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Title: SELF: Learning to Filter Noisy Labels with Self-Ensembling

Paper content:
Deep neural networks (DNNs) have been shown to over-fit a dataset when being trained with noisy labels for a long enough time.
To overcome this problem, we present a simple and effective method self-ensemble label filtering (SELF) to progressively filter out the wrong labels during training.
Our method improves the task performance by gradually allowing supervision only from the potentially non-noisy (clean) labels and stops learning on the filtered noisy labels.
For the filtering, we form running averages of predictions over the entire training dataset using the network output at different training epochs.
We show that these ensemble estimates yield more accurate identification of inconsistent predictions throughout training than the single estimates of the network at the most recent training epoch.
While filtered samples are removed entirely from the supervised training loss, we dynamically leverage them via semi-supervised learning in the unsupervised loss.
We demonstrate the positive effect of such an approach on various image classification tasks under both symmetric and asymmetric label noise and at different noise ratios.
It substantially outperforms all previous works on noise-aware learning across different datasets and can be applied to a broad set of network architectures.
The acquisition of large quantities of a high-quality human annotation is a frequent bottleneck in applying DNNs.
There are two cheap but imperfect alternatives to collect annotation at large scale: crowdsourcing from non-experts and web annotations, particularly for image data where the tags and online query keywords are treated as valid labels.
Both these alternatives typically introduce noisy (wrong) labels.
While Rolnick et al. (2017) empirically demonstrated that DNNs can be surprisingly robust to label noise under certain conditions, Zhang et al. (2017) has shown that DNNs have the capacity to memorize the data and will do so eventually when being confronted with too many noisy labels.
Consequently, training DNNs with traditional learning procedures on noisy data strongly deteriorates their ability to generalize -a severe problem.
Hence, limiting the influence of label noise is of great practical importance.
A common approach to mitigate the negative influence of noisy labels is to eliminate them from the training data and train deep learning models just with the clean labels (Frénay & Verleysen, 2013) .
Employing semi-supervised learning can even counteract the noisy labels (Laine & Aila, 2016; Luo et al., 2018) .
However, the decision which labels are noisy and which are not is decisive for learning robust models.
Otherwise, unfiltered noisy labels still influence the (supervised) loss and affect the task performance as in these previous works.
They use the entire label set to compute the loss and severely lack a mechanism to identify and filter out the erroneous labels from the labels set.
In this paper, we propose a self-ensemble label filtering (SELF) framework that identifies potentially noisy labels during training and keeps the network from receiving supervision from the filtered noisy labels.
This allows DNNs to gradually focus on learning from undoubtedly correct samples even with an extreme level of noise in the labels (e.g., 80% noise ratio) and leads to improved performance as the supervision become less noisy.
The key contribution of our work is progressive filtering, i.e., leverage the knowledge provided in the network's output over different training iterations to form a consensus of predictions (self-ensemble predictions) to progressively identify and filter out the noisy labels from the labeled data.
When learning under label noise, the network receives noisy updates and hence fluctuates strongly.
Such conduct of training would impede to learn stable neural representations and further mislead the consensus of the predictions.
Therefore, it is essential to incorporate a model with stable training behavior to obtain better estimates from the consensus.
Concretely, we employ the semi-supervised technique as a backbone to our framework to stabilize the learning process of the model.
Correctly, we maintain the running average model, such as proposed by Tarvainen & Valpola (2017) , a.k.a.
the Mean-Teacher model.
This model ensemble learning provides a more stable supervisory signal than the noisy model snapshots and provides a stable ground for progressive filtering to filter out potential noisy labels.
Note that this is different from just a mere combination of semi-supervised techniques with a noisy label filtering method.
We call our approach self-ensemble label filtering (SELF) -that establishes model ensemble learning as a backbone to form a solid consensus of the self-ensemble predictions to filter out the noisy labels progressively.
Our framework allows to compute supervised loss on cleaner subsets rather than the entire noisy labeled data as in previous works.
It further leverages the entire dataset, including the filtered out erroneous samples in the unsupervised loss.
To best of our knowledge, we are the first to identify and propose self-ensemble as a principled technique against learning under noisy labels.
Our motivation stems from the observation that DNNs start to learn from easy samples in initial phases and gradually adapt to hard ones during training.
When trained on wrongly labeled data, DNNs learn from clean labels at ease and receive inconsistent error signals from the noisy labels before over-fitting to the dataset.
The network's prediction is likely to be consistent on clean samples and inconsistent or oscillates strongly on wrongly labeled samples over different training iterations.
Based on this observation, we record the outputs of a single network made on different training epochs and treat them as an ensemble of predictions obtained from different individual networks.
We call these ensembles that are evolved from a single network self-ensemble predictions.
Subsequently, we identify the correctly labeled samples via the agreement between the provided label set and our running average of self-ensemble predictions.
The samples of ensemble predictions that agree with the provided labels are likely to be consistent and treated as clean samples.
In summary, our SELF framework stabilizes the training process and improves the generalization ability of DNNs.
We evaluate the proposed technique on image classification tasks using CI-FAR10, CIFAR100 & ImageNet.
We demonstrate that SELF consistently outperforms the existing approaches on asymmetric and symmetric noise at all noise levels, as shown in Fig. 1 .
Besides, SELF remains robust towards the choice of the network architecture.
Our work is transferable to other tasks without the need to modify the architecture or the primary learning objective.
Figure 2: Overview of the self-ensemble label filtering (SELF) framework.
The model starts in iteration 0 with training from the noisy label set.
During training, the model maintains a selfensemble, a running average of itself (Tarvainen & Valpola, 2017) to provide a stable learning signal.
Also, the model collects a self-ensemble prediction (moving-average) for the subsequent filtering.
Once the best model is found, these predictions identify and filter out noisy labels using the original label set L 0 .
The model performs this progressive filtering until there is no more better model.
For details see Algorithm 1.
2 SELF-ENSEMBLE LABEL FILTERING 2.1 OVERVIEW Fig. 2 shows an overview of our proposed approach.
In the beginning, we assume that the labels of the training set are noisy.
The model attempts to identify correct labels progressively using selfforming ensembles of models and predictions.
Since wrong labels cause strong fluctuations in the model's predictions, using ensembles is a natural way to counteract noisy labels.
Concretely, in each iteration, the model learns from a detected set of potentially correct labels and maintains a running average of model snapshots (realized by the Mean Teacher model Tarvainen & Valpola (2017) ).
This ensemble model is evaluated on the entire dataset and provides an additional learning signal for training the single models.
Additionally, our framework maintains the runningaverage of the model's predictions for the filtering process.
The model is trained until we find the best model w.r.t.
the performance on the validation set (e.g., by early-stopping).
The set of correct labels is detected based on the strategy defined in Sec. 2.2.
In the next iteration, we again use all data and the new filtered label set as input for the model training.
The iterative training procedure stops when no better model can be found.
In the following, we give more details about the combination of this training and filtering procedure.
Progressive detection of correctly labeled samples Our framework Self-Ensemble Label Filtering (Algorithm 1) focuses on the detection of certainly correct labels from the provided label set L 0 .
In each iteration i, the model is trained using the label set of potentially correct labels L i .
At the end of each iteration, the model determines the next correct label set L i+1 using the filtering strategy described in 2.2 The model stops learning when no improvement was achieved after training on the refined label set L i+1 .
In other words, in each iteration, the model attempts to learn from the easy, in some sense, obviously correct labels.
However, learning from easy samples also affects similar but harder samples from the same classes.
Therefore, by learning from these easy samples, the network can gradually distinguish between hard and wrongly-labeled samples.
identify it as noisy label & remove from label set end if end for
train Mean-Teacher model on filtered label set end while return M best Our framework does not focus on repairing all noisy labels.
Although the detection of wrong labels is sometimes easy, finding their correct hidden label might be extremely challenging in case of having many classes.
If the noise is sufficiently random, the set of correct labels will be representative to achieve high model performance.
Further, in our framework, the label filtering is performed on the original label set L 0 from iteration 0.
Clean labels erroneously removed in an earlier iteration (e.g., labels of hard to classify samples) can be reconsidered for model training again in later iterations.
The model can determine the set of potentially correct labels L i based on agreement between the label y and its maximal likelihood predictionŷ|x with L i = {(y, x) |ŷ x = y; ∀(y, x) ∈ L 0 }.
L 0 is the label set provided in the beginning, (y, x) are the samples and their respective noisy labels in the iteration i. In other words, the labels are only used for supervised training if in the current epoch, the model predicts the respective label to be the correct class with the highest likelihood.
In practice, our framework does not useŷ(x) of model snapshots for filtering but a moving-average of the ensemble models and predictions to improve the filtering decision.
The model's predictions for noisy samples tend to fluctuate.
For example, take a cat wrongly labeled as a tiger.
Other cat samples would encourage the model to predict the given cat image as a cat.
Contrary, the wrong label tiger regularly pulls the model back to predict the cat as a tiger.
Hence, using the model's predictions gathered in one single training epoch for filtering is sub-optimal.
Therefore, in our framework SELF, our model relies on ensembles of models and predictions.
Model ensemble with Mean Teacher A natural way to form a model ensemble is by using an exponential running average of model snapshots (Fig. 3a) .
This idea was proposed in Tarvainen & Valpola (2017) for semi-supervised learning and is known as the Mean Teacher model.
In our framework, both the mean teacher model and the normal model are evaluated on all data to preserve the consistency between both models.
The consistency loss between student and teacher output distribution can be realized with Mean-Square-Error loss or Kullback-Leibler-divergence.
More details for training with the model ensemble can be found in Appendix A.1
Prediction ensemble Additionally, we propose to collect the sample predictions over multiple training epochs: z j = αz j−1 + (1 − α)ẑ j , whereby z j depicts the moving-average prediction of sample k at epoch j, α is a momentum,ẑ j is the model prediction for sample k in epoch j.
This scheme is displayed in Fig. 3b .
For each sample, we store the moving-average predictions, accumulated over the past iterations.
Besides having a more stable basis for the filtering step, our proposed procedure also leads to negligible memory and computation overhead.
Further, due to continuous training of the best model from the previous model, computation time can be significantly reduced, compared to re-training the model from scratch.
On the new filtered dataset, the model must only slowly adapt to the new noise ratio contained in the training set.
Depending on the computation budget, a maximal number of iterations for filtering can be set to save time.
3 RELATED WORKS Reed et al. (2014) ; Azadi et al. (2015) performed early works on learning robustly under label noise for deep neural networks.
Recently, Rolnick et al. (2017) have shown for classification that deep neural networks come with natural robustness to label noise following a particular random distribution.
No modification of the network or the training procedure is required to achieve this robustness.
Following this insight, our framework SELF relies on this natural robustness to kickstart the self-ensemble filtering process to extend the robust behavior to more challenging scenarios.
Laine & Aila (2016); Luo et al. (2018) proposed to apply semi-supervised techniques on the data to counteract noise.
These and other semi-supervised learning techniques learn from a static, initial set of noisy labels and have no mechanisms to repair labels.
Therefore, the supervised losses in their learning objective are typically high until the model strongly overfits to the label noise.
Compared to these works, our framework performs a variant of self-supervised label corrections.
The network learns from a dynamic, variable set of labels, which is determined by the network itself.
Progressive filtering allows the network to (1) focus on a label set with a significantly lower noise ratio and (2) repair wrong decisions made by itself in an earlier iteration.
Other works assign weights to potentially wrong labels to reduce the learning signal (Jiang et al., 2017; Jenni & Favaro, 2018) .
These approaches tend to assign less extreme weights or hyperparameters that are hard to set.
Since the typical classification loss is highly non-linear, a lower weight might still lead to learning from wrong labels.
Compared to these works, the samples in SELF only receive extreme weights: either they are zero or one.
Further, SELF focuses only on self-detecting the correct samples, instead of repairing the wrong labels.
Typically, the set of correct samples are much easier to detect and are sufficiently representative to achieve high performance.
Han et al. (2018b); Jiang et al. (2017) employ two collaborating and simultaneously learning networks to determine which samples to learn from and which not.
However, the second network is free in its predictions and hence hard to tune.
Compared to these works, we use ensemble learning as a principled approach to counteract model fluctuations.
In SELF, the second network is extremely restricted and is only composed of running averages of the first network.
To realize the second network, we use the mean-teacher model (Tarvainen & Valpola, 2017) as a backbone.
Compared to their work, our self-ensemble label filtering gradually detects the correct labels and learns from them, so the label set is variable.
Further, we do use not only model ensembles but also an ensemble of predictions to detect correct labels.
Other works modify the primary loss function of the classification tasks.
Patrini et al. (2017) estimates the noise transition matrix to correct the loss, Han et al. (2018a) uses human-in-the-loop, Zhang & Sabuncu (2018); Thulasidasan et al. (2019) propose other forms of cross-entropy losses.
The loss modification impedes the transfer of these ideas to other tasks than classification.
Compared to these works, our framework SELF does not modify the primary loss.
However, many tasks rely on the presence of clean labels such as anomaly detection (Nguyen et al., 2019a) or self-supervised and unsupervised learning (Nguyen et al., 2019b) .
The progressive filtering procedure and self-ensemble learning proposed are also applicable in these tasks to counteract noise effectively.
We evaluate our approach on CIFAR-10, CIFAR-100, an ImageNet-ILSVRC on different noise scenarios.
For CIFAR-10, CIFAR-100, and ImageNet, we consider the typical situation with symmetric and asymmetric label noise.
In the case of the symmetric noise, a label is randomly flipped to another class with probability p. Following previous works, we also consider label flips of semantically similar classes on CIFAR-10, and pair-wise label flips on CIFAR-100.
Finally, we perform studies on the choice of the network architecture and the ablation of the components in our framework.
Tab.
6 (Appendix) shows the in-deep analysis of semi-supervised learning strategies combined with recent works.
Overall, the proposed framework SELF outperforms all these combinations.
We compare our work to previous methods from Reed-Hard (Reed et al., 2014 ), S-model (Goldberger & Ben-Reuven, 2016), , Rand.
weights , Bi-level-model (Jenni & Favaro, 2018) , D2L , SL (Wang et al., 2019) , L q (Zhang & Sabuncu, 2018) , Trunc L q (Zhang & Sabuncu, 2018) , ForwardT (Patrini et al., 2017) , DAC (Thulasidasan et al., 2019) , Random reweighting , and Learning to reweight .
For co-teaching (Han et al., 2018b) , MentorNet (Jiang et al., 2017) , JointOpt (Tanaka et al., 2018) , the source codes are available and hence used for evaluation.
and DAC (Thulasidasan et al., 2019) considered the setting of having a small clean validation set of 1000 and 5000 images respectively.
For comparison purposes, we also experiment with a small clean set of 1000 images additionally.
Further, we abandon oracle experiments or methods using additional information to keep the evaluation comparable.
For instance, Forward T (Patrini et al., 2017) uses the true underlying confusion matrix to correct the loss.
This information is neither known in typical scenarios nor used by other methods.
Whenever possible, we adopt the reported performance from the corresponding publications.
The testing scenarios are kept as similar as possible to enable a fair comparison.
All tested scenarios use a noisy validation set with the same noise distribution as the training set unless stated otherwise.
All model performances are reported on the clean test set. (He et al., 2016) with 26 layers with Shake-Shake-regularization (Gastaldi, 2017) .
We use the PyTorch (Paszke et al., 2017) implementation of the network and keep the training settings close to (Tarvainen & Valpola, 2017) .
The network is trained with Stochastic Gradient Descent.
In each filtering iteration, the model is trained for a maximum of 300 epochs, with patience of 50 epochs.
For more training details, see the appendix.
CIFAR-10 and 100 Results for typical uniform noise scenarios with noise ratios on CIFAR-10 and CIFAR-100 are shown in Tab.
1.
More results are visualized in Fig. 1a (CIFAR-10) and Fig. 1b (CIFAR-100).
Our approach SELF performs robustly in the case of lower noise ratios with up to 60% and outperforms previous works.
Although a strong performance loss occurs at 80% label noise, SELF still outperforms most of the previous approaches.
The experiment SELF* using a 1000 clean validation images shows that the performance loss mostly originates from the progressive filtering relying too strongly on the extremely noisy validation set.
ImageNet-ILSVRC Tab.
4 shows the precision@1 and @5 of various models, given 40% label noise in the training set.
Our networks are based on ResNext18 and Resnext50.
Note that MentorNet (Jiang et al., 2017) uses Resnet101 (P@1: 78.25) (Goyal et al., 2017) , which has higher performance compared to Resnext50 (P@1: 77.8) (Xie et al., 2017) on the standard ImageNet validation set.
Despite the weaker model, SELF (ResNext50) surpasses the best previously reported results by more than 5% absolute improvement.
Even the significantly weaker model ResNext18 outperforms MentorNet, which is based on a more powerful ResNet101 network.
Tab.
2 shows more challenging noise scenarios when the noise is not class-symmetric and uniform.
Concretely, labels are flipped among semantically similar classes such as CAT and DOG on CIFAR-10.
On CIFAR-100, each label is flipped to the next class with a probability p.
In these scenarios, our framework SELF also retains high performance and only shows a small performance drop at 40% noise.
The high label noise resistance of our framework indicates that the proposed self-ensemble filtering process helps the network identify correct samples, even under extreme noise ratios.
Previous works utilize a various set of different architectures, which hinders a fair comparison.
Tab.
3 shows the performance of our framework SELF compared to previous approaches.
SELF outperforms other works in all scenarios except for CIFAR-10 with 80% noise.
Typical robust learning approaches lead to significant accuracy losses at 40% noise, while SELF still retains high performance.
Further, note that SELF allows the network's performance to remain consistent across the different underlying architectures.
Tab.
5 shows the importance of each component in our framework.
See Fig. 4a, Fig. 4b for experiments on more noise ratios.
As expected, the Resnet-baseline rapidly breaks down with increasing noise ratios.
Adding self-supervised filtering increases the performance slightly in lower noise ratios.
However, the model has to rely on extremely noisy snapshots.
Contrary, using a model ensemble alone such as in Mean-Teacher can counteract noise on the noisy dataset CIFAR-10.
On the more challenging CIFAR-100, however, the performance decreases strongly.
With self-supervised filtering and model ensembles, SELF (without MVA-pred) is more robust and only impairs performance at 80% noise.
The last performance boost is given by using moving-average predictions so that the network can reliably detect correctly labeled samples gradually.
Tab.
6 shows different semi-supervised learning strategies: entropy learning, mean-teacher combined with recent works.
Note that Co-Teaching+Mean-Teacher cannot be implemented and run in the same configuration as other experiments, due to memory constraints.
The analysis indicates the semi-supervised losses mostly stabilize the baselines, compared to the model without semi-supervised learning.
However, Co-teaching and JointOpt sometimes perform worse than the purely semi-supervised model.
This result indicates that their proposed frameworks are not always compatible with semi-supervised losses.
The progressive filtering technique is seamlessly compatible with different semi-supervised losses.
The filtering outperforms its counterparts when combined with Entropy Learning or Mean-teacher model.
Overall, SELF outperforms all considered combinations.
We propose a simple and easy to implement a framework to train robust deep learning models under incorrect or noisy labels.
We filter out the training samples that are hard to learn (possibly noisy labeled samples) by leveraging ensemble of predictions of the single network's output over different training epochs.
Subsequently, we allow clean supervision from the non-hard samples and further leverage additional unsupervised loss from the entire dataset.
We show that our framework results in DNN models with superior generalization performance on CIFAR-10, CIFAR-100 & ImageNet and outperforms all previous works under symmetric (uniform) and asymmetric noises.
Furthermore, our models remain robust despite the increasing noise ratio and change in network architectures.
We apply the Mean Teacher algorithm in each iteration i in the train(D f ilter , D val ) procedure as follows.
• Input: examples with potentially clean labels D f ilter from the filtering procedure.
In the beginning (i = 0), here D f ilter refers to entire labeled dataset.
• Initialize a supervised neural network as the student model M s i .
• Initialize the Mean Teacher model M t i as a copy of the student model with all weights detached.
• Let the loss function be the sum of normal classification loss of M Natural robustness assumption of deep networks (Rolnick et al., 2017) : The networks attempt to learn the easiest way to explain most of the data.
SELF uses this assumption to kickstart the learning process.
Correct samples dominate over wrongly labeled samples At 80% noise on CIFAR-10, the correctly labeled cats (20% out of all cat images) still dominates over samples wrongly labeled as cat (8.8% for each class).
Independence results in less overfitting SELF performs best if the noises on the validation set and training set are i.i.d. .
SELF uses the validation data for early stopping.
Hence, a high correlation of label noise between train and valid increases the chance of model overfitting.
Sufficient label randomness assumption The subset of all correctly labeled samples capture all samples clusters.
In fact, many works from the active learning literature show that less than 100 % of the labeled samples are required to achieve the highest model performance.
SELF performs progressive expansion of the correct labels sets.
At larger noise ratios, not all clusters are covered by the identified samples.
Therefore on task containing many classes, e.g., CIFAR-100, the model performance decreases faster than on CIFAR-10.
The model performance reduces when these assumptions are strongly violated.
Each assumption should have its own "critical" threshold for violation.
A future in-depth analysis to challenge the assumptions is an interesting future research direction.
A.3.1 CIFAR-10 AND CIFAR-100
Dataset Tab.
7 shows the details of CIFAR-10 and 100 datasets in our evaluation pipeline.
The validation set is contaminated with the same noise ratio as the training data unless stated otherwise.
Network training For the training our model SELF, we use the standard configuration provided by Tarvainen & Valpola (2017) 2 .
Concretely, we use the SGD-optimizer with Nesterov Sutskever et al. (2013) momentum, a learning rate of 0.05 with cosine learning rate annealing Loshchilov & Hutter (2016) , a weight decay of 2e-4, max iteration per filtering step of 300, patience of 50 epochs, total epochs count of 600.
For basic training of baselines models without semi-supervised learning, we had to set the learning rate to 0.01.
In the case of higher learning rates, the loss typically explodes.
Every other option is kept the same.
Semi-supervised learning For the mean teacher training, additional hyperparameters are required.
In both cases of CIFAR-10 and CIFAR-100, we again take the standard configuration with the consistency loss to mean-squared-error and a consistency weight: 100.0, logit distance cost: 0.01, consistency-ramp-up:5.
The total batch-size is 512, with 124 samples being reserved for labeled samples, 388 for unlabeled data.
Each epoch is defined as a complete processing of all unlabeled data.
When training without semi-supervised-learning, the entire batch is used for labeled data.
The data are normalized to zero-mean and standard-variance of one.
Further, we use real-time data augmentation with random translation and reflection, subsequently random horizontal flip.
The standard PyTorch-library provides these transformations.
Network Training The network used for evaluation were ResNet He et al. (2016) and Resnext Xie et al. (2017) for training.
All ResNext variants use a cardinality of 32 and base width of 4 (32x4d).
ResNext models follow the same structure as their Resnet counterparts, except for the cardinality and base width.
All other configurations are kept as close as possible to Tarvainen & Valpola (2017) .
The initial learning rate to handle large batches Goyal et al. (2017) is set to 0.1; the base learning rate is 0.025 with a single cycle of cosine annealing.
Semi-supervised learning Due to the large images, the batch size is set to 40 in total with 20/20 for labeled and unlabeled samples, respectively.
We found the Kullback-divergence leads to no meaningful network training.
Hence, we set the consistency loss to mean-squared-error, with a weight of 1000.
We use consistency ramp up of 5 epochs to give the mean teacher more time in the beginning.
Weight decay is set to 5e-5; patience is four epochs to stop training in the current filtering iteration.
Filtering We filter noisy samples with the topk=5 strategy, instead of taking the maximumlikelihood ( reason is that each image of ImageNet might contain multiple objects.
Filtering with ML-predictions is too strict and would lead to a small recall of the detection of the correct sample.
Data Augmentation For all data, we normalize the RGB-images by the mean: (0.485, 0.456, 0.406) and the standard variance (0.229, 0.224, 0.225).
For training data, we perform a random rotation of up to 10 degrees, randomly resize images to 224x224, apply random horizontal flip and random color jittering.
This noise is needed in regular mean-teacher training.
The jittering setting are: brightness=0.4, contrast=0.4, saturation=0.4, hue=0.1.
The validation data are resized to 256x256 and randomly cropped to 224x224
For the learning of wrongly labeled samples, Fig. 6 shows the relationship between the typical reweighting scheme and our baseline push-away-loss.
Typically, reweighting is applied directly to the losses with samples weights w (k) for each sample k as shown in Eq. 4
D is the dataset, x (k) and y (k) label are the samples k and its noisy label.
w
is the samples weight for the sample k at step i. Negative samples weights w (k) i are often assigned to push the network away from the wrong labels.
Let w
Which results in:
In other words, we perform gradient ascent for wrongly labeled samples.
However, the Negativelog-likelihood is not designed for gradient ascent.
Hence the gradients of wrongly labeled samples vanish if the prediction is too close to the noisy label.
This effect is similar to the training of Generative Adversarial Network (GAN) Goodfellow et al..
In the GAN-framework, the generator loss is not simply set to the negated version of the discriminator's loss for the same reason.
Therefore, to provide a fair comparison with our framework, we suggest the push-away-loss L P ush−away (y
Whereby Y is the set of all classes in the training set.
This loss has improved gradients to push the model away from the potentially wrong labels.
Entropy minimization The typical entropy loss for semi-supervised learning is shown in Fig. 6 .
It encourages the model to provide extreme predictions (such as 0 or 1) for each sample.
Over a large number of samples, the model should balance its predictions over all classes.
The entropy loss can easily be applied to all samples to express the uncertainty about the provided labels.
Alternatively, the loss can be combined with a strict filtering strategy, as in our work, which removes the labels of potentially wrongly labeled samples.
For a large noise ratio, predictions of wrongly labeled samples fluctuate strongly over previous training iterations.
Amplifying these network decisions could lead to even noisier models model.
Combined with iterative filtering, the framework will have to rely on a single noisy model snapshot.
In the case of an unsuitable snapshot, the filtering step will make many wrong decisions.
A.4.1 COMPLETE REMOVAL OF SAMPLES Tab.
8 shows the results of deleting samples from the training set.
It leads to significant performances gaps compared to our strategy (SELF), which considers the removed samples as unlabeled data.
In case of a considerable label noise of 80%, the gap is close to 9%.
Continuously using the filtered samples lead to significantly better results.
The unsupervised-loss provides meaningful learning signals, which should be used for better model training.
(a) (b) Figure 7 : Sample training curves of our approach SELF on CIFAR-100 with (a) 60% and (b) 80% noise, using noisy validation data.
Note that with our approach, the training loss remains close to 0.
Further, note that the mean-teacher continously outperforms the noisy student models.
This shows the positive effect of temporal emsembling to counter label noise.
A.4.2 SAMPLE TRAINING PROCESS Fig. 7 shows the sample training processes of SELF under 60% and 80% noise on CIFAR-100.
The mean-teacher always outperform the student models.
Further, note that regular training leads to rapid over-fitting to label noise.
Contrary, with our effective filtering strategy, both models slowly increase their performance while the training accuracy approaches 100%.
Hence, by using progressive filtering, our model could erase the inconsistency in the provided labels set.

assistant: text: This paper proposes an algorithm for learning from data with noisy labels which alternates between updating the model and removing samples that look like they have noisy labels.