the lemma's assumptions, this expression can be evaluated and simplified:
RE(w") = p.Exx [T (I 1E xxxx)] 1 -
= Exx Eyx Ex -NExxx=
(10)
= EyxD
From (7) follows that a decrease inter-model agreement at step 8, which is implied by increased test variance among models, is indicated by the following inequality:
C C= AisAg(s) Dis DisAg(s 1)
1
Σ
Σ +1==1
Q
|e(ii - e(i >
(11)
2Q
2Q
+,==1
Theorem. Assume that all models see the same training set, denoted X X Vi [Q], and that the training data covariance matrix Exx is full rank.
We make the following asymptotic ussumptions, which are loosely phrused but can be rigorously defined with additional notations:
1. The learning rate y is small enough so that J |Exxll
< (from Lemma 2), and
additionally can neglect terms that are O
2. The number of gradient steps is large enough so that || xx can be neglected.
3. The number of models Q is large enough so that using the law of large numbers, get w)() Rd Rl(w).
1/ E2,
Finally, assume that overfit occurs at time in all the models of the ensemble. In other words, at time the generalization error does not decrease in all the models.
When these assumptions hold, the agreement between the models decreases.
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Proof. (11) can be rearranged follows
Q
C=
1
[[(e(i,)) (a(i, (e(i.t) -(GG))x(()))
1
Σ
[e((, - e(i. e(i.t)l1
2Q 4-=1
2Q
(-=
Σ
=le(i, (A(.0))))) -0, 0
Q²
1=11
Σ
(ii A(i,t+ A(j.) A(i - - - AC. +0,00)0((4+
Q²
1-==1
where the last transition follows from e(i,t)x(() = ()) Using assumption 2
(C' + 0(2²) R MM C")
(12)
where
2
2
C"
(ii A(E,)) A(. -(,,))
A(i, -((,))
(13)
Q
1.j=1
and
Q
1
C'
-(i,t)- A A(.)) A(i,t))
Q
i-=1
Q
Q
A(j.t) + 112 Q
Q
1
Σ
(i,
Σ
A(j)))
Σ
(i,
(14)
Q i=1
Q
Q
j=1
j=1
1=1
1 Q
Q
Σ
(i,
A(i
Q
Q
1=1
Next, we prove that C' approximately 0. We first deduce from assumptions and that
Q
1 Q
Σ
w wi))xxx
Evx =
Σ
wi)))
Exx - Evx e Elwo) Exx Evx
Q
From assumption and Lemma 3, we have that B(w)] 2 V'x 2xx Thus
Σ A(i,)) = Exw|Exx Eyx Eyx Exx Evx =0
From this derivation and (14) may conclude that C' ~ 0. Thus
2 Q C -pC" = - Σ A(i A A(i,t)
(15)
If overfit occurs time in all the models of the ensemble, then C from Lemma and (15). From (11) we may conclude that the inter-model agreement decreases, which concludes the proof.
B NOISY LABELS AND IODER-MODEL AGREEMENT
Here show empirical evidence, that noisy labels not being learned in the same order by an ensemble networks. To see this, we measure the distance between the TPA distribution, computed separately for clean examples and for noisy examples, and the binomial distribution, which is the
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Empirical
examples
(b) Empirical distribution Noisy examples
(c) Binomial distribution Clean examples
(d) Binomial distribution - Noisy examples
1.50
1.00
0.50
0.00
25
50 100
125
130
175
200
(e)
Figure 6: (a)-(d): The empirical distribution of the agreement values over epochs (X-axis: epochs, Y-axis: agreement, color code: blue for low and red for high). Clearly, the distribution of noisy examples resembles the binomial distribution with matched expected value, while the clean examples distribution is far from binomial. (e) Wasserstein distance between binomial distribution the empirical agreement distribution over epochs.
expected distribution of iid classifiers with the same overall accuracy. Specifically, we compute the Wasserstein distance between the agreement distribution at each epoch and the binomials BIN (k.Peteon) and BIN(k,Phnisy)) where Pelemn is the average accuracy on the clean examples, and Proisy the average accuracy on the noisy examples, see Fig. 6. We see that while the distribution of model agreement clean examples is very far from the binomial distribution, the distribution of model agreement on noisy examples much closer, which means that each DNN memorizes noisy examples approximately independent rate.
C COMPUTING THE ELP SCORE: PSEUDO-CODE
D ADDITIONAL RESULTS
D.1 NOISE LEVEL ESTIMATION ON ADDITIONAL DATASETS
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Algorithm 2: Computing the ELP score
Training dataset X with N examples, potentially noisy, network architecture A, batch size b, learning rate 7/, number of networks K, number of epochs E Output: Array, containing the EL.P score for each data point compute agreement during training;
Input:
initialization 0f..0% different initialization of A:; Initialize agreement arr[ENN] 0;
for 0; E do
for & = K do
sample indices, with size b from [1...N] uniformly; Tb, Ub t X (indicess]. Mindices))
/* Gets a mini batch */
compute ps on In using og:
compute loss I, with respect to and ys:
0f+1 SGD(0f;
agreement
cettmment_rrree arr (e, indices] += (argmax(ps) == yo); /+ Store whether the network predicted correctly the examples at epoch
+/
end end
agreement_eee __rrr_rrr___ agreement Brrremment_arrr(E-... K); ELP arr +- mean meean_over__e _epochs(agreementttoog return ELP _rrr
/x normaliztion x/ /* mean over X-axis */
DY-GMM
DY-BMM
AUM
CumLoss
MeanMargin
ELP
30
20
06
0--
0.1
02
24
0.6
54
011
02
32
0.
54
0.3
02
(d) CIFARIO asym estimation
CIFARIO F1
(b) CIFARIO estimation
(c) CIFARIO
-10
-20
-32
-42
10
0.2
(I) TiyLmmggenet estimation
(e) TinyImagenet Fi
ror
Figure 7: Additional results on CIFARIO and Tiny Imagenet.
D.2 PRECISION AND RECALL RESULTS
See fig.
E ABLATION STUDY
Table 3 summarize experiments relating to architecture, scheduler, and augmentation usage. Table provides additional support that our method can used with only a few networks, as the test accuracy after retraining does not improve when using more than 2-3 networks. In table 5 compared our method to two compatative methods from recent years that use semi-supervised learning or similar ideas (Li al., 2020; Liu al., 2020). These methods have different goal than ours (constructing robust classifier, and not noisy labels identification), which is why we did not compare to them in the main text. However, chose to include this comparison here, shows that semi-supervised
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DY-GMM
DY-BMM
AUM
CumLoss
MeanMargin
ELP
100
102
50
40
70
20
22
20
60
90
20
60
10
10
CIFARIO
(b) CIFARIOO
CIFARIO asym
(d) CIFAR 100 asym
195
02
60
20
20
20
20
10
20
40
00
90
20
60
90
10
20
30
20
(e) CIFARIO
(1) CIFARIOO
CIFARIO asym
(h) CHFARIOO asym
Figure 8: Noisy label identification. Top: precision; bottom: recall.
methods are not always stable and robust as solution for label noise, and sometimes its best to identify the noisy labels and retrain on the filtered dataset.
Table 3: score Cifar100 with levels of symmetric noise. Different ablation conditions are marked in columns: ResNet34 indicates a change of architecture, no Aug indicates that image augmentations are not used, and Ir 0.01 indicates that no scheduler or learning rate drop are used during training.
Noise level
No change
ResNet34
Aug
Constant Ir 0.01
0.01 no Aug
20%
0.903 0.01
0.839 + 0.0
0.832 + 0.0
0.859 + 0.01 0.877 + 0.0
0.869 + 0.01
40%
0.918 0.01
0.887 + 0.0
0.887 = 0.01
0.888 + 0.01
Table 4: test accuracy after retraining on filtered dataset when using DisagreeNet with different numbers of models.
Datasel
Noise
size of ensemble
Method
2
10
20%
93.8
0.1
93.7 : 0.1
93.1
0.2
Cifar10 sym
40%
91.5
1. 0.1
91.1
1 0.1
91.1 0.1
60%
86.4 +: 0.2
86.
+ 0.3
83.9 + 0.08
20%
76.3 0.2
76.2 = 0.2
77.3 0.2
Cifar100 sym
40%
72.0 0.5
71.8
0.4
71.8 0.3
60%
64.1 1 0.05
64.3 1 0.2
64.7 0.3
20%
93.1
9.1
911
Cifar asym
40%
90.9 0.1
91.25
1 0.2
91.9 = 0.0
20%
7.18
74.86
= 0.1
73.9 0.5
Cifar100 asym
40%
5..9 0.1
59.7
0.2
61.3
0.2
Alternative scores We evaluate the two alternative scores defined in Section 2.3: CumLoss and MeanMargin, in which case Step 2 of DisagreeNer is executed using one of them instead of the ELP score. Fig. 9 shows the Probability Distribution Function (PDF) of the three scores, revealing that ELP is more consistency bimodal (especially in the difficult asymmetric case), with modes (peaks) that appear more separable. This benefit translates to superior performance in the noise filtration task (Figs. 5b,5d). In addition, we evaluated the importance of using solely the last epoch instead of the entire history in Fig. 10, which shows that using ELP is superior to using the TPA for filtration, even one uses the best epoch for TPA filtration.
We believe that this empirical observation, of increased mode separation, is due to significant difference in the pace of change in agreement values during training between clean and noisy data, in contrast with the pace of change in smoother measures of confidence like Margin and Loss (see App. G). Note that with the easier symmetric noise, we do not see this difference, and indeed the other scores exhibit nicely separated modes, sometimes achieving better results in noise
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10 25
60
100
125
150
200
10
25
60
100
125
150
200
CumLoss
Meankargin
Meankargin
(a) Cifarl0 with 40% Symmetric noise
(b) Cifar100 with 20% Asymmetric noise
Figure 9: Distribution of the CumLoss, McanMargin and ELP scores during training. ELP remains bimodal even for hard noise models, where the other scores become unimodal.
Cifar100, 40% symmetric
0.8
0.6
0.4
Cifar100, 40% asymmetric
F1 score
0.6
0.5
0.4
Tinylmagenet, 40% symmetric
0.75
0.50
TPA
ELP
0.25
0
50
100
200
Epochs
Figure 10: F1 score over the epochs, when using the entire history (ELP) just the last epoch (TPA), evaluated with prior knowledge
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Table 5: Test accuracy (%), average and standard error, in the best epoch of retraining after filtration. Results of ELR and DivideMix were computed by us, using the official implementation for the methods, using same hyperparameters as ours.
Method/Dataset
Tiny Imagenet sym
Noise level
20%
40%
DivideMix (DenseNet)
39.88 0.3
37.02 = 0.3
ELR (DenseNet)
63.8 = 0.0
57.4 + 0.2
DisagreeNet+SL
64.5 + 0.1
58.5 + 0.2
Table 6: Final accuracy results when changing the backbone architecture.
Method/Datasst
CIFAR-10 sym
CIFA R-100 sym
Noise level
20%
40%
60%
20%
40%
60%
DisogreeNer+S5 St. Ri8
93.3 + 0.1
91.1 + 0.6
87.6 0.1
75.1 0.1
71.5
63. 13.10..0
0.4
DisogreeNessS. R50
93.4 + 0.1
91.0 0.2
8.1
75.7 + 0.3
7
0.4
filtration than ELP (Fig. 7 in App. D.1). However, when comparing the test accuracy after retraining (see App. D), we observe that ELP still achieves superior results.
Additionally, in table we evaluate the confusion score in (Simsek et al., 2022), which is the mean (over the epochs) entropy of the mean (over multiple networks) logit of each class (used in the original paper for our of distribution study). We see that this score is also much inferior to ours in the binary classification task of noisy labels identification.
Table AUC (area under the curve) score for noisy labels identification using our ELP score and the confusion score from (Simsek et al., 2022)
Dataset
CIFAR-10 sym
CIFAR-100 sym
Noise level
20%
40%
20%
40%
Confusion
0.809
0.819
0.820
0.824
ELP+SL
0.997
0.994
0.991
0.986
F METHODOLOGY AND TECHNICAL DETAILS
Datasets We evaluated our method on a few standard image classification datasets, including Cifar 10 and Cifar100 100 (Krizhevsky et al., 2009) and Tiny imagenet (Le and Yang, 2015). Cifar10/100 consist of 60k 32 x 32 color images of 10 and 100 classes respectivaly. Tiny ImageNet consists of 100,000 images from 200 classes of ImageNet (Deng et al., 2009), downsampled size 64 64. AnimallON dataset contains 5 pairs of confusing animals with a total of 55,000 64x64 images. Clothing IM (Xiao al., 2015) contains IM clothing images in 14 classes. These datasets were used in earlier work to evaluate the success of noise estimation (Pleiss et al., 2020; Arazo et al., 2019; Li et al., 2020; Liu al., 2020).
Baseline methods for comparison We evaluate our method in the context of two approaches designed to deal with label noise: methods that focus on improving the supervised learning by identifying noisy labels and removing/reducing their influence on the training, and methods that use iterative methods and utilize semi-supervised algorithms in order learn with noisy labels. First approach:
DY-BMM and DY-GMM (Arazo et al., 2019) estimate mixture models on the loss to separate noisy and clean examples. o INCV (Chen et al., 2019) iteratively filter out noisy examples by using cross-validation. o AUM (Pleiss et al., 2020) inserts corrupted examples to determine filtration threshold, using the mean margin as score. Bootstrap (Reed et al., 2014) interpolates between the net predictions and the given label. o D2L (Ma et al., 2018) follows Bootstrap, and uses the examples dimensional attributes for the interpolation. o Co-teaching (Han et al., 2018) use two networks to filter clean data for the other net training. o 02U (Huang et al., 2019b) varies the learning rate to identify the noisy samples, based on a loss-based metric. MentorNet (Jiang et al., 2018) trains a mentor network, whose outputs are used as curriculum to the student network. LEC (Lee and Chung, 2019) trains multiple networks, and uses the intersection of their small loss examples (using a given noise rate threshold) construct filtered dataset for the next epoch.
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Second approach: SELF (Nguyen al., 2019) iteratively uses exponential moving average of a net prediction over the epochs, compared to the ground truth labels, to filter noisy labels and retrain. Meta learning (Li et al., 2019) uses gradient based technique to update the networks weights with noise tolerance. o DivideMix (Li et al., 2020) uses 2 networks to flag examples as noisy and clean with two component mixture, after which the SSL. technique MixMatch (Berthelot et al., 2019) is used. o ELR (Liu et al., 2020) identifies early learned example, and uses them to regulate the learning process. o C2D (Zheltonozhskii et al., 2022) uses the same algorithm as ELR and Dividemix, and uses pretrain net with unsupervised loss.
Technical Details Unless stated otherwise, we used an SGD optimizer with 0.9 momentum and a learning rate of 0.01, weight decay of 5e-4, and batch size of 32. We used a Cosine-annealing scheduler in all of our experiments and used standard augmentation (horizontal flips, random crops) during training. We inspected the effect of different hyperparameters in the ablation study. All of our experiments were conducted on the internal cluster of the Hebrew University, on GPU type AmpereA10.
G COMPARING AGREEMENT TO CONFIDENCE IN NOISE FILTRATION
While the learning time of an example has been shown to be effective for noise filtration, it fails to separate noisy and clean data that are learned more less at the same time. To tackle this problem, one needs additional information, beyond the learning time of a single network. When using an ensemble, we
the TPA score, or else the average probability assigned to the ground truth label (denoted the "correct" logit) by the networks. The latter score conveys the model's confidence in the ground truth label, and is used by our two alternative scores Cuml and MeanMargin.
Going beyond learning time, we propose to look at "how quickly" the agreement value rises from to 1, denoted the "slope" of the agreement. Since empirical results indicate that the learning time of noisy data is much more varied, we expect a slower rise in agreement over noisy data as compared clean data. In our experiments, ELP achieved superior results in noise filtration. We hypothesize that the difference in slope between clean and noisy data may underlie the superiority of ELP in noise filtration.
To check this hypothesis, we compare between two scores computed at each data example: ELP and Logits Mean (denoted LM for simplicity). LM is defined as follows:
LM(x) Σ - (Pt,(())
kT
where l is the number of networks, T is the number of epochs during training, (1,, y) is data example and its assigned label, and [pi, is the probability assigned by network in epoch j to (the ground truth label).
In order to compare between the pace of increase (slope) of ELP and LM, we conduct the following analysis: We select the two groups of clean and noisy data that are learned (roughly) at the same time by some net in the ensemble, and then compute the average agreement and "correct" logit functions as function of epoch, separately for clean and noisy data. We then compute the difference per epoch between the noisy and clean average agreement, which we denote as AAgremeet and Alogit, Note that A AAgreement and Alogit encode the difference in the slope between noisy and clean data, since they begin to rise at (roughly) the same time. Finally, we plot in Fig. 11 the difference between Agreement and Alogit, recalling that larger A indicates stronger separation between the clean and noisy data.
Indeed, our analysis shows that with asymmetric noise, the difference between the agreement slope on clean and noisy data of the ELP score is consistently larger than the agreement slope difference between the average logits on clean and noisy data. This, we believe, is the key reason as to why ELP outperforms LM in noise filtration. Note that this effect is much less pronounced when using the easier symmetric noise, and indeed, our empirical results show that ELP does not outperform LM significantly in this case.
To conclude, we believe that the signal encoded by the agreement values is stronger than the signal encoded in measures of confidence in the networks' prediction when true labels concerned, which
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Avd Mon
(a) 20% symmetric noise
(b) 40% symmetric noise
(c) 20% Asymmetric noise
(d) 40% Asymmetric noise
(e) 20% symmetric noise
(i) 40% symmettic noise
(g) 20% Asymmetric noise
(b) 40% Asymmetric noise
Figure 11: Top: X-axis is the learning time of the chosen clean and noisy data; Yaxxis is the difference between AAgreement and Alogit. We that for most of the training, the difference is positive, implying that ELP provides stronger separation between these groups. Bottom: X Xaxxs is difference between AAgremment and Alogit; -axis is the ratio between time of the groups. These graphs show that while at the end of the training the difference between A Agreement and Alogit negative, implying that LM would be better at separating these groups, these are in fact very small sets of data, most of the data learned some network at earlier stage of the training
amount clean
noisy data. The color represents the learning
explains its capability to classify correctly even some hard-clean examples and easy-noisy examples clean and noise (respectively). This, we believe, result of the polarization effect caused by the binary indicators inside TPA, which disregard misleading positive probabilities assigned to noisy labels even before they are learned by the networks.
H COMPARING TO METHODS WITH DIFFERENT ASSUMPTIONS
Here we compare DisagreeNet to methods that assume known noise level O2U (Huang al., 2019b) and LEC (Lee and Chung, 2019), using 9-layered CNN for the training (with standard hyper parameters as detailed App. F). Since the noise level assumed known, we replace the estimation provided by DisagreeNet with the actual noise level. The results are summarized in Table. 8. We also compare DisagreeNet to other methods that use prior knowledge, where DisagreeNet does not use prior knowledge. The results are summarized in Table. 9
Dataset
Noise level
Method
Dataset noise type
Noise level
02U
LEC
DisagroeNet
10%
87.64%
92.57%
Cifarl0 sym
88.31%
.44%
40%
79.61%
88 48%
60%
80.52%.
81.81%
10%
32%
89.86%
20%
60.53%
59.98%
67.99%
Cifar100 sym
52.47%
89%
60%
16.63%
53.765 76%
10%
88.22%
91. 11.96%
Cifar10 asym
89.41%
90.94%
40%
86.50%
86, 86.93%
10%
64.50%
69.83%
100 asym
20%
58.86%.
67. 67.99%
40%
47 82%.
62 89%
Table 8: Test accuracy (%) comparison with methods that utilize prior knowledge with 9-layered CNN
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Method/Dataset
CIFAR-10 sym
C-FAR-100 sym
Noise level
20%
40%
60%
20%
40%
60%
Co-teaching
88.8 + 0.1
86.5 = 0.1
80.7 + 0.1
64.1 = 0.1
60.2 + 0.2
48.0 + 0.3
LEC
88.3
80.5
60
46.63
O2U
92.5
90.3
74.1
69.2
DisagreeNer+SL
93.1 + 0.2
91.1 + 0.1
83.9 = 0.08
77.3 + 0.2
71.8 + 0.3
64.7 + 0.3
(8o prior knowlodge)
Methoc//Dtaset
CIFAR- 10 asym
CIFAR-100 asym
Tiny Imagenet sym 20%
Noise level
20%
40%
20%
40%
40%
LEC
89.4
86.5
58.9
47.8
DisagreeNet+SL
94.4 0.1
91.9 0.0
73.9 0.5
61.3 0.2
62.5 0.2
55.7 0.4
(no prior knowledge)
Method/Dataset
animal1ON, 8% noise
Noise level
noise est
test accuracy
Co-teaching
82.5 0.1
SELFIE
83 0.1
DisagreeNet+SI. (no prior knowledge)
85.1 0.1
Table 9: Test accuracy (%) comparison with methods that utilize prior knowledge of the real noise level.
25


Reviews:
[{"review_id": "igR5Yiha6g", "reviewer": "Reviewer_gseX", "summary": "", "questions": "", "limitations": "", "rating": 5, "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": "The paper shows that when training an ensemble of deep models with noisy data, different models learn different noisy data points at different times. However, as far as clean examples are considered, the training times are highly similar. The authors propose a method called ELP to predict which examples in a dataset are mislabeled and worth filtering out. The key idea is to calculate the average rate of training of an example across multiple models in an ensemble and use it as a robust method of estimating the learning time of the example. The authors show an interesting analysis of agreement between models and the existence of a bimodal trend of learning speed in Section 3.2 which I find to be the most interesting section of the paper.\n\nThe results on multiple datasets, noise types, and noise strengths are strong and perform competitively with the state of the art. Applications of the work include noise filtration and estimation, and training after dataset cleansing.\n\n\n", "summary_of_the_review": "While the paper achieves strong results in removing mislabeled examples from a dataset, the method is very similar to a past method that was not as extensively evaluated. I am split on the significance of the paper.", "strength_and_weaknesses": "## Strengths\n1. Paper is well-written and easy to follow, and the experiments and ablation studies are comprehensive.\n2. I find the result on noise estimation by fitting a bimodal distribution very interesting. (Has this been used in prior work as well?)\n3. The paper shows strong results in filtering out mislabeled examples, and estimating noise level. This helps achieve close to oracle generalization accuracy.\n\n## Weaknesses\n1. The theoretical argument requires all the models to overfit at the same iteration to cleanly observe the decrease in correlation. This appears to be a very strong assumption that will not hold in practice in an ensemble of models, especially because the goal is to enhance diversity between them.\n2. Missing comparisons with state-of-the-art methods like ELR and SOP (https://proceedings.mlr.press/v162/liu22w/liu22w.pdf). We need to compare the numbers on the same training splits, hence, looking at table numbers will not be a fair comparison, but it appears that SOP outperforms the proposed method in some settings, especially in high noise or asymmetric settings.\n3. The objective of the removal of examples seems sub-optimal. If you can identify the noisy examples, it might be helpful to train the model with their corrected label (this should be easy to estimate using training dynamics).\n4. I am concerned about the novelty of the work. The ELP method when averaged over the entire training process is the same as the method by Jiang 2021 when averaged over multiple random runs of the same dataset (which in this case becomes the equivalent of the ensemble)\n\n**Questions**\n1. \"Additionally, many of these methods work in an end-to-end manner, and thus neither provide noise level estimation nor do they deliver separate sets of clean and noisy data for novel future usages.\" What do you mean by this, and why can't the prior methods help clean data?\n\n**Minor Comments**\n1. Use \\citep{} in 1st paragraph of the Introduction and \\citet{} in last paragraph on Page 2.\n2. We then show that this statistics -> statistic\n3. Use `quotation' rather than 'quotation' for correct compilation.\n4. Usage of overfit v/s overfitting\n5. Please edit Figure 5 with smaller legend, and different limits for the third subfigure\n\n", "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": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "dmdEGSgY2K", "reviewer": "Reviewer_skxN", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "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 studies the problem of noisy label learning and proposes a method that computes a score based on the agreements over an ensemble of models to identify the samples with the correct given labels. The paper conducts experiments and shows that the disagreements among the ensemble of models strongly correlate with the overfitting behavior, indicating that the labels could be noisy. The paper utilizes such an observation to identify samples with clean labels and use other noisy-label learning or semi-supervised learning method to do the training.", "summary_of_the_review": "Given the limitations in the novelty, the problems in the experiments, and the overall presentation of the paper, I don't think the paper is ready to be published for now.", "strength_and_weaknesses": "Strengths:\n1. The paper shows an interesting observation and correlates the identification of noisy labels to the disagreements of an ensemble of models.\n\n2. The paper proposes a very simple method to identify noisy-labeled samples based on observations about disagreements among an ensemble of models.\n\nWeaknesses:\n1. The novelty of the paper is limited. Many previous papers share similar spirits that disagreements among multiple models are utilized to identify noisy labels. For example, a line of research including co-teaching, co-teaching+ and etc uses two models to help find noisy labels. Also, SELF uses the self-ensembling of one model at various training epochs to identify noises.\n\n2. The proposed method has significantly increased computational costs as it requires the training of an ensemble of models. Based on results in Section 5.4, it seems that as many as 7 models are required to get the best performance.\n\n3. The proposed method only considers the problem of noisy label identification for noisy label learning. It relies on other methods to utilize the noisy-labeled samples. Moreover, it is not clear how to utilize the method adaptively, i.e., identify certain noisy labels, train the model using the correct labels, and re-identify more labels with the better-trained models.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "bQmYW3jrCi", "reviewer": "Reviewer_d5tP", "summary": "", "questions": "", "limitations": "", "rating": 5, "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": "This paper observes that the dynamics of the ensemble model provide a distinction between clean and noisy labeled data in the training phase. The diversity of noisy labeled data is much larger than that of clean labeled data. Based on this observation, author proposes DisagreeNet which composes of the three steps : (1) noise rate estimation (2) noise filtration (3) supervised learning. Experiments show that DisagreeNet beats other competitors.", "summary_of_the_review": "While the subject of this experimental paper is interesting and novel, I believe the authors' claims are not adequately supported due to a series of weaknesses of the experimental evaluation. I am more than willing to increase my score if the authors address the aforementioned limitations.", "strength_and_weaknesses": "Strength\n- This paper is well written and easy to follow.\n- It seems to outperforms other competitors with large margin in various benchmark dataset.\n\nWeakness\n- For computing ELP score, the set of epochs \\mathcal{\\epsilon} could be prespecified. How did you choose it? I think it needs the validation set for determining it. In this respect, The argument that the author does not need a validation set may not be valid.\n- What happens when an ensemble technique is applied to standard methods based on the memorization effct. My conjecture is that similar improvements could be achieved. Extensive comparisons should be done.\n- The competitors are outdated. The recent works relevant with this paper are [1, 2, 3, 4].\n\n[1] Yazhou Yao, Zeren Sun, Chuanyi Zhang, Fumin Shen, Qi Wu, Jian Zhang, Zhenmin Tang, Jo-SRC: A Contrastive Approach for Combating Noisy Labels, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2021, pp. 5192-5201.\n[2] Taehyeon Kim, Jongwoo Ko, Sangwook Cho, Jinhwan Choi, Se-Young Yun, FINE Samples for Learning with Noisy Labels, In NeurIPS, 2021.\n[3] Yingbin Bai*, Erkun Yang*, Bo Han, Yanhua Yang, Jiatong Li, Yinian Mao, Gang Niu, and Tongliang Liu, Understanding and Improving Early Stopping for Learning with Noisy Labels, In NeurIPS, 2021.\n[4] Junnan Li, Richard Socher, Steven C.H. Hoi, DivideMix: Learning with Noisy Labels as Semi-supervised Learning, ICLR 2020.", "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": "VQ5gvNZSJf", "reviewer": "Reviewer_thYY", "summary": "", "questions": "", "limitations": "", "rating": 5, "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": "This paper introduce an interesting idea to distinguish between noisy and clean samples. Specifically, they start from the observation that an emsemble of models disagree on the noisy samples during training. Based on this, the author further propose to select the clean samples according to the consistency between models. The proposed method is justfied by a theoretical analysis and empirical experiments. ", "summary_of_the_review": "In summary of the discussion above,  I suggest the authors to enhance the novlty of the proposed algorithm and empirical perfomance.  Personally, I tend to give a boardline reject recommendation.", "strength_and_weaknesses": "Strength:\n* The algorithm is inspired by interesting observations.\n* The paper is well written and easy to follow.\n\nMajor Weaknesses:\n* Though existing works haven't explicity discuss / show how the emsemble models perform on the noisy data (disagree/agree with each other), the idea itself is not surprising. Because it is well known that the models are less confident on the noisy data samples, so we can expect the models that start from different initializations will disagree with each other. The famous co-teaching series of works have already built lots algorithms on the fact that models are less certain on noisy data.\n* The empirical results are weak, e.g., it only has 70.8 on Clothing1M. Much inferior to existing works, e.g., VolMinNet 72.42 [1].\n[1] Provably End-to-end Label-noise Learning without Anchor Points\n\nMinor Issue:\n* I suggest to use \"Theorem(informal)\" in Page 4. \n\nQuestion:\n* On the theretical part: intuitively, why the agreement would decrease when overfitting occurs? Since the models overfit the data, they will predict the noisy label perfectly because all models remember the data. For example, given any $(x_i, y_i)$ in a dataset,for any function $f$ that overfits the dataset, it means $f(x_i) = y_i$.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "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": "ILiID4i_ZV", "reviewer": "Reviewer_ft5z", "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": "The paper observes experimentally that different deep network models learn datapoints at the different paces when trained with noisy labels, in contrast to the same learning dynamics known to hold for different deep network models when the labels are clean. It uses this observation to estimate the presence and level of label noise using a simple algorithm (DisagreeNet) that computes the difference between the training paces of different models via the ELP (\"Ensemble Learning Pace\") metric. ", "summary_of_the_review": "This is a paper over an interesting and timely topic, which proposes a solution that comes with practical advantages, such as its simplicity and the absence of the need for a clean fraction of the dataset or for priors on the noise level. Despite its simplicity, the method may be computationally heavy. A couple of similar schemes have been proposed earlier this year, and the novelty with respect to these should be clarified. The experiments should include them as benchmarks, but they are otherwise extensive and strong (contrary to the theoretical contribution). ", "strength_and_weaknesses": "Strengths:\n\n+ The method is simple and practical, with the additional benefit of avoiding the need to set aside clean label dataset. \n\n+ The experiments are extensive, the results convincingly show that DisagreeNet performs well in general in regard to the state of the art. Some minor details such as confidence intervals in Fig 2 (a) would be welcome.\n\nWeaknesses or questions:\n\n- The main question is related to the novelty, as the use of the predictions of ensembles of models to filter noisy labeled data is not novel (See point 2 below).\n\n- The theoretical claim of Section 3.1 does not bring much to the paper (and it weakens it in my opinion): first it applies only a linear regression with GD, which is a very easy setting to handle since it can be solved exactly, and second the proof is not clear despite the simplicity of the setting (see point 3 below). \n\n- Despite its simplicity, the method can be computationally heavy because it can require some ten models (for instance in hard noise scenarios, as mentioned in Section 5.4). Although the experimental comparison is extensive on the performance of estimating label noise level, it does not include this metric.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject