Robust training with ensemble consensus
Authors: Jisoo Lee
Sae-Young Chung
Venue:  (2020)
Keywords: Annotation noise
Noisy label
Robustness
Ensemble
Perturbation

Abstract: Since deep neural networks are over-parameterized, they can memorize noisy examples. We address such a memorization issue in the presence of label noise. From the fact that deep neural networks cannot generalize to neighborhoods of memorized features, we hypothesize that noisy examples do not consistently incur small losses on the network under a certain perturbation. Based on this, we propose a novel training method called Learning with Ensemble Consensus (LEC) that prevents overfitting to noisy examples by removing them based on the consensus of an ensemble of perturbed networks. One of the proposed LECs, LTEC outperforms the current state-of-the-art methods on noisy MNIST, CIFAR-10, and CIFAR-100 in an efficient manner.

Published as a conference paper at ICLR 2020
ROBUST TRAINING WITH ENSEMBLE CONSENSUS
Jisoo Lee & Yae-Young Chung Korea Advanced Institute of Science and Technology Daejeon, South Korea {j iisoolee, schung; @kaist ac.kr
ABSTRACT
Since deep neural networks are wwrrpeaameterized they can memorize noisy ex- amples. We address such memorization issue in the presence of label noise. From the fact that deep neural networks cannot generalize to neighborhoods memorized features, cur small losses on the network under a certain perturbation. Based on this, we propose novel training method called Learning with Ensemble Consensus (LEC) that prevents overfitting to noisy examples by removing them based on the con- sensus of an ensemble of perturbed networks. One of the proposed LECs, LTEC outperforms the current state-of of-the-art methods on noisy MNIST, CIFAR-10, and CIFAR- in an efficient manner.
hypothesize that noisy examples do not consistently in-
INTRODUCTION
Deep neural networks (DNNs) have shown excellent performance (Krizhevsky et al. 2012 He et al., 2016) on visual recognition datasets (Deng et al., 2009). However, it is difficult to obtain high- quality labeled datasets in practice (Wang et al. |00 Sa). Even worse, DNNs might not learn patterns from the training data the presence of noisy examples (Zhang et al., (016). Therefore, there an increasing demand for robust training methods. In general, DNNs optimized with SGD first learn patterns relevant to clean examples under label noise (Arpit et al.) 2017). Based on this, recent studies regard examples that incur small losses on the network that does not overfit noisy examples as clean (Han et al. 2018 8 Shen & Sanghavi 2019). However, such small-loss examples could be noisy, especially under high level of noise. Therefore, sampling trainable examples from noisy dataset by relying on small-loss criteria might be impractical.
To address this, find the method to identify noisy examples among small-loss ones based well- known observations: (i) noisy examples are learned via memorization rather than via pattern learning and (ii) under certain perturbation, network predictions for memorized features easily fluctuate, while those for generalized features do not. Based on these two observations, we hypothesize that of small-loss examples, training losses of noisy examples would increase by injecting certain perturbation to network parameters, while those of clean examples would not. This suggests that examples that consistently incur small losses under multiple perturbations can be regarded clean. This idea comes from an artifact of SGD optimization, thereby being applicable to any architecture optimized with SGD.
In this work, we introduce method to perturb parameters to distinguish noisy examples from small- loss examples. We then propose a method to robustly train neural networks under label noise, which is termed learning with ensemble consensus (LEC). In LEC, the network is initially trained on the entire training set for a while and then trained on the intersection of small-loss examples of the ensemble of perturbed networks. We present three LECs with different perturbations and evaluate their effectiveness on three benchmark datasets with random label noise (Goldberger & Ben- Ben-Reuuenn] 2016 Ma et al. 2018), open-set noise (Wang al., 2018b), and semantic noise. Our proposed LEC outperforms existing robust training methods by efficiently removing noisy examples from training batches.

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Published as a conference paper at ICLR 2020
2 RELATED WORK
Generalization of DNNs. Although DNNs are over-parameterized, they have impressive gener- alization ability (Krizhevsky al.) 2012 He et al. 2016). Some studies argue that gradient-based optimization plays an important role in regularizing DNNs (Neyshabur et al. 2014 Zhang et al., 2016). Arpit al. (0017) show that DNNs optimized with gradient-based methods learn patterns relevant to clean examples in the early stage of training. Since mislabeling reduces the correlation with other training examples, it is likely that noisy examples are learned via memorization. There- fore, we analyze the difference between generalized and memorized features to discriminate clean and noisy examples.
Training DNNs with Noisy datasets. Label noise issues can be addressed by reducing negative impact of noisy examples. One direction to train with a modified loss function based on the noise distribution. Most studies of this direction estimate the noise distribution prior to training it is not accessible in general (Sukhbaatar et al. 2014] Goldberger& & Ben-Reuven 2016 Patrini et al. 2017 Hendrycks al. 2018). Another direction is to train with modified labels using the current model prediction (Reed et al. 20144) Ma et al., 2018). Aside from these directions, recent work suggests method of exploiting small-loss examples (Jiang al. 2017 Han et al. 2018 Yu et al. 2019 Shen & Sanghavi 2019) based on the generalization ability of DNNs. However, it is still hard to find clean examples by relying on training losses. This study presents a simple method to overcome such problem of small-loss criteria.
3 ROBUST TRAINING WITH ENSEMBLE CONSENSUS
3.1 PROBLEM STATEMENT
Suppose that 5% of examples in a dataset D = Datean U'nnnisy are noisy. Let St,D, denote the set of (100-e)% small-loss examples of the network parameterized by 0 out of examples in D. Since is generally hard learn only clean examples especially on the highly corrupted training set, problematic to regard all examples in S, P.a as being clean. To mitigate this, suggest simple idea: to find noisy examples among examples in S.D,,
3.2 LEARNING WITH ENSEMBLE CONSENSUS (LEC)
Since noisy examples are little correlated with other training examples, they are likely to be learned via memorization. However, DNNs cannot generalize to neighborhoods of the memorized features. This means that even if training losses of noisy examples are small, they can be easily increased under certain perturbation 8, ie., for (x, y) E DD Dnoisy:
(x. v) E Se, = v) & S..D...5
Unlike noisy examples, the network í trained on the entire set D can lear patterns from some clean examples in the early stage of training. Thus, their training losses are consistently small in the presence of the perturbation d, i.e., for (I, y) E Delean.
(x. v) E Sep = (x, E S.,,,445-
This suggests that noisy examples can be identified from the inconsistency of losses under certain perturbation 6. Based on this, we regard examples in the intersection (100-e)% small-loss exam- ples of ensemble of M networks generated by adding perturbations 51, d2, 5M to 6, iee.
M m- Se,D,045..
as clean. We call it ensemble consensus filtering because examples are selected via ensemble con- sensus. With this filtering, we develop training method termed learning with ensemble consensus (LEC) described in Algorithms [ and 2 Both algorithms consist of warming- up and filtering pro- cesses. The difference between these two lies in the filtering process. During the filtering process of Algorithm I the network is trained on the intersection of (100-c)% small-loss examples of M networks within mini batch B. Therefore, the number of examples updated once is changing.
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Published as a conference paper at ICLR 2020
We can encourage more stable training with fixed number of examples to be updated described in Algorithm? 2 During the filtering process of Algorithm 2 we first obtain the intersec- tion of small-loss examples of M networks within full batch D at each epoch. We then sample subset of batchsize from the intersection and train them at each update like a normal SGD.
as
Algorithm LEC
Algorithm 2 LEC-full
Require: moisy datasel D with noise ratio cit,, duraation of warming. up Two # networks used filtering perturbation à
Require:
moisy dataset D with noise ratio es, duration of warming- up T... of networks used for filtering M. perturbation
1: Initialize randomiy
1: Initiaizze 0 randomly
2: for epoch x The do
Warming up process
2: for epuch
Warming up process
3: for mini-batch index b 1
lanusez do
HPI
mini-batch index b = IP1 do
4: Sample subset of butchsize &s from a full batch D < V a T57 (i.es, CB(fo(a)),
Sample subset of batchsize B5 from a batch D 4- Vo 1.. E Lia,ee,, CB(ff(m),
5:
5:
6: end for
end for
7:
end for
7:
8: opech 1 +1: Tend do
Filtering process
for epoch
N. +1
TTnnd do do
Filtering process
9:
for mini batch
[P]
m
10:
Sample a subset of batehsize Bg from a full batch 11: for =1:: do
10:
Om 11 8m,t
Adding perturhation
11:
S. 5..0.0m := [100 e)% small-loss examples fum.
12:
6n 00 0-+ 5m.6.4
Adding perturbution
within full batch D end for
13:
S,. := (100 4 small-Koe -los- examples
12:
fe..
within mimi buich B,
13:
D' 1
& Ensemble cousensus filtering
end for 15: By' nmm S. 8m
14:
14:
for mini-batch index b = 1: 1 do
bi Ensemble consensus
15: Sample subset of batchsize 8 from D
fitering
16:
- B - Vo T Eieeen CE(fo(e).))
16:
+ a EOT Eir.ie CE((o(r)).)
17:
end for
17:
end for
88
end for
18:
for
3.3 PERTURBATION TO IDENTIFY NOISY EXAMPLES
Now we aim to find a perturbation to be injected to discriminate memorized features from gener- alized ones. We present three LECs with different perturbations in the following. The pseudocodes can be found in Section A.1.3
Detwork-Ensembll Consensus (LNEC): Inspired by the observation that an ensemble of networks with the same architecture is correlated during generalization and is decorrelated during memorization (Morcos et al. 2018), the perturbation 8 comes from the difference between M networks. During the warming-up process, M networks trained indepen- dently. During the filtering process, M networks are trained on the intersection of (100-e)% small-loss examples of M networks.
Sell-Ensemble Consensus (LSEC): We focus on the relationship between Morcos et al. (2018) and Lakshminarayanaa et al. 2017): network predictions for memorized features are uncertain and those for generalized features are certain. Since the uncertainty of predic- tions also can be captured by multiple stochastic predictions (Gal & Ghahramani 2016), the perturbation å comes from the difference between M stochastic predictions sin- gle network[]] During the filtering process, the network is trained on the intersection of (100-e)% small-loss examples obtained with M stochastic predictions.
Temporal-Ensemble Consensus (LTEC): Inspired by the observation that during train- ing, atypical features are more easily forgetful compared typical features (Toneva al. 2018), the perturbation ó comes from the difference between networks at current and preceding epochs. During the filtering process, the network is trained on the intersection of (100-c)% small-loss examples at the current epoch and preceding min M - 1, epochs. We collect (100-e)% small-loss examples the preceding epochs, rather than network parameters to reduce memory usage.
As in Gal & Ghahramani 2016), the stochasticity of predictions is caused by stochastic operations such dropout (Srivastava et al. 2014).
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Published as a conference paper at ICLR 2020
4 EXPERIMENTS
In this section, we show (i) the effectiveness of three perturbations at removing noisy examples from small-loss examples and (ii) the comparison of LEC and other existing methods under various annotation noises.
4.1 EXPERIMENTAL SETUP
Annotation noise. We study random label noise (Goldberger & Ben-Reuven 2016; Ma et al, 2018), open-set noise (Wang et al. 2018b), and semantic noise. To generate these noises, we use 1998). CIFAR-101100 (Krizhevsky et al. 2009) that are commonly used to assess the robustness. For each benchmark dataset, only coruupt its training set, while leaving its test set intact for testing. The details can be found in Section A.1.1
MNIST (LeCun et al.
Random label noise. Annotation issues can happen in easy images as well as hard im- ages (Wang et al. [0188). This is simulated in two ways: sym-c% and asym-c%. For sym-c%, <% of the entire set are randomly mislabeled to one of the other labels and for asym-e%, each label i of e% of the entire set is changed to i + 1. We study four types: sym-20% and asym-20% to simulate a low level of noise, and sym-60% and asym-40% to simulate high level of noise.
Open-set noise. In reality, annotated datasets may contain out-of-distribution (OOD) ex- amples. As in Yu et al. (2019), to make OOD examples, images of e% examples randomly sampled from the original dataset are replaced with images from another dataset, while labels are left intact. SVHN (Netzer et al. 201T is used to make open-set noise of CIFAR- 100, and ImageNet-32 (Chrabaszzz et al. 2017) and CIFAR- 100 are used to make open-set noise of CIFAR-10. 10. We study two types: 20% and 40% open-set noise.
Semantic noise. In general, images with easy patterns are correctly labeled, while images with ambiguous patterns are obscurely mislabeled. To simulate this, we select the top e% most uncertain images and then flip their labels to the confusing ones. The uncertainty of each image is computed by the amount of disagreement between predictions of networks trained with clean dataset in Lakshminarayanan et al. 22017 2
Then, the label of each image is assigned to the label with the highest value of averaged softmax outputs of the networks trained with clean dataset except for its ground-truth label. We study two types: 20% and 40% semantic noise.
Architecture and optimization. Unless otherwise specified, we use a variant of 9-convolutional layer architecture (Laine& & Aila 2016 Han et al. (018)). All parameters are trained for 200 epochs with Adam (Kingma & Ba 2014) with a batch size of 128. The details can be found in Aection[A.1..
Hyperparameter. The proposed LEC involves three hyperparameters: duration of warming-up Tw. noise ratio e%, and the number of networks used for filtering M. Unless otherwise specified, To is set to 10, and M is set to 5 for random label noise and open-set noise, and 10 for semantic noise. We assume that noise ratio of e% is given. Further study can be found in Section 5.2
Evaluation. We use two metrics: test accuracy and label precision (Han et al. 2018). At the end of each epoch, test accuracy is measured as the ratio of correctly predicted test examples to all test examples, and label precision is measured as the ratio of clean examples used for training to examples used for training. Thus, for both metrics, higher is better. For methods with multiple networks, the averaged values reported. We report peak as well as final accuracy because a small validation set may be available in reality.
For each noise type, every method is run four times with four random seeds, e.g., four runs of Standard on CIFAR-10 with sym-20%. A noisy dataset is randomly generated and initial network parameters randomized for each run of both random label noise and open-set noise. Note that four noisy datasets generated in four runs are the same for all methods. On the other hand, semantic noise is generated in deterministic way. Thus, only initial network parameters are randomized for each run of semantic noise.
2The uncertainty of image x is defined by >N [I[f(<;; 0,) softmax output of network parameterized by 8. Here, N is set to Takshmmaarayana et al. (2017)
N f(z; (m)) where f(:0) denotes
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Published as a conference paper at ICLR 2020
Self-training
LNEC
LSEC
LTEC
CIFAR-30, kyth-20%
102
CRAS-ID, sym-6254
100
CIFAR-1A, axyth-20
CIFAR-15, asym-42%
Drp 10000001
25
50
25
100
Cooch
Spoch
Ed007
Cooch
Figure 1: Label precision (%) of Self-training and three LECs on CIFAR-I0 with random label noise. We plot the average solid line and the standard deviation shadow around the line.
Table I:
Average of final/peak test accuracy (%) of Self-training and three LECs on CIFAR-10 with random label noise. The best is highlighted in bold.
type
Self-training
LNFCC
CIFAR-
sym 20%
84,96/ 84.96/85.00 /85.00
86.72/86.. 86.778
85.42/85.63
18.18/88..
sym 60%
11.99/74.35
79.61 79.61/79.66 /79.64
76.73/76.92
80.38/80.55
asym- 20%
85.02/ 88.24
86.90/87.11
83.44/85.66
88.86 /88.93
asym
78.84/79.66
84.01 /4.01/84.48
80.74/81.49
86.36 /8.50
CIFAR 36,
CFAR-10,
CIFAR:
CIFAR: 10, 40%
30
26
25
16-
04
82
82
30
1.20
200
200
50
300
150
220
30
1.0
150
200
50
100
150
220
Figure 2: Label precision (%) of small-loss examples of the current network (in green) and the intersection of small-loss examples of the current and preceding networks (in red) during running LTEC on CIFAR-10 with random label noise. We report the precision from epoch 11 when the filtering process starts.
4.2 EFFECTIVENESS OF LECS IDENTIFYING NOISY EXAMPLES
Comparison with Self-training. In Section 3.1 we argue that (100-c)% small-loss examples may be corrupted. To show this, we run LEC with M = I, which a method of training on (100-e)% small-loss examples. Note that this method is similar to the idea of Jiang et al. 2011 Shen & Sanghavi] 2019). We call it Self-training for simplicity. Figure shows the label precision of Self- training low especially under the high level of noise, i.e., sym-604 600. Compared to Self-trainine three LECss are trained on higher precision data, achieving higher test accuracy as shown in Table Out of these three, LTEC performs the best in both label precision and test accuracy.
Noisy examples are removed through ensemble consensus filtering. In LTEC, at every batch update, we first obtain (100-e)% small-loss examples of the current network and then train on the intersection of small-loss examples of the current and preceding networks. We plot label precisions of small-loss examples of the current network (in green) and the intersection (in red) during running LTEC on CIFAR-10 with random noise in Figure 2 We observe that label precision of the inter- section always higher, indicating that noisy examples are removed through ensemble consensus filtering.
4.3 COMPARISON WITH STATE-OF-THE-ARR METHODS
Competing methods. The competing methods include a regular training method: Standard, a method of training with corrected labels: D2L. (Ma et al. 2018). method of training with modified loss function based on the noise distribution: Forward (Patrini et al.] (017). and a method of ex- ploiting small-loss examples: Co-teaching (Han al. 2018). We tune all the methods individually as described in Section A.1.4
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Standard
D2L
Forward
Co-teaching
LTEC
LTEC-Full
MNST. 20% 20%
NW ST. zym 60%
NNIST. a5ym 20%
VIST.. 50ym
22.0
22.5
$3.0
Eaach
Esee
Spxch
Fpom
CIRAR-30
CITAR-10, 6005
CIAR 20%
GFAR-16, arym-4088
04.
323 K00000000
22
1.00
300
232
L83
200
20%
LOO, syth
100, asym 20%
CFAR100, 40ym
Arp BCARRCY
ANg. AOOUPYY
1.0 Bacch
232
250
230
50
150
183 Fpem
200
Esem
9p
Figure 3: Test accuracy (%) of different algorithms on MNIST/CIFAR with random label noise.
Co-teaching
LTEC
LTEC-full
MYD1.Sym-22%
Any 110
20
80
00
24
100
1.50
300
50
300
356
200
100
150
203
180
150
200
Egech
CIRAR 10. 20%
CIFAR 10, sym 60%
CIFRR 10, asym 20%
GFAR-10 96yth-400
100
25
ArOS (111
15
1:00
202
1566
160
Cooch
E2007
Spach
Spech
CIRAR 50%
CIFAR 100, 60%
CIFAR: 100. 20%
CFAR1000,
1.00
202
350
232
183
Figure 4: Label precision (%) of diffferent algorithms on MNIST/CIFAR with random label noise.
Results MNIST/CIFAR with random label noise. The overall results be found in Fig- ures and and Table We plot the average as solid line and the standard deviation as a shadow around the line. Figure states that the accuracy of D2L increases at the low level of label noise as training progresses, but it does not increase at the high level of label noise. This is because D2L puts large weights on given labels in the early stage of training even under the high level of noise. Forward shows its strength only in limited scenarios such as MNIST. Co-teaching does not work well on CIFAR-100 100 with asym-40% indicating that its cross-training scheme is vulnerable to small- loss examples of low label precision (see Figure 4). Unlike Co-teaching, our methods attempt to remove noisy examples in small-loss examples. Thus, on CIFAR- 100 with asym-40% noise, both LTEC and LTEC-full surpass Co-teaching by a wide margin of about 6% and 5%, respectively.

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Published as a conference paper at ICLR 2020
Table 2: Average of final/peak test accuracy (%) of different algorithms on MNIST/CIFAR with random label noise. The best is highlighted in bold.
type
Standard
Forward
Co-teaching
LTEC
LTBCC-uul
MNIST
sym-200%
95.21/99.36
98.38/99.38 38/99.35
96.88/ 00.88/99.22 /99.29
97.84 97.84/99.24
99.52/99..8
99.58 /99.64
sym 60%
55.88 /98.5
59.40/98.37
64.03/90 105/98..25
91.52/98.53
99. 99.16/99.25
99.38/ 999.44
usym- 20%
89.74/99.32
92. 92.88/ 199.41
97.71/99.55 52.52
96.11/99.40
99. 29.9999..5
99.61 66.66
asym-40%
65. 13/96.58
66.44/96.99
996999
95.76/99.51
91.10/98.81
98. 98.47 98.47/99.33 /99.32
99.40/ 48
CIFAR
sym 20%
79.50/ 80.74
84.60/84
80.29 /80.91
85.46/85.52
18, 18/88.28
88.16/
sym 60%%
41.91/65 41.91/65.00 /65.6
44.10/65,26
44.38 661.89
15.01/75.11
80.38 /80.52
79.13/ 02.13/779.22 779.26
asym 20%
79.24/ 81.39
84.27/ 88,44
79.89 /82. 08
85,24/85
88. 86, 888.93
89:04, /89.14
asym-40%
57.50/688 68.77
60.63/67.46
58.53/67.
79.53/80.19
86.36/ /66.56886.00 866.5
14.566 /84.69
CIFAR
sym 20%
50.28/50.88
55.47/55.58
50.01/50.55
57.87/57.88
59.73/59
/59,98
sym-60%
20.79/ 20.79/34.26
34.26
23.72/34.89
34.89
43.36 06.36/43.66 68
46. 24, 46.44
45.77 /45./99
asymn-20%
22.40//2..42
57.31/57.55
52.44/52.56
55.88/55.9 91
58. 72/ 58..6
58.05
asym-40%
37.64/37.66
40.12/40.37
36.95/37.61
40.99/41.01
47.70/47.88
45.49/45.55
Table 3: Average of final/peak test accuracy (%) of different algorithms on CIFAR with open-set noise. The best is highlighted bold.
Datasct + Opca-sct
Noise type
Standard
D2L
Forward
Co-teaching
LTBC
LTEC-full
CIFAR 10+ CIFAR-10 100
20%
86.74/86683
89. 19.42/89.49
86.87/ 157786..0 96
88.58 /88.61
88, /8.69/88.82
89.07/89.11
40%
82.64/82.71
85.32/85.41
82.57/ (.577/82.88
86.18/ 66.18/86.22
86.37/86.41 /86.41
86.26/86.33
CIFAR-10 ImageNet-32
20%
88.27 00.27/88.36 88.36
90.60/90.66
/8.229
88 99.99 99.99/9
89. 15 15/89.24
39,34/99.42
40%
85,90/ 95,99
87.91/ /87.98779
85.84 /8599
86,99 /87.08
86.63 /86.78
87.00/87.12
(IFAR-100++ SVHN
20%
59 59.08/59.11 19
62, 89/ 29/8699929
99/ /59.00 08
60.69 /60,75
61 61.65/61.77
61.87/61,90 98
53.32/53.35
56.30/56.38
53.18/53.30
56.45/56.52
56.95/57.18
57.77/57.90
Table 4: Average of final/peak test accuracy (%) of different algorithms on CIFAR with semantic noise. The best is highlighted in bold.
Dataset
Noise type
Standard
D2L
Forward
Co-teaching
LTEC
LTBC-full
CIFAR-10
20%
81.29/81.36
83.96/83.99
81.10/81.22 23
83,53/83.56
84.48, 884.6
84.48/ 84.48/84.58
/84,58
40%
71.64/74.36
74.72/74.94
71.38/73.47
76.61/76.89
75.52/76.52
76.57/ 1..77/7..66..
CIFAR-100
20%
56.88/50 068866.96 96
60.23/60.40
56.60/56.74 74
$8.45/58.50 50
58. 38.75/58,78
58.73/58 58.80
40%
49.56/49.69
53.04/53.19
49.57/49.69
52.96/52.98
52.58/52.78
53.15/54.15 /54.18
All the methods including LTEC and I.TEC-ful perform well under open-set noise. We speculate that this is due to a low correlation between open-set noisy examples. This is supported by the results on CIFAR-10, i.e., all the methods perform better on ImageNet-32 noise than on CIFAR-100 noise, as ImageNet-32 has more classes than CIFAR-100. Similar to poorly annotated examples, it is hard for deep networks to learn patterns relevant to diito--distriuution examples during the warming- up process. Therefore, those examples can be removed from training batches through ensemble consensus filtering.
Results on CIFAR with open-set noise. The overall results can be found in Table 3
Results on CIFAR with semantic noise. The overall results can be found in Table 4 The se- mantically generated noisy examples are highly correlated with each other, making it difficult to filter out those examples through ensemble consensus. We use 10 as the value of M for semantic noise because ensemble consensus with a bigger M is more conservative. On CIFAR with semantic noise, LTEC and LTEC-full perform comparably or best, compared to the other methods. Of the two, LTEC-full performs better on 40% semantic noise due to its training stability.
DISCUSSION
5.1 HARD-TO-CLASSIFY BUT CLEAN EXAMPLES
It is hard to learn all clean examples during the warming-up up process. Therefore, clean examples with large losses may be excluded from training batches during the filtering process. However, we expect that the number of clean examples used for training would increase gradually as training
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LTEC
LTEC-fUll
LIPAN-10 sym-40%
CIPAR--1,, 4Ry
CIPAR-10 4aymh-45%
102.0
130
120
320
23.0
67.
110
102
Opecc
trach
Loedh
Epec1
Figure 5: Recall (%) of LTEC and LTEC-full on CIFAR- with random label noise. We plot the average solid line and the standard deviation shadow around the line.
Table 5: Average of final/peak test accuracy (%) of LTEC with varying the number of networks used for filtering M. The best is highlighted in bold.
Noise type
LTEC
M
3
M
M
M
CIFAR-I0
sym-20%
84,96/85 02
87.68 87.68/87.77 /87.78
88. 18/ 88888
88 88.63/88.77
88.79/88.87
88.79/ 888.87
86.57 86.57/86.62
sym-60%
73.99/74.35
79.73/79.80
80.38/80.52
80.39/80.45
80.28/
71.63/71.86
usym-20%
85.02/855
87.85 /88.15
88.86/ 188993
88.96 /89007
88.99/ /9999/
/K5.5/
asym
78.84/79.66
85.44/85.59
86.36/86.50
86.78/86.82 /86.82
86.59/866
77.30/77.40
Table Average of final/peak test accuracy (%) of Co-teaching and LTEC with estimates noise ratio (simulated). The best is highlighted in bold.
Dataset
Noise type
under-estimated (0.9e)
correctlyy estimated (e)
over-eatimated (1.1c)
Co-teaching
LTTC
Co Co-teaching
LTEC
Co Co-teaching
LTEC
CIFAR-10 10
sym-20%
84.51/84.58
87.93 /88.08
15.55/855.52
88. 18 /88 28
86.40/86.45
88.72/88.75
sym-600 60%
70.47/73.11
77.98 /9822222
75.01/75.19
80.38/80.52
79.15/79.17
79.34/79.45
asym-20%
84.61 /84.73
88. 18.15/88.39
/5.24/855444
88 88.86/88. 36/88.93
86,41/86.57
89 89.04/89.22
asym asmm-405
76.14/77.41
94.42/84.52
79.53/80.19
86.36/86.4 /86.50
82.19/82.63
86.93/86.96
proceeds since LEC allows the network to learn from patterns clean examples without overfitting. To confirm this, we measure recall defined by the ratio clean examples used for training to all clean examples at the end of each epoch during running LTEC and LTEC-full. As expected, recalls of both LTEC and LTEC-full sharply increase in the first 50 epochs as described Figure [3] Pre- training (Hendrycks et al., 2019) prior to the filtering process may help prevent the removal of clean examples from training batches.
5.2 ABLATION STUDY
The number of networks used for filtering. During the filtering process of LEC, we use only the intersection of small-loss examples of M perturbed networks for training. This means that the number of examples used for training highly depends on M. To understand the effect of M, we run LTEC with varying M on CIFAR-10 with random label noise. In particular, the range of M is ( (1, 7, 9, x.). 5| that a larger M is not always lead to better performance. This is because too many examples may be removed from training batches M increases. Indeed, the total number of examples used for training is critical for the robustness as claimed in Rolnick et al. (2117): al. (2017).
Noise ratio. In reality, only a poorly estimated noise ratio may be accessible. To study the effect of poor noise estimates, we run LTEC on CIFAR-10 with random label noise using bit lower and higher values than the actual noise ratio as in Han et al.) (2018). We also run Co-teaching that requires the noise ratio for comparison. The overall results can found in Table 6 Since it is generally difficult to learn all clean examples, training on small-loss examples selected using the over-estimated ratio (i.., 1.1c) is often helpful in both Co-teaching and LTEC. In contrast, small- loss examples selected using the under-estimated ratio may be highly corrupted. In this case, LTEC robust to the estimation error noise ratio, while Co-teaching is not. Such robustness of LTEC against noise estimation error comes from ensemble consensus filtering.
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Table Average of final/peak test accuracy (%) of Standard and LTEC with ResNet. The best is highlighted in bold.
Noise Type
Standard (ResNet)
LTEC (ResNet)
CIFAR-10
sym-20%
81.31/ /85.30
89.01 /89.12
sym 60%
61,94/7 79.872880
$1.46/81.4
asym 20%
81.93/87.32
88.90/89.04
62.76/77.10
86.62/86.85
Applicability to different architecture. The key idea of LEC is rooted in the difference between generalizaton and memorization, i.e., the ways of learning clean examples and noisy examples in the early SGD optimization (Arpit et al.] 2017). Therefore, we expect that LECC would be appli- cable any architecture optimized with SGD.. To support this, we run Standard and LTEC with ResNet-20 (He et al. 20166. The architecture is optimized based on Chollet et al. (2015), achieving the final test accuracy 90.67% on clean CIFAR-10. Here, Tw set to 30 for the optimization details. Table shows LTEC (ResNet) beats Standard (ResNet) in both peak and final accuracies, as expected.
6 CONCLUSION
This work presents the method of generating and using the ensemble for robust training. We explore three simple perturbation methods to generate the ensemble and then develop the way of identifying noisy examples through ensemble consensus small-loss examples. Along with growing attention to the use small-loss examples for robust training, we expect that our ensemble method will be useful for such training methods.
ACKNOWLEDGMENTS
We thank Changho Suh, Jinwoo Shin, Su-Young Lee, Minguk Jang, and anonymous reviewers for their great suggestions, This work was supported by the ICT R&D program of MSIP/IITP. [2016- 0-00563, Research on Adaptive Machine Learning Technology Development for Intelligent Au- tonomous Digital Companion]
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Bo Han, Quanming Yao, Xingrui Yu, Gang Niu, Miao Xu, Weihua Hu, Ivor Tsang, and Masashi Sugiyama. Co-teaching: Robust training of deep neural networks with extremely noisy labels. In Advances in neural information processing systems, pp. 8527-8532 2018.
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Dan Hendrycks, Kimin Lee, and Mantas Mazeika. Using pre-training can improve model robustness and uncertainty. arXiv preprint arXiv: 1901. 199019999660 2019.
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Giorgio Patrini, Alessandro Rozza, Aditya Krishna Menon, Richard Nock, and Lizhen Qu Making deep neural networks robust to label noise: A loss correction approach. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, pp. 1944-1952. 2017.
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A APPENDIX
A.1 IMPLEMENTATION DETAILS
A.1.1 ANNOTATION NOISES
For sym-c%, e% of the entire set are randomly mislabeled to one of the other labels and for asym-e%, each label of e% of the entire set changed + 1. The corruption matrices of sym-c% and asym-c% are described in Figures Ala and Alb respectively.
Random label noise:
Open-set noise: For e% open-set noise, images of e% examples randomly sampled from the original dataset are replaced with images from external sources, while labels are left intact. For CIFAR-10 10 with open-set noise, we sample images from 75 classes of CIFAR- 100 (Abbasi et al. 2018) and 748 classes of ImageNet (Oliver et al. 2018) to avoid sam- pling similar images with CIFAR-10.
Semantic noise: For semantic noise, we choose uncertain images and then mislabel them ambiguously. In Figure A2 we see that clean examples have simple and easy images, while noisy examples have not. Also, its corruption matrix (see Figure Alc) describes the similarity between classes, e.g., cat and dog, car and truck, etc.
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(a) Random-syne -ym
(b) Random-asym
(c) Semantic
Figure A1: Corruption matrices of CIFAR-10 with random label noise and semantic noise.
deer
truck
Car
deer
deer
horse
deer
plane
frog
Figure A2: Clean examples (top) and noisy examples (bottom) randomly sampled from CIFAR- 10 with 20% semantic noise. We observe that noisy examples contain atypical features and are semantically mislabeled.
A.1.2 ARCHITECTURE AND OPTIMIZATION DETAILS
The 9-convolutional layer architecture used this study can be found in Table A1 The network optimized with Adam (Kingma & Ba 2014) with batchsize of 128 for 200 epochs. The initial learning rate a is set to 0.I. The learning rate is linearly annealed to zero during the last 120 epochs for MNIST and CIFAR-IO, and during the last 100 epochs for CIFAR-100. The momentum parameters 31 and 32 are set to 0.9 and 0.999, respectively. 31 is linearly annealed to 0.1 during the last 120 epochs for MNIST and CIFAR-10 10, and during the last 100 epochs for CIFAR-100. The images of CIFAR are divided by 255 and are whitened with ZCA. Additional regularizations such as data augmentation not applied. The results on clean MNIST, CIFAR-10. 10, and CIFAR-100 can be found in Table A2
Table Al: 9-conv layer architecture.
Input image
Gaussian noise 0.15)
conv, padding batch norm, L.Rel.f (ar 0.01)
x 3 conv, 128, padding "same" batch norm, LReL. 0.01)
x 3 conv, 128, padding "same' batch
LRcLU
2 x 2 maxpooling, padding 'same' dropout (drop zale 0.25)
Table A2: Avg (#: stddev) of final test accuracy of a regular training on clean MNIST, CIFAR-10, and CIFAR-100.
x 3 conv, 256, padding = "same" batch norm, LReLU (a 0.01) x conv, 256, padding = 'smee'
(a=
Datasel
MNIST
CIFAR-10 10
CIFAR 100
x 3 conv, 256, padding 'same' batch norm, LReLU (o 0.01)
Test accuracy
99.60-100.0
90.59:10.15
64.38:10.20
x maxpooling, padding 'same' dropout (drop rate 0.25)
3 x 3 conv, 512, padding 'valid' butch LReLU (a x conv, 256, padding= 'valid' batch norm. LReLU (a= 0.01)
x 128, padling 'valid' batch norm,
I.Rel.U (o 0.01)
global average pooling classes)
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A.1.3 PSEUDOCODES FOR LECs
We present three LECs with different perturbations in Section 3.3 LSEC, LTEC, and LTEC-full are described in the following. In LTEC-full, we obtain small-loss examples utilized for filtering from the second epoch encourage its stability.
The pseudocodes for LNEC,
Algorithm A1 LNEC
Require:
noisy datasct D with noise ratio e&, duration of warming-up Tw. The number of networks used for filtering M
1: Initialize 0,, o....., 0. randomly
2:
for epoch = 1: T do
Warming process
3: Tor mini butch index 6
bacbaux do
4:
Sumple subset of hatchsize from full batch for network index m M do
5:
6:
6m 8m T9pT L(,y)em, C'E
7:
end for
8:
end end for
9:
for epoch Tur + 1: Tand do
Filtering process
11:
for mini-batch index 1: bactaur do
IP
12:
Sample subset of batchsize B, from a full batch 2 for
13:
14:
S..B,.0m (100 <)% small-loss examples of fem within Bg end for
15:
16:
B.
n =n.- nmm=SS.e,,ee
D. Network-cnsemble consensus filtering
17:
for network index m 1: MM da
18:
Om 6m a 6m T8," ( CE(fem (#),
19:
for end for
20:
21:
Algorithm A2 LSEC
Require: noisy dataset D with noise ratio e%, duration of warming-up Tw. The number of networks used for filtering M Initialize 0 randomly
2: for epoch 1 do
Warming up process
3: mini-batch index
do hatchsize # +- VVo Tégi Σ DEN CB(fo(2),
4:
Sample
5:
6:
end for end for
7:
8:
for opoch = Tw : Tend do
Filtering process
9:
for mini-hatch index 6 1: hardeom do
PD
10:
Sample subset of batchsize B, from a full batch D
for forward pass index m
12:
O.n + 8.n where 8.,, from the stuchusticity network architecture S..5g. = (100 <) % small loss examples from within 19, end for
14:
B.' S S..m + V T.5 Eiowles CE(fo(z).v)
D. Self-ensemble consensus filtering
end
18:
end for
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Algorithm A3 LTEC
Require: noisy dataset with
duration warming-up Tw. The aumber networks used for filtering M
1:
Initialize randomly
2:
epach
and
3: P.
4: for mini-batch index 1: Favmare do
1D
5: Sample subset of batchsize B, from full batch D
6: SS. 66.0 (100 e)% small-Jos loss examples fa within 8,
7:
Pe +- P. S..S,,
8:
if Tw + then
Warming-up process
9:
+ aVo T8gT SO.DEEs CE(fo(z).))
10:
else
Filtering process
11:
if: then
12:
8,' S,
13:
else i then
14:
8,' Pi
P S,,8, 5,' = PC--M-
15:
else
16:
0 n S..
b. Temporal ensembll consensus filtering
17:
end if
18:
0 0 V.. 1857 Elenice CE(fa(s).))
19:
20:
end for
21:
end
Algorithm A4 LTEC-full
Require: noisy dataset with noise ratio eRt duration warming-up Tu., The number networks used for filtering A
1: Initialize ranionly
2: mini-batch index
do
3: Sample
batchsize
4: 8 4- VVe TÉgi Een,iee, CB(fo(z),
5: end for
6: for epuch
Tond P. :- (100- - +)%6 small-loss examples of fo within TD
7:
Small-Loss examples are computed from the 2nd epoch Warming up process
8:
it
9:
mini-batch index b 1: 12 do
10:
Sample subset batchsize B, from a full batch D 0 + 0 V.a Toy E(r,EE, C'I(fo(z)
11:
12:
end for
13:
Filtering process
14:
if < M + then
15:
D' P2nps n.... PP
16:
17:
D PI-(M--1) 0 PM- n... PnP
Temporal-ensemhll consensus filtering
18:
end if
19:
20:
Sample subset batchsize 15,, from Di
21:
0 V 1881 Eiawie, CE(fo(s).))
22:
end
23:
end
24:
1.1.4 COMPETING METHODS
The competing methods include regular training method: Standard, a method of training with corrected labels: D2L (Ma et al.) (2018), a method of training with modified loss function based on the noise distribution: Forward (Patrini al., (017). and method of exploiting small-loss examples: Co-teaching (Han et al. 2018). We tune all the methods individually as follows:
Standard The network is trained using the cross-entropy loss.
D2L: The input vector a fully connected layer in the architecture is used to measure the LID estimates. The parameter involved with identifying the turning point, window size W is set to 12. The network trained using original labels until the turning point is found and then trained using the bootstrapping target with adaptively tunable mixing coefficient.
Forward: Prior to training, the corruption matrix C' where C = Ply = ilpirue = j) is es- timated based on the 97th percentile of probabilities for each class MNIST and CIFAR-
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10, and the 100th percentile of probabilities for each class CIFAR-100 as in Henndrycks ct al. (2018). The network is then trained using the corrected labels for 200 epochs.
Co-teaching: Two networks are employed. At every update, they select their small-loss examples within minibatch and then provide them to each other. The ratio of selected examples based on training losses is linearly annealed from 100% to (100-c)% over the first 10 epochs.
A.2 COMPLEXITY ANALYSIS
We compute space complexity the number of network parameters and computational complexity as the number of forward and backward passes. Here we assume that early stopping is not used and the noise ratio of e% is given. Note that the computational complexity of each method depends on its hyperparameter values, e.g., the duration of the warming-up process Twr and the noise ratio e %. The analysis is reported in Table A3 Our proposed LTEC is the most efficient because it can be implemented with single network based on Section A.1.3 and only a subset of the entire training set is updated after the warming-up up process.
Table A3: Complexity analysis: M indicates the number of networks for filtering in LECs.
Complexity
Standard
Self-training
Co-teaching
INEC
LSEC
LTFCALTFC-fll
Space complexity of network parameters
2m
Mm
Computational complexity
of forward passes # of backward passes
1
2n
Mn
Mr.
n
Mn
$
A.3 ADDITIONAL RESULTS
A.3.1 RESULTS OF LTEC WITH M =0
shows that ensemble consensus filtering with too large M removes clean examples from training batches in the early stage of the filtering process. Unlike LTEC with M 5, the recall of LTEC with M = 3o does not increase as training proceeds, suggesting that its generalization performance not enhanced. This shows that a larger M does not always lead better performance. We expect that pre-training (Hendrycks et al. (019)) prior to the filtering process helps to reduce the number clean examples removed by ensemble consensus filtering regardless of M.
Figure A3
LTEC (M=5)
LTEC-full (M=5)
LTEC (M==)
LTEC-full (M=
sym-22%
sym-40%
Dmn ROCK 1902
15
50
100
350
200
100
150
200
50
103
152
270
30
1.5
330
200
Figure A3: Recall (%) of LTECs with varying M CIFAR-10 10 with random label noise.
15


Reviews:
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The authors then propose 3 concrete instantiations of the idea, and do a thorough empirical study (including ablations) across multiple architectures, datasets, noise types, and comparing to multiple related methods. The results show pretty convincingly that one of the new methods (LTEC) that uses past networks outputs to build an ensemble performs really well.\n\nCaveats: \n1) I’m an emergency reviewer and had less time to do an in-depth review.\n2) While my research is sufficiently close to review the paper, I’m not an expert on label noise specifically, so I cannot comment much on novelty and related work questions.\n\nComments:\n* The readability of the paper could be dramatically improved by reporting results visually (eg bar-plots) and moving all tables into the appendix.\n* The authors state that peak performance is valid because it *could* have been found using a validation set -- then why not just do that, and report this early-stopping performance everywhere, instead of always two numbers (peak and final)?\n* Please make the perturbation properties in section 3.2 more precise: do you mean “there exists a threshold and perturbation such that for some (x, y)”? Or “For any threshold and any perturbation then for all (x, y) it holds...”? Or something in-between?\n* For the “competing methods” paragraph, please cite the relevant papers in the main text, not only in the appendix.\n* “over 4 runs” did you randomize the data noise in each run (and in the same way for each method?), or only the network initialisation?\n* Table 5 is cool, but it raises the question: is 1.1epsilon the best, or would performance keep going up?\n* Looking at the actual implementation of LTEC (Algorithm 4), I cannot resist the thought that M=infinity could work even better (at no extra cost): just maintain a monotonically shrinking set of samples?\n\nMinor comments:\n- Define the threshold symbol in section 3.2\n- Define M in Algorithm 1\n- Define (initial) \\mathcal{P}_0 in Algorithm 4\n- Fig 2: can you clarify what green is, does it correspond to “self-training”? \n- “label precision … does not decrease” -- well, not a lot, but it does decrease!\n- Fig 1, Fig 2: set max y to 100\n- Table 4: Include M=1 (which is self-training) for comparison", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I carefully checked the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "N/A"}, "extra_text": {}}, {"review_id": "SyxRhFeaYH", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": null, "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "In this paper, the authors proposed to identify noisy training examples using ensemble consensus. The authors argued and demonstrated through numeric studies that, to the contrary of some earlier work, training examples with low training loss are not necessarily mislabeled. Rather, the authors hypothesized that examples with high noise require memorization, which is sensitive to perturbations. Thus, the authors proposed to identify and subsequently remove those examples from training by looking at the loss after small perturbations to the model parameters. Examples with consistently low training loss are retained for training. The authors also provided several alternatives of perturbations, including examining the consensus between an ensemble of networks, between multiple stochastic predictions, or between predictions from prior training epochs. Finally, the authors demonstrated the performance of their procedures using numerical studies.\n\nThis paper is well motivated and clearly presented. The idea of identifying noisy examples through ensemble consensus is novel and plausible. The numerical studies are relatively comprehensive and in-depth. I think this is a solid conference paper.\n\nSome questions:\n1. The authors proposed to perturb model parameters in order to find noisy training examples. Is there any reason that the authors did not perturb feature values in order to find noisy training examples? I would suppose that memorized examples are sensitive to feature value perturbation.\n2. The intersection of small-loss examples in Line 13 of Algorithm 1 could be much smaller than (1 - epsilon / 100) * Bb, and could vary in size throughout training. Are there computationally efficient methods that can guarantee the size of the intersection is stable and not too small? I suppose that we do not want the mini-batch size to vary too much throughout training.\n3. How to distinguish hard-to-classify, high-loss examples from high-noise, low-loss examples in Line 11 of Algorithm 1? Using the proposed algorithm, in addition to the noisy low-loss examples, we will also remove those hard-to-classify examples, which is arguably undesirable.\n3. The authors should clearly discuss the computational complexity and space complexity of their proposals.", "extra_scores": {"experience_assessment": "I have read many papers in this area.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I carefully checked the derivations and theory."}, "extra_text": {}}, {"review_id": "BJgtvXIzYB", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": null, "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": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Caveat: I admit that I am not incredibly familiar with this particular research area, so I am probably not the best person to review this paper.  I am not certain what part of the matching and bidding process ended up with this paper assigned to me.\n\nThis paper presents a method for filtering out noisy training examples, assuming that there is a known percentage of label noise present in the data.  The gist of the method is to repeatedly perturb the weights in the network slightly, and only accept as training data examples that consistently get small loss across all perturbations.  The intuition is that the loss for noisily labeled examples will not be stable under these perturbations, so using an ensemble of perturbed models should find the label noise.  This intuition seems reasonable enough, and the method seems straightforward.\n\nThe reason I am giving a \"weak reject\" score is largely because the experiments seem weak to me.  It seems pretty unrealistic to randomly corrupt 20% or more of your data.  In what scenario will you actually have data that has 20%+ label noise?  If you actually have one, why not use that to show the effectiveness of your method, instead of an artificial setting?  You have shown that your method achieves better performance in a contrived setting, but in order for it to actually be _useful_, it needs to work on real data, which hasn't been shown.\n\nOne example of a real scenario where you might have a very high degree of label noise is in weakly-supervised semantic parsing.  This paper (https://openreview.net/forum?id=ryxjnREFwH), for example, uses confidence thresholding (though without an ensemble) to filter the training data.  It might be fruitful for you to try demonstrating the benefits of your method on this kind of task.\n\nMinor issues:\n\nSection 3.2 presents math suggesting that the perturbations are additive, with deltas drawn from some distribution.  Section 3.3 then presents the actual perturbation methods, which seem difficult to characterize as drawing a delta from a distribution.\n\nSection 4.3 - citations for the baseline methods should be in the main paper, not only in the appendix.\n\nSome things weren't explained well enough for the paper to be self-contained.  For example, the description of LSEC says that there are \"stochastic operations\", but these are not described anywhere, even with a simple sentence.  Instead the reader must refer to another paper.", "extra_scores": {"experience_assessment": "I do not know much about this area.", "review_assessment:_checking_correctness_of_derivations_and_theory": "I did not assess the derivations or theory.", "review_assessment:_checking_correctness_of_experiments": "I assessed the sensibility of the experiments.", "review_assessment:_thoroughness_in_paper_reading": "I read the paper at least twice and used my best judgement in assessing the paper."}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposes an ensemble method to identify noisy labels in the training data of supervised learning.  The underlying hypothesis is that examples with label noise require memorization.  The paper proposes methods to identify and remove bad training examples by retaining only the training data that maintains low losses after perturbations to the model parameters.  This idea is developed in several candidate ensemble algorithms.  One of the proposed ensemble methods exceeds the performance of state-of-the-art methods on MNIST, CIFAR-10 and CIFAR-100.

The reviewers found several strengths and a few weaknesses in the paper.  The paper was well motivated and clear.  The proposed solution was novel and plausible.  The experiments were comprehensive.  The reviewers identified several parts of the paper that could be more clear or where more detail could be provided, including a complexity analysis and 
extended experiments.  The author response addressed the reviewer questions directly and also in a revised document.  In the discussion phase, the reviewers were largely satisfied that their concerns were addressed.

This paper should be accepted for publication as the paper presents a clear problem and solution method along with convincing evidence of method's merits.

Decision: Accept (Poster)