Title: Neural Relation Graph: A Unified Framework for Identifying Label Noise and Outlier Data
Venue: NeurIPS 2023
Accepted: yes
Keywords: Dataset cleaning

Label error detection

Outlier detection

Neural Networks

Robustness
Abstract: Diagnosing and cleaning data is a crucial step for building robust machine learning systems. However, identifying problems within large-scale datasets with real-world distributions is challenging due to the presence of complex issues such as label errors, under-representation, and outliers. In this paper, we propose a unified approach for identifying the problematic data by utilizing a largely ignored source of information: a relational structure of data in the feature-embedded space. To this end, we present scalable and effective algorithms for detecting label errors and outlier data based on the relational graph structure of data. We further introduce a visualization tool that provides contextual information of a data point in the feature-embedded space, serving as an effective tool for interactively diagnosing data. We evaluate the label error and outlier/out-of-distribution (OOD) detection performances of our approach on the large-scale image, speech, and language domain tasks, including ImageNet, ESC-50, and SST2. Our approach achieves state-of-the-art detection performance on all tasks considered and demonstrates its effectiveness in debugging large-scale real-world datasets across various domains. We release codes at https://github.com/snu-mllab/Neural-Relation-Graph.

Neural Relation Graph: A Unified Framework for Identifying Label Noise and Outlier Data

Abstract

Diagnosing and cleaning data is a crucial step for building robust machine learning systems. However, identifying problems within large-scale datasets with real-world distributions is challenging due to the presence of complex issues such as label errors, under-representation, and outliers. In this paper, we propose a unified approach for identifying the problematic data by utilizing a largely ignored source of information: a relational structure of data in the feature-embedded space. To this end, we present scalable and effective algorithms for detecting label errors and outlier data based on the relational graph structure of data. We further introduce a visualization tool that provides contextual information of a data point in the featureembedded space, serving as an effective tool for interactively diagnosing data. We evaluate the label error and outlier/out-of-distribution (OOD) detection performances of our approach on the large-scale image, speech, and language domain tasks, including ImageNet, ESC-50, and SST2. Our approach achieves state-of-theart detection performance on all tasks considered and demonstrates its effectiveness in debugging large-scale real-world datasets across various domains. We release codes at https://github.com/snu-mllab/Neural-Relation-Graph .

1 Introduction

Identifying problems within datasets is crucial for improving the robustness of machine learning systems and analyzing the model failures [45]. For instance, identifying mislabeled or uninformative data helps construct concise and effective training datasets [33], while identifying whether test data is OOD or corrupted allows for more accurate model evaluation and analysis [54].

In recent years, efforts have been made to identify problematic data by utilizing unary scores on individual data from trained models, such as estimating data influence [22], monitoring prediction variability throughout training [52], and calculating prediction error margins [34]. However, identifying such data can be challenging, particularly when dealing with large-scale datasets from real-world distributions. In real-world settings, datasets may have complex problems, including label errors, under-representation, and outliers, each of which can lead to the model error and prediction sensitivity [23]. For example, Figure 1 shows that a neural network exhibits low negative prediction margins and high loss values for both a sample with label error and outlier data. This observation indicates that previous unary scoring methods may have limitations in discerning whether the problem lies with the label or the data itself.

In this work, we propose a unified framework for identifying label errors and outliers by leveraging the feature-embedded structure of a dataset that provides richer information than individual data alone [47, 36]. We measure the relationship among data in the feature embedding space while comparing the assigned labels independently. By comparing input data and labels separately, we are able to

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isolate the factors contributing to model errors, resulting in improved identification of label errors and outlier data, respectively. Based on the relational information, we construct a novel graph structure on the dataset and identify whether the data itself or the label is problematic (Figure 2). To this end, we develop scalable graph algorithms that accurately identify label errors and outlier data points.

In Section 3.5, we further introduce a visualization tool named data relation map that captures the relational structure of a data point. Through the map, we can understand the underlying relational structure and interactively diagnose data. In Figure 1, we observe different patterns in the relation maps of the second and third samples, despite their similar margin and loss scores. This highlights that the relational structure provides complementary information not captured by the unary scoring methods.

Our approach only requires the model's feature embedding and prediction score on data, making it more scalable compared to methods that require calculating the network gradient on each data point or retraining models multiple times to estimate data influence [39, 17]. Furthermore, our method is domain- and model-agnostic, and thus is applicable to various tasks. We evaluate our approach on label error and outlier/OOD detection tasks with large-scale image, speech, and language datasets: ImageNet [43], ESC-50 [37], and SST2 [55]. Our experiments show state-of-the-art performance on all tasks, demonstrating its effectiveness for debugging and cleaning datasets over various domains.

2 Related works

Label error detection Label errors in datasets can negatively impact model generalization and destabilize evaluation systems [16, 34]. Prior works address this issue through label error detection using bagging and bootstrapping [46, 41], or employing neural networks [18, 27, 9, 19]. To mitigate overfitting on label errors, Pleiss et al. [38] propose tracking the training process to measure the area under the margin curve. Recent studies demonstrate that simple scoring methods with large pre-trained models, such as prediction margins or loss values, achieve comparable results to previous complex approaches [33, 5]. Meanwhile, Wu et al. [57] propose a unified approach for learning with open-world noisy data. However, the method involves a complicated optimization process during training, which is not suitable for large-scale settings. Another line of approach to identifying label errors involves measuring the influence of a training data point on its own loss [22, 39]. However, these approaches require calculating computationally expensive network gradients on each data point, and their performance is known to be sensitive to outliers and training schemes [2, 3]. In this work, we present a scalable approach that leverages the data relational structure of trained models without additional training procedures, facilitating practical analysis of label issues.

Outlier/OOD detection Detecting outlier data is crucial for building robust machine learning systems in real-world environments [23]. A recent survey paper defines the problem of finding outliers in training set as outlier detection and finding outliers in the inference process as OOD detection [59]. The conventional approach for detecting outliers involves measuring k-nearest distance using efficient sampling methods [48]. More recently, attempts have been made to detect outlier data using scores obtained from trained neural networks, such as Maximum Softmax Probability [14], Energy score [29], and Max Logit score [15]. Other approaches suggest adding perturbations on the inputs or rectifying the activation values to identify the outlier data [28, 49]. Lee et al. [26] propose fitting a Gaussian probabilistic model to estimate the data distribution. Recently, Sun et al. [50] propose a non-parametric approach measuring the k -nearest feature distance. In our work, we explore the use of the relational structure on the feature-embedded space for identifying outlier data. Our approach is applicable to a wide range of domains without requiring additional training while outperforming existing scoring methods on large-scale outlier/OOD detection benchmarks.

3 Methods

In this section, we describe our method for identifying label errors and outliers using a model trained on the noisy training dataset. We exploit the feature-embedded structure of the learned neural networks, which are known to effectively capture the underlying semantics of the data [40]. We define data relation to construct a data relation graph on the feature space, and introduce our novel graph algorithms for identifying label errors and outlier data. In Section 3.5, we introduce the data relation map as an effective visualization tool for diagnosing and contextualizing data.

3.1 Data relation

We describe our approach in the context of a classification task, while also noting that the ideas are generalizable to other types of tasks as well. We assume the presence of a trained neural network on a noisy training dataset with label errors and outliers, T = { ( x i , y i ) | i = 1 , . . . , n } . By utilizing data features extracted from the network, we measure the semantic similarity between data points with a bounded kernel k : X × X → [0 , M ] , where a higher kernel value indicates greater similarity between data points. Our framework can accommodate various bounded kernels such as RBF kernel or cosine similarity [60]. We provide detailed information on the kernel function used in our main experiments in Section 3.4.

By incorporating the assigned label information with the similarity kernel k , we define the relation function r : X × Y × X × Y → [ -M,M ] :

where 1( y i = y j ) ∈ {-1 , 1 } is a signed indicator value. The relation function reflects the degree to which data samples are complementary or conflicting with each other. In Figure 3, the center image with a label error has negative relations to the left samples that belong to the same ground-truth class. In contrast, the two left samples with correct labels have a positive relation. We also note that samples with dissimilar semantics exhibit near-zero relations.

Our relation function r relies solely on the parallelizable forward computation of neural networks, ensuring scalability in large-scale settings.

3.2 Label error detection

Weconsider a fully-connected undirected graph G = ( V , E , W ) , where the set of nodes V corresponds to T and the weights W on edges E are the negative relation values defined in Equation (1). For notation clarity, we denote a data point by an index, i.e. , T = { 1 , . . . , n } . Then, for nodes i and j , the edge weight is w ( i, j ) = -r ( i, j ) = -r (( x i , y i ) , ( x j , y j )) . We set w ( i, i ) to 0, which does not

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correspond to any edges in the graph. Consistent with previous works [33], we aim to measure the label noisiness score for each data, where a higher score indicates a higher likelihood of label error. We denote the label noisiness scores for T as s ∈ R n , where s [ i ] is the score for data i .

As depicted in Figure 3, data with label errors exhibit negative relations with other samples, implying that the data have similar features in the embedding space yet have dissimilarly assigned labels. This suggests that the edge weights w ( i, · ) quantify the extent to which the label assigned to node i conflicts with the labels of other nodes. However, simply aggregating all edge weights of a node can yield suboptimal results, as negative relations can also contribute to the score for clean data, as shown in Figure 3. In Appendix D.2, we provide a more detailed experimental analysis of this issue.

To rectify this issue, we develop an algorithm that considers the global structure of the graph instead of simply summing the edge weights of individual nodes. Specifically, we identify subsets of data likely to have correct/incorrect labels and calculate the label noisiness score based on the subsets. We partition the nodes in T into two groups, where N ⊂ T denotes the estimated noisy subset and T \N denotes the clean subset. To optimize N , we aim to maximize the sum of the edges between the two groups, indicating that the label information of the two groups is the most conflicting. To ensure that N contains data with incorrect labels, which constitute a relatively small proportion of T , we impose regularization to the cardinality of N with λ ≥ 0 and formulate the following max-cut problem:

The max-cut problem is NP-complete [11]. To solve this problem, we adopt the Kerninghan-Lin algorithm, which finds a local optimum by iteratively updating the solution [20]. However, the original algorithm that swaps data one by one at each optimization iteration is not suitable for large-scale settings. To this end, we propose an efficient set-level algorithm in Algorithm 1 that alternatively updates the noisy set N and label noisiness score vector s .

Specifically, given the current estimation of N , the cut value excluding edges of node i ∈ T is cut ( N\{ i } , T \N\{ i } ) . Algorithm 1 measures the label noisiness score of node i by comparing the objective cut values when including i in N and when including i in T \N :

Here we use the assumption w ( i, i ) = 0 . In practice, the cardinality of N is small, so we can efficiently update the score vector s by caching the initial score vector ¯ s as in Algorithm 1. After calculating the score vector s , we update the noisy set N by selecting nodes with score values above the value λ . Figure 4 illustrates the optimization process. Here larger values of λ result in smaller N consisting of data samples that are more likely to have label noise. We provide the sensitivity analysis of λ in Appendix C.1, with Table 7.

Algorithm 1 satisfies the convergence property in Proposition 1. In Appendix A, we provide proof and present an empirical convergence analysis on large-scale datasets. We also conduct a runtime

Algorithm 1 Label noise identification

analysis of our algorithm in Appendix A.3, demonstrating that the computation overhead of Algorithm 1 is negligible in large-scale settings.

Proposition 1. Algorithm 1 with a single node update at each iteration converges to local optimum.

Complexity analysis The time complexity of Algorithm 1 is O ( n 2 ) , proportional to the number of edges in a graph. It is noteworthy that our method maintains the best performance when used with graphs consisting of a small number of nodes, as shown in Figure 5. This implies that we can partition large datasets and run the algorithm repeatedly for each partition to enhance efficiency while maintaining performance. In this case, the complexity becomes O ( n/k · k 2 ) = O ( nk ) , with k representing the size of each partition and n/k being the number of partitions. Also, computations on these partitions are embarrassingly parallelizable, meaning that the complexity becomes O ( k 2 ) for k ≪ n in distributed computing environments.

3.3 Outlier/OOD detection

In the previous section, we presented a method for detecting label errors based on data relations with similar feature embeddings but different label information. By employing the identical feature embedding structure, we identify outlier data by measuring the extent to which similar data are absent in the feature embedding space. To quantify the extent of a data point being an outlier, we aggregate the similarity kernel values of a data point in Equation (3), thereby processing the entire relational information of the data point. Our approach leverages global information about the data distribution, resulting in a more robust performance across a range of experimental settings compared to existing methods that rely on local information such as k -nearest distance [50]. Specifically, for a subset S ⊆ T and data x , we measure the outlier score as

Higher values in the outlier score indicate that the data are more distributionally outliers. We propose to use a uniform random sampling for S , adjusting the computational cost and memory requirements for the outlier score calculation to suit the inference environment. In Section 4.2, we verify our method maintains the best OOD detection performance even when using only 0.4% of the data in ImageNet.

3.4 Proposed similarity kernel

For x i ∈ X , we extract the feature representation f i and the prediction probability vector p i from the trained model. We propose a class of bounded kernel k : X × X → [0 , M ] with the following form:

A positive scalar value t controls the sharpness of the kernel value distribution. A larger value of t makes a small kernel value smaller, which is effective in handling small noisy kernel values. A scalar value s ( f i , f j ) ∈ R + denotes a similarity measurement between features. In our main experiments, we adopt the truncated cosine-similarity that has been widely used in representation learning [44, 42]. We use the hinge function at zero, resulting in the following positive feature-similarity function:

It is worth noting the utility of our framework is not limited to a specific kernel design. In Section 4.3, we verify our approach maintains the best performance with s ( f i , f j ) defined as the RBF kernel [60].

While the feature similarity captures the meaningful semantic relationship between data points, we observe that considering the prediction scores p i can further improve the identification of problematic data. To incorporate prediction scores into our approach, we introduce a scalar term c ( p i , p j ) that measures the compatibility between the predictions on data points. Any positive and bounded compatibility function is suitable for the kernel class defined in Equation (3). In our main experiments, we use the predicted probability of belonging to the same class as the compatibility term c ( p i , p j ) . Specifically, given the predicted label random variables ˆ y i and ˆ y j , the proposed compatibility term is

From a different perspective, we interpret this term as a measure of confidence for feature similarity. In Section 4.3, we verify the effectiveness of the compatibility term through an ablation study.

Interpretation To better understand our relation function with kernel defined in Equation (3), we draw a connection to the influence function [39], which estimates the influence between data points by computing the inner product of the network gradient on the loss function ℓ of each data point as ∇ w ℓ ( x i ) ⊺ ∇ w ℓ ( x j ) , where w denotes the network weights. Following the convention, we consider an influence function on the feed-forward layer, where ℓ ( x i ) = h ( f ′ i ) = h ( w ⊺ f i ) . By the chain rule, we can decompose the network gradient as ∇ w ℓ ( x i ) = ∇ f ′ h ( f ′ i ) f ⊺ i , and represent the influence as ∇ f ′ h ( f ′ i ) ⊺ ∇ f ′ h ( f ′ j ) · f ⊺ i f j . Our relation function differs from the influence function in that it does not rely on feature gradients ∇ f ′ h ( f ′ i ) to evaluate the relationship between data points. Instead, our relation function compares model predictions and assigned labels independently using the terms c ( p i , p j ) and 1( y i , y j ) . Our formulation does not require computationally expensive back-propagation and more robustly identifies conflicting data information than influence functions which are known to be sensitive to outliers [2]. We provide a more detailed theoretical analysis in Appendix A.4.

3.5 Data relation map

In this section, we present a visualization method based on our data relation function to contextualize data and comprehend its relational structure. One of the effective approaches for visualizing a dataset is dataset cartography [51], which projects the dataset onto a 2D plot. This approach draws a scatter plot of the mean and standard deviation of the model's prediction probabilities for each data sample during training. Inspired by the dataset cartography, we propose a data relation map , which visualizes the relationship between data along the training process. To this end, we uniformly store checkpoints during training. We denote a set of these checkpoints as K , where r k refers to the relation function for checkpoint k ∈ K . For each data sample i ∈ T , we draw a scatter plot of the mean and standard deviation of relation values { r k ( i, j ) | k ∈ K} for j ∈ T \{ i } .

In Figure 1, we provide relation maps of three samples from ImageNet, using 10 checkpoints of MAE-Large [13]. The three samples each represent clean data, data with a label error, and outlier data. From the figure, samples show different relation map patterns. Specifically, the relation map of a clean data sample exhibits a majority of positive relations with relatively small variability. We note that there are gray-colored relations in high variability regions (0.2 < std), indicating that the model resolves conflicting relations at convergence. On the other hand, the relation map of the sample with a label error demonstrates a majority of negative relations. Notably, high variance relations result in largely negative relations at convergence, suggesting that conflicts intensify. Lastly, the relation map of the outlier data sample reveals that relations are close to 0 during training. These relation maps can serve as a model-based fingerprint of the data, which our algorithm effectively exploits to identify problematic data. We provide additional data relational maps for various models in Appendix E.1.

4 Experimental results

In this section, we experimentally verify the effectiveness of our approach in detecting label errors and outliers. We provide implementation details, including hyperparameter settings in Appendix C.1. We provide qualitative results including detected label errors and outlier samples in Appendix E.2.

4.1 Label error detection

4.1.1 Setting

Datasets We conduct label error detection experiments on large-scale datasets: ImageNet [43], ESC-50 [37], and SST2 [55]. ImageNet consists of about 1.2M image data from 1,000 classes. ESC-50 consists of 2,000 5-second environmental audio recordings organized into 50 classes. SST2 is a binary text sentiment classification dataset, consisting of 67k movie review sentences. We also conduct experiments on MNLI [55] and provide results in Appendix, Table 13.

Following Pruthi et al. [39], we construct a noisy training set by flipping labels of certain percentages of correctly classified training data with the top-2 prediction of the trained model. We use different neural network architectures for constructing a noisy training set and detecting label errors to avoid possible correlation. We leave a more detailed procedure for constructing the noisy training set in Appendix C.2. When training the MAE-Large model [13] on ImageNet with 8% label noise, the validation top1-accuracy decreases by 1.7% compared to the performance of the model trained on the orig-

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inal training set, as reported in Appendix Table 8. The decrease becomes more significant with 15% label noise, with a drop of 4.4%, highlighting the importance of label noise detection and cleaning.

Baselines We compare our method ( Relation ) to six baselines that are suitable for large-scale datasets. We consider fine-tuned loss from pre-trained models ( Loss ) [5], prediction probability margin score ( Margin ) [33], and the influence-based approach called TracIn [39]. We also evaluate modelagnostic scoring methods: Entropy , Least-confidence , and Confidence-weighted Entropy ( CWE ) [24]. For a fair comparison, we evaluate methods using a single converged neural network in our main experiments, while also providing results with a temporal ensemble suggested by [39] in Appendix D.1.

Metric We evaluate the detection performance based on label noisiness scores by each method. We note that detecting label errors is an imbalanced detection problem, which makes the AUROC metric prone to being optimistic and misleading [7]. In this respect, we mainly report the AP (average precision) and TNR95 (TNR at 0.95 TPR), and provide AUROC results in Appendix D.3.

4.1.2 Results and analysis

ImageNet We measure the label error detection performance on ImageNet with the synthetic label noise by training an MAE-Large model [13]. Note that the model does not have access to information about the changed clean labels during the entire training process. Figure 5 (a) shows the detection performance over a wide range of label noise ratios from 4% to 15%. As shown in the figure, our approach achieves the best AP and TNR95 performance compared to the baselines. Especially, our method maintains a high TNR95 over a wide range of noise ratios, indicating that the number of data that need to be reviewed by human annotators is significantly smaller when cleaning the dataset. In Figure 9, we present detected label error samples by our algorithm.

It is worth noting that our method relies on the number of data for constructing a relation graph. To measure the sensitivity of our algorithm to the number of data, we evaluate the detection performance using a reduced number of data with uniform random sampling. Figure 5 (b) shows the detection performance on 8% label noise with MAE-Large. From the figure, we find that our algorithm maintains the best detection performance even with 1% of the data (12k). This demonstrates that our algorithm is effective even when only a small portion of the training data is available, such as continual learning or federated learning [35, 32]. In Table 1 (a), we provide detection performance for different scales of MAE models on 8% label noise. The table shows our approach achieves the best AP with MAE-Base, verifying the robustness of our approach to the network scales. From the table, we note that larger models are more robust to label noise and show better detection performance.

Speech and language domains We apply our method to speech and language domain datasets: ESC-50 [37] and SST2 [55]. We design the label noise detection settings identical to the previous ImageNet section. Specifically, we train the AST model [10] for ESC-50 and the RoBERTa-Base model [30] for SST2 under the 10% label noise setting. Table 1 (b) shows our approach achieves the best AP and TNR95 on the speech and language datasets, demonstrating the generality of our approach across various data types.

(a) Model architecture scales

(b) Speech/language domains

(c) Realistic label noise scenario

Realistic label noise The ImageNet validation set is known to contain numerous label errors [34]. To tackle this issue, Beyer et al. [4] cleaned the labels with human experts and corrected around 29% of the labels via multi-labeling. With this re-labeled validation set, we conduct experiments under the realistic label noise, with the task of detecting the data samples with changed labels. We measure the detection performance with MAE-Large [13], BEIT-Large [1], and ConvNeXt-Large [31] models. To examine the impact of pre-training on external data, we also include ConvNeXt pre-trained on ImageNet-22k, denoted as ConvNeXt-22k. We construct the relation graph using only the validation set, considering scenarios where the training data are not available. Table 1 (c) verifies that our approach outperforms the best baseline across various models. The results on ConvNeXt-22k indicate that pre-training on external data improves the detection performance.

Memorization issue We investigate the impact of large neural networks' ability to memorize label errors on detection performance [61]. In the left figure of Figure 6, we find that the AP score decreases as the training progresses after 30 epochs with MAE-Large which converges at 50 epochs. The right figure of Figure 6 plots the precision-recall curves, where we observe that precision increases at low recall area but decreases at mid-level recall ( ∼ 0 . 5 ) as the training progresses. This suggests that training has both positive and negative effects on detecting label noise, and we speculate that memorization

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4.2 Outlier/OOD detection

Baselines We consider the following representative outlier scoring approaches: Maximum Softmax Probability ( MSP ) [14], Max Logit [15], Mahalanobis [26], Energy score [29], ReAct [49], KLMatching [15], and KNN [50]. We tune the KNN method's hyperparameter k based on the paper's guidance as k = 1000 × α , where α represents the ratio of training data used for OOD detection. We also evaluate outlier detection approaches, Iterative sampling [48] and Local outlier factor [56].

OODdetection Following Sun et al. [50], we evaluate OOD detection performance on the ImageNet validation set consisting of 50k in-distribution data samples, along with four distinct OOD datasets: Places [62], SUN [58], iNaturalist [53], and Textures [6]. Each of these OOD datasets consists of 10k data samples except for Textures which has 5,640 data samples. We also combine these four datasets, denoted as ALL , and measure the overall OOD detection performance on this dataset.

Figure 7 shows OOD detection performance of MAE-Large on ALL outlier dataset. Note that our approach and KNN both rely on the number of training data samples ( |S| ) for outlier score calculation. We examine the effect of training set size by measuring the performance with a reduced number of data using uniform random sampling. Figure 7 verifies that our approach outperforms other baselines while maintaining performance even with 0.4% of the training dataset (5k). Note that KNN requires hyperparameter tuning according to the training set size, whereas our approach uses the identical

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hyperparameter ( t = 1 ) regardless of the size. In Appendix D.4, Tables 15 and 16, we provide OOD detection results on four individual OOD datasets as well as the performance with ResNet-50 [12], where our approach achieves the best OOD detection performance over the nine baselines considered.

Outlier detection We perform outlier detection experiments following the methodology by Wang et al. [56], where the training set contains outlier data with random labels. We construct the noisy ImageNet-100 training sets by using iNaturalist [53] and SUN [58] datasets. We train a ViT-Base model [8] from scratch on these noisy training datasets, and measure outlier detection performance using the trained model. For a more detailed description, please refer to Appendix C.3.

Table 2 shows the outlier detection results on two outlier datasets. As indicated, our method achieves the best performance in both outlier settings, demonstrating its effectiveness in outlier detection. It is worth noting that the considered OOD scoring methods (MSP, Max Logit, Energy) do not achieve good outlier detection performance. We speculate that this is due to the overfitting of the neural network's predictions on outliers.

Detecting outliers in validation set We further utilize our method for identifying outliers in the validation set by retrieving data samples with the highest outlier score (Section 3.3). In Figure 10, we present samples detected by our algorithm from ImageNet and SST2. In the figure, we observe that these samples are not suitable for measuring the predictive performance on labels, which should be excluded from the evaluation dataset.

4.3 Ablation study

Temperature t In Equation (3), we introduced a temperature t , where a large value of t increases the influence of large relation values in our algorithm. We conduct sensitivity analysis on t with MAE-Large on ImageNet under 8% label noise. Figure 8 shows the effect of the temperature value

Water ouzel

Junco (-0.754)

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'entertaining and informative documentary"

Impala

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'entertaining movie"

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'fascinating and timely content"

Flute

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Alligator lizard

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'leather pants"

'give a backbone to the company"

'the israeli/palestinian conflict as"

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on our detection algorithm's performance. From the figure, we observe that the label error detection performance increases as the t value increases, saturating at t = 6 . In the case of OOD detection, we achieve the best performance at around t = 1 . Our algorithm outperforms the best baseline over a wide range of hyperparameters, demonstrating the robustness of our algorithm to the hyperparameter.

Similarity kernel design We present an empirical analysis of the kernel design choices. Specifically, we replace the cosine similarity term in Equation (3) as the RBF kernel and evaluate the detection performance. We further conduct an ablation study on compatibility terms (Equation (4)). Table 3 summarizes the label error detection performance with different kernel functions on ImageNet with 8% noise ratio. The table shows that our approach largely outperforms the best baseline even with the RBF

kernel. Also, we find that our approach without the compatibility term shows comparable AP performance while significantly outperforming baselines in TNR95. These results demonstrate the generality and utility of our relational structure-based framework, which is not limited to a specific kernel design.

5 Conclusion

In this paper, we propose a novel data relation function and graph algorithms for detecting label errors and outlier data using the relational structure of data in the feature embedding space. Our approach achieves state-of-the-art performance in both label error and outlier/OOD detection tasks, as demonstrated through extensive experiments on large-scale benchmarks. Furthermore, we introduce a data contextualization tool based on our data relation that can aid in data diagnosis. Our algorithms and tools can facilitate the analysis of large-scale datasets, which is crucial for the development of robust machine-learning systems.

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A Algorithm analysis

A.1 Proof

In this section, we provide proof for Proposition 1. Recall that Algorithm 1 updates an estimated noisy set N at a set-level as N = { i | s [ i ] > λ } . We can conduct Algorithm 1 with a single node update at each iteration using the criterion s [ i ] > λ , referred to as a sample-level version of Algorithm 1. Specifically, let us define v ∈ R n such that v [ i ] = -1 for i ∈ N and v [ i ] = 1 for else. Then the algorithm moves a sample k to another partition at each iteration, where k = argmax i ∈T v [ i ]( s [ i ] -λ ) . The algorithm stops when v [ k ]( s [ k ] -λ ) ≤ 0 .

Proposition 1. Algorithm 1 with a single node update at each iteration converges to local optimum.

Proof. The change in the objective value of Equation (2) by moving data i from T \N to N is

where the change by moving data i from N to T \N is

Note the score s in Algorithm 1 is

Thus the change in the objective value by moving data i to another partition is s [ i ] -λ for i ∈ T \N and -s [ i ] + λ for i ∈ N , which can be represented as v [ i ]( s [ i ] -λ ) . Therefore, moving a sample with a positive value of v [ i ]( s [ i ] -λ ) to another partition guarantees an increase in the objective function value. Because a cut value in a graph is bounded, the algorithm converges to the local optimum by the monotone convergence theorem.

A.2 Empirical convergence analysis

We conduct an empirical study on the convergence of Algorithm 1. Specifically, we randomly sample 100,000 data from ImageNet and construct a relation graph. We compare the set-level Algorithm 1 and the original Kerninghan-Lin algorithm in Figure 11. The figure indicates that both algorithms converge to the local optimum, while our set-level algorithm converges faster. Additionally, we observe that the set-level algorithm achieves a lower objective value, verifying its effectiveness in large-scale settings.

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A.3 Computation time comparison

In this section, we measure the time spent on detection algorithms. We use 1 RTX3090-Ti GPU and conduct experiments on the full ImageNet training set. Table 4 compares computation time for Algorithm 1 and feature calculation. Note that all existing methods based on neural networks, including ours, require the calculation of features. The table shows that Algorithm 1 (excluding

feature calculation) requires significantly less computation time than forward computation. We also observe that our algorithm efficiently scales up to larger neural networks which have a larger number of feature embedding dimensions. It is also worth noting that computing gradient takes a much longer time and also requires a large memory budget, demonstrating the efficiency of our algorithm in large-scale label error detection.

In Table 5, we measure the time spent for OOD detection on the full ImageNet training set. The computation of our similarity kernel is embarrassingly parallelizable on GPUs. As shown in the table, the overhead time for computing our outlier scores is negligible compared to the time spent for the neural networks' forward computation on a single data point. We can further reduce the time and memory requirements by measuring the outlier score on a subset of the training set (Figure 7).

A.4 Interpretation of relation function

We establish an understanding of our relation function in Equation (1) by drawing a connection to the influence function [39]. For simplicity, we consider the influence function with a single checkpoint, where the influence between data x i and x j is given by ∇ w ℓ ( x i ) ⊺ ∇ w ℓ ( x j ) . Here, ℓ denotes the loss function, and w denotes the weight of the checkpoint. We consider the influence function at the feed-forward layer, where ℓ ( x i ) = h ( f ′ i ) = h ( w ⊺ f i ) , following the convention [39]. By the chain rule, we can decompose the weight gradient as ∇ w ℓ ( x i ) = ∇ f ′ h ( f ′ i ) f ⊺ i , and represent the influence as ∇ f ′ h ( f ′ i ) ⊺ ∇ f ′ h ( f ′ j ) · f ⊺ i f j . In contrast, our relation function has a form of 1( y i = y j ) · | s ( f i , f j ) · c ( p i , p j ) | t .

The main distinction between our relation function and the influence function is the existence of the feature gradient term ∇ f ′ h ( f ′ i ) . As observed in Barshan et al. [2], outliers have a large featuregradient norm, leading to difficulties in detecting label errors. Specifically, let us consider the weight w at the classifier layer, where the function h is the softmax cross-entropy loss function. As Pruthi et al. [39], we can express the feature gradient inner-product as

where y i denote the one-hot label. The equation above shows that the correctly classified data with y i ≈ p i yields near zero inner-product values, whereas outliers with high entropy predictions exhibit large inner-product values. Consequently, existing influence-based label error detection methods, which detect label errors by identifying data with high influence values, have degraded performance in the presence of outliers [2].

Our relation function differs from influence functions in that it separates label and prediction information using a label comparison term 1( y i = y j ) and a compatibility term c ( p i , p j ) , respectively. Outlier data typically have a high entropy of model predictions, resulting in lower compatibility values with other data [14]. On the other hand, normal data with label errors exhibit high compatibility values with other normal data. Our detection algorithms exploit these differences and achieve improved detection performance compared to the influence functions.

B Additional discussions

Why does relation graph work? We discuss the conceptual differences between our relation graphbased approach and previous baselines. Firstly, our method is data-centric, whereas the previous

approaches rely on a unary score by models. Our approach identifies problematic data by comparing them to other data, which leads to more reliable identification of problematic data than unary scoring methods that are vulnerable to overfitting [38]. Secondly, our approach aggregates global relational information, whereas previous methods rely on local information such as k -nearest distance [50]. Considering all edge connections, our method obtains more representative information about the data distribution. Through temperature parameter t and efficient graph algorithms, we effectively process the entire relations and achieve the improved identification of problematic data.

Limitations and future works There are several promising future directions for our work. Firstly, the current experiments are limited to the classification task, and it would be valuable to apply our approach to a wider range of tasks, such as segmentation or generative models. These tasks may introduce new and interesting categories of problematic data arising from different label spaces and data structures. Secondly, integrating our method with human annotation and model training processes will also be valuable. This could involve using our approach to identify inconsistencies in label assignments or to conduct a fine-grained evaluation of models.

Broader impact Regarding social impact, we anticipate that our method will largely reduce the cost of the data cleaning and annotation process, while also providing developers with valuable insights into their data and training process through our data relation map. We do not anticipate negative social effects, as our method does not deal with socially sensitive issues.

C Experiment settings

C.1 Implementation details

Models For label error detection, we train models on datasets with label noise. In the case of ImageNet, we fine-tune the pre-trained MAE models following the official training codes 2 , which train MAE-Large for 50 epochs and MAE-Base for 100 epochs. The MAE-Large model has a feature dimension of 1024, where the MAE-Base model has a dimension of 768. It is worth noting that the masked auto-encoding pre-training process of MAE does not utilize label information. We use 8 RTX3090-Ti GPUs for the training and 1 RTX3090-Ti GPU for executing our algorithm. In the case of ESC-50, we fine-tune the AST model with a 768 feature dimension for 25 epochs following the official training codes 3 . In the case of language domain tasks, we fine-tune RoBERTa-Base with a 768 feature dimension following the official training codes 4 , where we train models for 5 epochs. For other models, we use the trained models provided by the Timm library 5 . For all experiments, we use the inputs of the classification layers as feature embeddings. In the case of RoBERTa, this corresponds to the encoder output of the [CLS] token.

Hyperparameter As shown in Figure 8, we observe that a large value of temperature t benefits label error detection, while a moderate temperature value around 1 shows the best performance on OOD detection. We summarized the hyperparameter used in our experiments in Table 6. Note we use λ = 0 . 05 in Algorithm 1 after scaling the label noisiness score to have a maximum absolute value of 1. We observe that the conservative estimation of noisy set N by using small positive λ values leads to better results than λ = 0 , as shown in Table 7. The results in the table confirm that our method

performs effectively over a wide range of λ values, outperforming the best scores of 0.484 AP and 0.521 TNR95 from the six baselines tested.

Other tricks We find that small noisy kernel values accumulate errors as we consider large numbers of data. To resolve this issue, we clamp small similarity kernel values that fall below an absolute value of 0.03 as zero in Equation (3).

C.2 Synthetic label noise

In Section 4.1, we conduct controlled experiments by generating synthetic label noise. Specifically, we flip labels of a certain percentage of training data with the top-2 prediction of trained models on correctly classified data. For the label flip, we use MAE-Huge for ImageNet and RoBERTa-Large for language datasets. Note that we did not use these models for detecting label errors to prevent possible correlations. In the case of speech domain, we use the identical AST architecture. We note that the original ImageNet training set may contain label issues which can lead to misleading experimental results [34]. Therefore, we remove about 4% of data that are likely to have label issues by following Northcutt et al. [33] with MAE-Huge, resulting in a total of 1,242,890 data samples. We conduct label error detection experiments on this pre-cleaned training set. In Table 8, we provide the top-1 validation accuracy of MAE-Large trained on training sets with noisy labels, demonstrating the importance of label noise identification and cleaning.

C.3 Outlier detection setting

As outlier detection is not well-benchmarked in modern computer vision [59], we design an experimental setup with the ImageNet dataset and two outlier datasets: SUN [58] and iNaturalist [53], each with 10k outlier data. To ensure an appropriate outlier data ratio ( ∼ 8%), we use ImageNet-100 [21], a subset of ImageNet consisting of 120k data from 100 classes. We adopt the outlier detection setting of Wang et al. [56], where the training set has the outlier data with random labels. To consider multiple types of outlier data, we construct two noisy training sets: ImageNet-100 with SUN and ImageNet-100 with iNaturalist. We train a ViT-Base model [8] from scratch for 300 epochs on these noisy training datasets and measure outlier detection performance using the trained model.

D Additional experimental results

D.1 Temporal model ensemble

Following Pruthi et al. [39], we measure the label error detection performance by using the temporal model ensemble. Specifically, we average the label noisiness scores from 4 checkpoints that are uniformly sampled throughout training. Table 9 shows that this technique improves the performance of all methods, with our approach still exhibiting the best performance. These results confirm the effectiveness of temporal ensembles when more computation and storage are available.

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In this section, we analyze the difference between label noisiness scores calculated using max-cut and simple edge sum. Specifically, in Figure 12, we draw histograms of label noisiness scores for two groups of data: one with clean labels and the other with label errors. The figure shows that the score calculated through max-cut shifts the density in a positive direction for data with clean labels and in a negative direction for data with label errors, compared to the simple edge sum. This indicates that the label noisiness score calculated with max-cut better separates label errors from the clean data. In this case, TNR95 increases from 0.628 to 0.647 by applying the max-cut.

D.3 Label error detection

In this section, we provide the exact performance values for Figure 5, including AUROC results. We report label error detection performances under various noise levels in Table 10, and provide performances according to the number of data in Table 11. The tables confirm that our relation graph approach achieves the best label error detection performances in all three metrics, regardless of the noise ratio and the number of data. In Tables 12 to 14, we provide performance values of all baselines considered in Table 1.

D.4 OODdetection

In Tables 15 and 16, we provide OOD detection results on individual datasets mentioned in Section 4.2: Places, SUN, iNaturalist, and Textures. We report the OOD detection performance of MAE-Large in Table 15 and the performance of ResNet-50 in Table 16. The tables demonstrate that our approach achieves the best OOD detection performance on three out of four datasets considered, while achieving the best overall performance. Furthermore, our method shows the best performance on all three metrics with both models, which highlights its effectiveness in detecting OOD data.

E Additional qualitative results

E.1 Relation map

In Figure 13, we present additional relation maps on ImageNet. We draw the relation maps with MAE-Large and ResNet-50. Note, MAE-Large utilizes masked auto-encoding pre-training whereas ResNet-50 is trained from scratch. From the figure, we observe that the models exhibit similar distributions of positive and negative relations for each data point. However, the ResNet model tends to have an overall larger variance of relation, indicating that the pre-training process reduces the relation variance and is helpful in forming relationships between data.

The visualization tool helps us to comprehend the distribution of complementary and conflicting relations associated with a data point, aiding dataset analysis and debugging. For example, in Figure 13, the relation map of the Ram sample exhibits a combination of positive and negative relations. Specifically, it exhibits positive relations with other Ram class samples while showing negative relations with samples from the Big Horn class, which are visually challenging to distinguish.

This observation suggests the need for multi-labeling or refinement of the label space definition. In this way, we can intuitively identify problems in the dataset by using the visualization tool.

E.2 Qualitative results

We present problematic data samples detected by our algorithm. Specifically, Figure 14 shows ImageNet samples with label errors and their most conflicting data samples having negative relation values. Figure 15 shows the outlier data detected by our algorithm on the ImageNet validation set, indicating the existence of inappropriate data for evaluation. We also present results on SST2 [55], a binary text sentiment classification dataset, in Tables 17 and 18.

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BAATH

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JerryLINDA

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cell:

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Kite

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Bald eagle (-0.760)

Bald eagle (-0.760)

Bald eagle (-0.759)

Weasel

Lesser panda (-0.761)

Lesser panda (-0.761)

Lesser panda (-0.758)

Lesser panda (-0.757)

Ringlet

Monarch (-0.763)

Monarch (-0.754)

Monarch (-0.753)

Monarch (-0.753)

Impala

Hartebeest (-0.794)

Hartebeest (-0.768)

Hartebeest (-0.763)

Hartebeest (-0.761)

Passenger car

Steam locomotive (-0.751)

Steam locomotive (-0.751)

Steam locomotive (-0.749)

Steam locomotive (-0.747)

Redshank

Ruddy turnstone (-0.761)

Ruddy turnstone (-0.761)

Ruddy turnstone (-0.758)

Ruddy turnstone (-0.757)

735

Maze

Stopwatch

Barrow

Cockroach

Airship

Stone wall

Vault

Apiary

Torch

Wig

African grey

Stretcher

Teddy

Breastplate

Hammer

Honeycomb

Pretzel

Alligator lizard

Vase

Gasmask

Flute

5CM

Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a novel approach called the Neural Relation Graph framework for identifying label noise and outlier data in large-scale datasets with real-world distributions. The approach utilizes a relational structure of data in the feature-embedded space to detect label errors and outlier data, and introduces a visualization tool for interactive data diagnosis. The authors conduct extensive experiments on various tasks and demonstrate that their approach achieves state-of-the-art detection performance and is effective in debugging real-world datasets. The contributions of this paper include a unified approach for diagnosing and cleaning large-scale datasets, a data relation function and graph algorithms for detecting label errors and outlier data, and a visualization tool for interactive data diagnosis.\n\nSTRENGTHS:\nOriginality:\nThe Neural Relation Graph framework proposed in this paper is a novel approach for identifying label noise and outlier data in large-scale datasets. The authors utilize a relational structure of data in the feature-embedded space to detect label errors and outlier data, which is a unique and innovative approach. The paper also introduces a visualization tool for interactive data diagnosis, which is a novel contribution to the field. Overall, the paper is highly original and presents a new perspective on diagnosing and cleaning large-scale datasets.\n\nQuality:\nThe paper is of high quality, with a well-designed methodology and extensive experiments conducted on various tasks. The authors provide detailed descriptions of the proposed approach and the experiments conducted, which makes it easy to understand and replicate the results. The paper also includes a thorough evaluation of the proposed approach, comparing it to existing methods and demonstrating its effectiveness in detecting label errors and outlier data. The quality of the paper is further enhanced by the use of clear and concise language, making it easy to follow and understand.\n\nClarity:\nThe paper is well-written and easy to understand, with clear descriptions of the proposed approach and the experiments conducted. The authors provide detailed explanations of the technical terms used, making it accessible to a wide range of readers. The paper also includes visual aids, such as figures and tables, which help to illustrate the concepts presented. Overall, the clarity of the paper is excellent, making it easy to follow and understand.\n\nSignificance:\nThe paper is highly significant, as it presents a novel approach for diagnosing and cleaning large-scale datasets with real-world distributions. The proposed approach utilizes a relational structure of data in the feature-embedded space to detect label errors and outlier data, which is a unique and innovative approach. The paper also introduces a visualization tool for interactive data diagnosis, which is a valuable contribution to the field. The results of the experiments conducted demonstrate the effectiveness of the proposed approach, making it a significant contribution to the field of machine learning.\n\nWEAKNESSES:\nOne potential weakness of the paper is that the authors do not provide a detailed analysis of the limitations of their approach. While the proposed approach achieves state-of-the-art detection performance on various tasks, it is unclear how it would perform on datasets with different characteristics or in different domains. The authors could address this weakness by conducting experiments on a wider range of datasets and providing a more detailed analysis of the limitations of their approach.\n\nAnother weakness of the paper is that the authors do not provide a detailed discussion of the computational complexity of their approach. While the paper mentions that the proposed algorithms are scalable, it is unclear how they would perform on very large datasets or in real-time applications. The authors could address this weakness by providing a more detailed analysis of the computational complexity of their approach and discussing potential strategies for improving its scalability.\n\nFinally, the paper could benefit from a more detailed discussion of the practical implications of the proposed approach. While the paper demonstrates the effectiveness of the approach in detecting label errors and outlier data, it is unclear how it could be applied in real-world scenarios. The authors could address this weakness by discussing potential use cases for the proposed approach and providing guidance on how it could be integrated into existing machine learning pipelines.\n\nOverall, the paper presents a novel and innovative approach for diagnosing and cleaning large-scale datasets, but could benefit from a more detailed analysis of its limitations, computational complexity, and practical implications.\n\nQUESTIONS:\nCan you provide a more detailed analysis of the limitations of your approach? While the proposed approach achieves state-of-the-art detection performance on various tasks, it is unclear how it would perform on datasets with different characteristics or in different domains.\n\nCan you provide a more detailed discussion of the computational complexity of your approach? While the paper mentions that the proposed algorithms are scalable, it is unclear how they would perform on very large datasets or in real-time applications.\n\nCan you discuss potential use cases for the proposed approach and provide guidance on how it could be integrated into existing machine learning pipelines? While the paper demonstrates the effectiveness of the approach in detecting label errors and outlier data, it is unclear how it could be applied in real-world scenarios.\n\nCan you provide more details on the visualization tool introduced in the paper? While the tool is mentioned briefly, it would be helpful to have a more detailed description of its functionality and how it can be used to diagnose data.\n\nCan you provide more details on the datasets used in the experiments? While the paper mentions that experiments were conducted on various tasks, it would be helpful to have more information on the characteristics of the datasets and how they were selected.\n\nCan you provide more details on the hyperparameters used in the experiments? While the paper mentions that hyperparameters were tuned using cross-validation, it would be helpful to have more information on the specific values used and how they were selected.\n\nCan you provide more details on the implementation of the proposed algorithms? While the paper mentions that the algorithms were implemented using PyTorch, it would be helpful to have more information on the specific implementation details and any potential optimizations that were made.\n\nCan you discuss potential future directions for this research? While the paper presents a novel and innovative approach, it would be helpful to have a discussion on potential future directions for this research and how it could be extended or improved upon.\n\nLIMITATIONS:\nThe paper does not explicitly address the potential negative societal impact of the proposed approach. While the focus of the paper is on diagnosing and cleaning large-scale datasets, it is possible that the approach could be used for other purposes, such as identifying individuals or groups based on their data. This could potentially lead to privacy concerns or other negative societal impacts.\n\nHowever, it should be noted that the paper does not provide any evidence that the proposed approach has been used for such purposes, and the authors do not make any claims about the potential negative societal impact of their work. Additionally, the paper does not explicitly address the limitations of the proposed approach, which could potentially lead to unintended consequences if the approach is used in real-world scenarios.\n\nOverall, while the paper does not explicitly address the potential negative societal impact of the proposed approach, it should be noted that the authors do not make any claims about the potential negative impact of their work, and the focus of the paper is on diagnosing and cleaning large-scale datasets.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-05"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe authors identified the issue of how existing label errors in the training data and the OOD in the test set can affect the model training and evaluation and further proposed a novel approach utilizing the learned feature embeddings and label information to compute the relations between data instances. The relations represent how similar the two data instances are in terms of their feature embeddings and also assigned labels. This is further used to construct a relational graph structure. Based on the graph structure, they introduce a min-cut algorithm based on the label noisiness score to identify a subset of label errors. They further visualized the derived graph structure for the purpose of interactive data error diagnosis. Extensive experiments are conducted on multiple data types (images, audio, texts), and all show superior performance over the baseline methods. Through comparison, authors showed their relational data structure provides complementary information not captured by the unary scoring methods. Generally, this paper is well-written, the ideas are pretty clear, the methods are novel, and results are solid.\n\nSTRENGTHS:\nA substantive assessment of the paper's strengths, touching on each of the following dimensions: originality, quality, clarity, and significance. We encourage reviewers to be broad in their definitions of originality and significance. For example, originality may arise from a new definition or problem formulation, creative combinations of existing ideas, application to a new domain, or removing limitations from prior results. You can incorporate Markdown and Latex into your review. See /faq.\n\n1.\tThis paper is well-written, and the authors explain the ideas clearly. The method is novel, and experiments and results are solid. \n2.\tThe example provided in Figure 1 explained well the limitations of using the unary scoring method when identifying the label error and the outlier data.\n3.\tThe design of the data relation function in Section 3.1 looks simple but still effective.\n4.\tIn section 3.2, the authors pointed out that simply aggregating all edges of a node can yield suboptimal results, which makes much sense, and they further proposed using the min-cut method as a walkaround. This looks interesting.\n5.\tThe experiments are conducted using various data types, including images, speeches, and texts. This also covers multi-class tasks and binary tasks. All experiments show the effectiveness of their methods, which is solid.\n\nWEAKNESSES:\n1.\tIn Figure 1, the difference between the Coil (label error) and the Envelope (outlier) is not very clear. More elaborations will be helpful.\n2.\tConstructing the relational graph is a fully connected graph, the time complexity would be O(N^2), and the scalability to a large dataset is a concern.\n3.\tIn section 3.2, pp3 line 115, ‘a lower (label noisiness) score indicates a higher likelihood of label error’. A lower label noisiness indicates a higher error possibility, this is a bit confusing and not very intuitive.\n\nQUESTIONS:\n1.\tIn Figure 1, What makes the Coil example a label error, while the Envelope example an outlier? Some elaboration on this would be helpful.\n2.\tIn Section 3.2, pp3 line114, authors set $r(i,i)=0$, this is not very straightforward and the reason is not clear to me. More elaboration on this would be helpful.\n3.\tIn section 3.2, pp4 line 127, authors minimize the sum of the edges between two groups. One question comes naturally - what about the sums of edges within each group? \n4.\tIn terms of different datasets used in this work, several data types were involved (images, speeches, texts), it would be helpful to see what the embedding dimensions are for each dataset.\n\nLIMITATIONS:\nMinor edit suggestion: pp8 line309, ‘3.6%p’ should be ‘3.6%’.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-06"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a new method using graph structure for detecting label errors and outlier data. Briefly speaking, the algorithm utilizes data feature embeddings to generate relation graph and using the new defined data relation function, its algorithm can capture mislabeled and outlier data from a global prospective. A large number of experimental results show that the performance of this method is greatly improved compared with the existing detection methods.\n\nSTRENGTHS:\n(1) This paper presents a novel relation graph-based approach to achieve better utility and considers error label and outlier detection in a global way. \n(2) Extensive experiments on datasets from different domains show the improvement of the new method is promising.\n(3) Comprehensive ablation study is performed, which helps to understand the proposed model better.\n(4) The overall expression of the article is clearer and easier to understand, and related works are adequately cited.\n\nWEAKNESSES:\n(1) Certain statements in this paper lack justification. For example, the method is based on building graph on feature space, but there is a little discussion about feature spaces and how to generate it.\n(2) Lack of sufficient theoretical analysis (e.g. convergence but not only empirical analysis) , the proof of proposition and analysis of relation function are relatively simple.\n(3) Lack of explanation of choosing parameter in baseline method, like whether there is a finetune on the choice of K in KNN method.\n\nQUESTIONS:\n(1)\tLine 159 in Complexity analysis, the paper demonstrates the complexity can be reduced to O(nk). But in the fourth last row in algo 1 each point in partition seems also need to calculate n relation score instead of k. Can you deeper explain the improvement in complexity？ And there is no empirical results of the acceleration.\n(2)\tThe paper mentions it’s the first using data relation graph on the feature space. The “first” points to “relation graph” or “feature space”? Are there any other methods using graph to detect error data and need to be compared with?\n\nLIMITATIONS:\n(1)\tAlthough extensive experiments on real-world datasets corroborate the effectiveness of the proposed method, there is lack of theoretical analysis of the effectiveness of the method.\n(2)\tSome content lacks detailed explanations.", "TITLE": "Official Review", "RECOMMENDATION": 6, "REVIEWER_CONFIDENCE": 3, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-06"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper under review outlines a novel method utilizing graph structure to identify label errors and outlier data. It proposes an algorithm that makes use of data feature embeddings to produce relation graphs. By incorporating a newly defined data relation function, the algorithm can globally capture mislabeled and outlier data. The experiments conducted exhibit a marked improvement in performance compared to extant detection methods.\n\nSTRENGTHS:\n+ Innovation: The paper introduces a novel method, which is an important contribution to the field. This new approach potentially provides a fresh perspective and further insights into the problem at hand.\n\n+ Clarity and Comprehensiveness: The paper is well-structured and clearly written, making it easy for readers to understand the content. The authors have adequately cited related works, showing a thorough understanding of the existing literature and situating their work appropriately within that context.\n\n+ Important Problem: The paper tackles an important problem, making its potential impact highly relevant and timely. This problem is pertinent to many real-world scenarios, amplifying the value of the proposed solution.\n\nWEAKNESSES:\n+ Unclear Advantage: Despite the introduction of a new method, the paper lacks clear explanation of the motivation and advantages of the chosen approach compared to existing methods. The authors proposed to use the feature similarity ( 'semantic similarity between data points') to help learn a noise-robust classifier, which exploits $P(X)$ to help learn $P(Y|X)$. It shares the same underlying physiology with semi-supervised based methods (e.g., DividMix, ICLR20) or self-supervised based methods (e.g., UNICON, CVPR22). \n\n+ Lack of Explicit Assumptions: The authors do not clarify the assumptions under which the proposed method is expected to perform well. This lack of clarity could impede understanding and application of the method in practical scenarios.\n\n+ Unknown Motivation for Kernel Usage: The motivation for using a kernel in the proposed method is not explained. Without this, it's hard to understand the reason behind the choice of a kernel and how it contributes to the method's effectiveness.\n\n+ Absence of Baseline Comparisons: The paper does not compare the proposed method with significant baselines in the field of learning with noisy labels (e.g., DividMix, ICLR20; ELR, NeurIPS20; CausalNL, NeurIPS21; C2D, WACV23; UNICON, CVPR22). Such comparisons are crucial for evaluating the performance of the new method and understanding its standing relative to existing techniques.\n\nQUESTIONS:\n+ Could you elaborate on the unique advantages of your proposed method over existing semi-supervised and self-supervised techniques, especially considering the shared approach of using feature similarity to help learn a noise-robust classifier? What distinguishes your method from others that also exploit $P(X)$ to help learn $P(Y|X)$?\n\n+ Could you specify the assumptions under which your method is expected to perform well?\n\n+ Could you provide the reasoning behind the choice of using a kernel in your method? How does the kernel contribute to the effectiveness of the method and why was this specific kernel chosen over potential alternatives?\n\n+ To convince others about the method's practical significance, could you include a comparison of your method with DividMix (ICLR20) and  UNICON (CVPR22) in the field of learning with noisy labels?\n\nLIMITATIONS:\nI did not come across a sufficient discussion of the limitations of the proposed method. I would highly recommend the authors include a section on potential limitations in their revision.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2023-07-26"}