Handling Label Noise via Instance-Level Difficulty Modeling and Dynamic Optimization
Authors: Kuan Zhang
Chengliang Chai
Jingzhe Xu
Chi Zhang
Han Han
Ye Yuan
Guoren Wang
Lei Cao
Venue: NeurIPS 2025 poster ()
Keywords: computer vision
learning with noisy labels
robustness
Primary area: applications

Abstract: Recent studies indicate that deep neural networks degrade in generalization performance under noisy supervision. Existing methods focus on isolating clean subsets or correcting noisy labels, facing limitations such as high computational costs, heavy hyperparameter tuning process, and coarse-grained optimization. To address these challenges, we propose a novel two-stage noisy learning framework that enables instance-level optimization through a dynamically weighted loss function, avoiding hyperparameter tuning. To obtain stable and accurate information about noise modeling, we introduce a simple yet effective metric, termed $\textit{wrong event}$, which dynamically models the cleanliness and difficulty of individual samples while maintaining computational costs. Our framework first collects $\textit{wrong event}$ information and builds a strong base model. Then we perform noise-robust training on the base model, using a probabilistic model to handle the $\textit{wrong event}$ information of samples. Experiments on six synthetic and real-world LNL benchmarks demonstrate our method surpasses state-of-the-art methods in performance, achieves a nearly 75\% reduction in storage and computational time, strongly improving model scalability. Our code is available at https://github.com/iTheresaApocalypse/IDO.

Handling Label Noise via Instance-Level Difficulty Modeling and Dynamic Optimization
Kuan Zhang', Chengliang Chai', Jingzhe Xu', Chi Zhang' Han Han? Ye Yuan', Guoren Wang', Lei Cao²
Beijing Institute of Technology
University of Arizona
(zhangkuan, ccl)@bit edu.
Abstract
Recent studies indicate that deep neural networks degrade in generalization per- formance under label noise. Existing methods focus on data selection or label correction, facing limitations such high computational costs, heavy hyperparam- eter tuning process, and coarse-graine optimization. To address these challenges, we propose novel two-stage noisy learning framework that enables instance-level optimization through dynamically weighted loss function, avoiding hyperparam- eter tuning. To obtain stable and accurate information about noise modeling, we introduce a simple yet effective metric, termed wrong event, which dynamically models the cleanliness and difficulty of individual samples while maintaining com- putational costs. Our framework first collects wrong event information and builds strong base model. Then we perform noise-robust training on the base model, using a probabilistic model to handle the wrong event information of samples. Experiments on six synthetic and real-world LNL benchmarks demonstrate our method surpasses tfte--of-thh-ar methods in performance, achieves a nearly 75% reduction in storage and computational time, strongly improving model scalability. Our code is available at https: // thub. com/ http///eeeesapaalyppsseees IDO.
Introduction
Curating large training datasets through web scraping [ crowd-sourcing (2), pre-trained models 3 inevitably introduces label noise. tends to degrade the performance of the trained deep neural network (DNN) model [4] due to DNN memorizing and thus overfitting the noisy samples (5).
To mitigate the negative impact of label noise, many works 15 consider the patterns of the clean and noisy samples shown in the DNN training process. i.e., DNNs first learn clean patterns early training, then start fitting noise later, and eventually overfit the noisy dataset. However, one key problem of this strategy is that the noisy samples tend to show behavior similar to the clean but difficult samples the clean examples that are close to the decision boundary of the model. To solve this problem, the most recent approaches [1] try distinguish noisy examples from hard examples by introducing the hardness of the samples into the loss function. However, these methods have the following limitations.
Limitations. (1) These methods are computationally intensive due to the overhead for measuring the hardness and cleanness of the samples and grouping them into different categories, e.g., clean, noisy, and difficult [16]: (2) these methods introduce extra hyperparametters, such as coefficients of loss terms, cutoff threshold for grouping the samples, and a training epoch threshold to avoid the model fitting the noise, which are hard to tune [10 12]: (3) these methods always assign identical
"Chengliang Chai is the corresponding author
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Figure 1: A bar chart illustrates the distribution of wrong events. In terms of sample cleanness, clean samples show lower wrong event, while noisy sam- ples tend to have higher wrong event. In terms of sample difficulty, samples located at the extremes of the distribution represent easy samples, far from the decision boundaries (e.g., cat and bird in the figure). In contrast, samples located in the central depression of the distribution are often near the de- coefficient to all samples within the same category, neglecting the differences of individual samples in both cleanliness and difficulty [T]
Our Proposal. To address these limitations, we propose IDO, Instance-level Difficulty Mod- eling and Dynamic Optimization framework to achieve robust learning over noisy training data. Rather than relying on hyperparameters to regularize different terms in the loss function, IDO designs dynamically weighted loss func-
5000
Dectwon
Number of Examples
leopard
4000
cat
tion that captures both the cleanliness and dif- ficulty of each individual sample. This enables
3000
bird
instance-level optimization without introducing any additional hyperparameters.
2000
1000
IDO makes this possible by proposing a new noise-robust metric to replace the classical loss- based metric which is known be unstable and thus ineffective in distinguishing hard and noisy samples [8]. This metric, called wrong event, simply counts the frequency of mismatches be- tween model predictions and the given labels, thus computationally efficient. Moreover, fit- ting two-component beta mixture model to its distribution w.r.t. the training samples ef- fectively measures the cleanliness and difficulty of each sample in a tuning-free manner (see T. Replacing the hard-coded coefficients of the loss terms with the corresponding mea- sures that dynamically update epoch by epoch, IDO ensures accurate and robust modeling at any training stage (see Fig[2 yet achieves high computational efficiency.
0
10
20
30
40
50
60
Wrong Event Distribution
cision boundaries of similar classes, representing hard samples (e.g., cat and leopard in the figure).
We summarize our main contributions as follows: (1) We propose wrong event, a simple but effective metric that reliably separates noisy samples from clean ones at any stage of training, regardless of pretraining or not. We provide theoretical and experimental analysis to explain why wrong event works well whether the model has fitted noise. (2) We propose IDO that trains robust model with dynamically weighted loss using wrong event information where we are first to leverage probabilistic model to model data difficulty. (3) Our extensive experiments confirm that without hyperparameter tuning, IDO outperforms the state-of- thee-hhrtt methods by an average accuracy of 1.6% on synthetic and 0.7% real-world datasets for LNL tasks, with 75% reduction in computational time, and better scalability to larger models compared to previous methods.
2 Related works
Memorization & Forgetting. (4) observe that DNNs are sufficient for memorizing the entire dataset. 5 shows that DNNs follow the memorization effect, i.e., clean samples and noisy samples exhibit distinct behaviors during the training process. Leveraging this observation, researchers have proposed other metrics to deal with noisy datasets. [19] proposed forgetting event, which counts how many times a model forgets a prediction of given labels. However, for easy noisy samples, the model tends to consistently predict ground truth labels rather than the given labels, resulting in the values of forgetting event all being zero in early stage. This makes it difficult to distinguish clean and noisy samples. (20] proposed first k-epoch learning (fkl), i.e., the time when sample has been predicted to its given label for consecutive k epochs for the first time. Samples with larger fkl are more likely to be noisy. However, & a hyperparameter that varies on different datasets. Although these metrics work well once the model training gets into the overfitting phase, they are less effective than loss in the early stage. Our proposed wrong event metric demonstrates strong discriminative capabilities regardless of the stages of model training (see Fig 2 More discussion about metrics is in Appendix C.3

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Spach
Soach
Olen
2006
13000
20
of
1300
1.5
Loss
100
500
17500
530
Helpy
Osen Data
thoy a Konn hord
4.03
1000
19000
000
Witonng
2303
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Clcch
Figure 2: A comparison between wrong event and loss. The baseline model is ResNet-18 trained on CIFAR-10 10 with 40% symmetric noise training for 100 epochs. We show the loss distributions (the first row) and wrong event distribution (the second row) during training. The four columns, (a) (b) (c) (d), represent the distributions at epoch 20, 60, 100 and the entire training phase. (a), (b), and (c) represent the early, middle, and late stages, respectively. In (d), the heavy lines represent the mean value and the shaded areas are the interquartile ranges. Since wrong events are monotonically increasing based on historical statistics instead of current model prediction, when model overfits the dataset, wrong event values for all samples do not change, rather than converging to zero as loss values typically do. As result, wrong event can clearly separate noisy data and clean data in all training stages, even if the model fits noise.
Learning with Noise Labels (LNL). LNL problem has been extensively explored in recent research [3] There are many variants of the LNL. problem. Some methods (2 (2 assume the existence of a small subset of clean data, which our method does not require. In our more challenging scenario, which has to distinguish noisy and difficult samples, recent studies leverage techniques such as co-training frameworks [6, 17 [6), k-means clustering [23], and contrastive loss [24] [6]. which unfortunately incur high computational and memory costs. Dynamic loss functions can be considered as instance-level optimization. However, previous methods (25 22 mainly focus on modeling clean and noisy samples, while overlooking the challenge of modeling hard data, which our work targets.
Pre-trained Models for LNL, Pre-trained models are known for their strong generalization ability learn the representations avoid label noise, by using self- supervised pre-trained models such as SimCLR (30) and MoCo [31]. Recent LNL. methods 12 [3]
26
277. Previous studies 28 29
15
27 and ConyNeXt to improve effectiveness and efficiency of LNL. However, large pre-trained models restrict the applicability of complex modeling approaches. Therefore, they [12 [3] primarily rely on simple strategies such as the small-loss criterion or similarity threshold to discard the potential noisy data from training. This loses the opportunity to explore the valuable information hidden in these noisy data. Our approach is much more scalable because of the lightweight wrong event- event-based strategy. It thus able to fully utilize both clean and noisy data, turn achieving superior model performance.
leverage pre-trained vision models such ResNet 332. ViT (26). CLIP
33
3 Key ideas: wrong event and instance-level optimization
In this section, we first introduce the problem of LNL. Subsequently, we define the concept of wrong event and present empirical evidence to demonstrate its robustness. Finally, we discuss how to fully leverage wrong event in LNL.
3.1 Noise label learning
In the context of a C-class image classification problem. , we denote a training dataset as Dimin (.)) which consists of N pairs of input images 2; and their given labels y/ E (1,..., C). In real-world scenarios, the given labels yi may be corrupted due to various factors. We use ys to represent the ground truth label of (z,, D.). which remains inaccessible during training.
3

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3.2 Observation of wrong event
We begin by formally defining the concept of wrong event. Consider model f(-) trained over T epochs. For a given sample (z,, Dt), the wrong event is computed as follows:
wrong event, = Σ I(arg max f(,.)) # Ut)
(I)
where I(.) denotes the indicator function. This metric quantifies the cumulative number of epochs in which the prediction of the model f(zz;) disagrees with the given label Øi- We observe that wrong event can reliably separate noisy samples from clean samples any stage of training, even if the model has fitted noisy samples, as shown in Fig 2
In addition to the robustness of wrong event, Le.. the variance of wrong event across consecutive epochs is much smaller than that of loss values, where the high variance tends to make loss ineffec- tive (18) in separating hard and noisy samples, wrong event effectively reflects both the cleanliness and difficulty of the training samples. Easy samples, which no matter clean or noisy, are located far from the decision boundary, exhibit consistent prediction behavior in consecutive epochs: clean (noisy) samples are consistently predicted correctly (incorrectly). ) As a result, these samples tend occupy the extremes of the wrong event distribution. In contrast, hard samples, which lie close to the decision boundary, often experience fluctuating predictions, with their outcomes frequently flipping between similar classes. This instability causes hard samples gather at the middle region of the wrong event distribution, forming a low-lying trough. Therefore, the distribution of wrong event offers valuable insights into both the cleanliness and the difficulty of each sample.
Our extensive theoretical and experimental analysis shows that wrong event is indeed more robust and informative metric than loss with less variance, regardless of pretraining not (see Appendix C and provides more accurate measures than other metrics (see Table 4) in cleanliness and difficulty.
3.3 Measuring cleanliness and difficulty
To extract cleanliness and difficulty information from wrong event, we employ a two-component probabilistic model to fit the distribution of wrong event. In all the following equations, the symbol w is used to denote the wrong event. The probability density function (pdf) of two-component mixture model on wrong event is defined as:
p(w)= Σ m, - (ww(k))
where my are the mixing coefficients for the convex combination of each individual pdf p(w)))
Existing methods commonly use the Gaussian mixture model (GMM) to distinguish clean samples from noisy ones 17 16 However, our case, the wrong event of easy samples, especially easy noisy samples, often focuses on the distribution tails, leading to monotonically increasing rather than unimodal distribution (see Figs [ making Gaussian distribution models inadequate for fitting. This phenomenon can be attributed to three main factors: 1) Hard samples [34] 35 often exhibit a long-tailed distribution in training: 2) Curriculum learning (36 suggests that models learn easy samples quickly but struggle with hard samples; 3) Training typically stops before the model fully
memorizes the dataset, leading to an accumulation of easy noisy samples at the tail of the noise distribution.
To better model such distributions, we adopt two-component beta mixture model (BMM), which is well suited to capture both symmetric, skewed, and monotonically increasing distributions due to the flexibility of the beta distribution [37]. We use an Expectation Maximization (EM) procedure [25] [7] to fit the BMM to the observations. Unlike previous method [75] specifically, we introduce two more variables to fully use statistical information to build sample cleanliness and difficulty:
The (w) p(k]w) p(k) p(w(k)
p(w)
which defines the posterior probability of given w having been generated by mixture component k
A (w) = F(w; ax 3x) fo 1aa-1(1 1) dl
B(ar, 3x)

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which defines the cumulative distribution function value of mixture component ls for given w.
The fitting process yielded two beta distributions, B1 and B2, with means 141 and μ22 (assuming that jan is smaller than (22). We need to utilize B1 and B3 to measure the cleanliness and difficulty of the samples. 1) Cleanliness. We associate B1 with the clean distribution for lower mean, as it captures the characteristics of correctly labeled samples, while B2 is attributed to the noisy distribution, representing mislabeled samples. Thus, Ti (-) corresponds to the probability of sample being drawn from the clean distribution, while (2)) = 1 - Ti (-) represents the probability of a sample originating from the noisy distribution. 2) Difficulty. In the clean distribution, samples with larger wrong event values tend to be closer to the decision boundary. Conversely, in the noisy distribution, samples with smaller wrong event values are closer to the decision boundary. We use posterior probabilities r(-) and the cumulative distribution function X(-) to measure the difficulty level of the samples:
(5) where e(w) represents the difficulty of a sample with the given wrong event. T(w) reflects the posterior probability in w belonging clean noisy distribution. X(w) measures how extreme is within its assigned distribution. Low <(w) indicates w lies in a high-confidence, typical region of one component, while high c(w) suggests w resides in ambiguous regions. The larger (smaller) c(w) is, the closer (farther) the sample is to the decision boundary, indicating a higher (lower) difficulty level of the sample. We analyze the bounds of e(w):
<(w) ri (w) (w) + +2(w)- (1 -22(w)
(6) Then we analyze its trend. When w z min wu T== we have Ti (w) 1,r2(w) = 0, A (w) = 0, (2 = O, then e(w) x 1 x 0 + have (w) se 0.5, rw( 0.5, A1 (w) 2 1, (w)) O. then e(w) 1.
S <(w) I Ti (w) + +2())= =
0
x 1 = O, as does w ve m LN When w + middle, we
Due to the heterogeneous distribution of wrong event across different classes where simpler classes typically exhibit lower wrong event means compared to harder ones, fitting a single distribution to the entire dataset proves ineffective. To achieve more accurate modeling and maintain class balance, we establish C BMM models to independently model the distribution of each class. For samples i where yΙ = c, the posterior probabilities are derived from the corresponding BMM components Bi and B5, achieving more accurate and fine-grained modeling.
4 Robust denoising framework
We design a two-stage learning framework (see Fig which obtains the prior knowledge, i.e.. wrong event information and competitive base model in the first stage, and then utilizes this prior knowledge produce noise-robust model in the second stage.
4.1 Two stage training
Stage 1: Obtain prior knowledge. The first phase has two main objectives. Firstly, we adopted a typical training strategy, which involves training the model using the cross-entropy loss function for certain period and collecting wrong event information.
(ee D) -ÿ log(f(z;))
Secondly, we aim capture a competitive base model during training serve as the initial model for stage 2, thereby improving training quality. Recent research (38) introduced a metric called label wave, which records the number of prediction changes per epoch. The model the first local minimum of prediction changes exhibits strong competitiveness in LNL settings. In particular, this technique does not increase the computational cost of IDO. Notably, multiple fine-tuning approaches can be employed in stage 1, including Linear Probing (LP) or Full Fine Tuning (FFT). For smaller models such as ResNet-50, we recommend using FFT to achieve a more competitive base model and improve the accuracy of wrong event estimation. For larger models such as 1/6- we suggest using LP to accelerate training. The stage process is illustrated in the left side of Fig
Stage 2: Robust Model Adaptation. The second phase of the algorithm aims to train a noise-robust
model on top of the base model, incorporating the prior knowledge acquired in the first phase. The overall training objective of second phase is:
N
Imi (w:) Le + e(wi)) -STM + T2(WE) Lxl
(8)
5

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Whong Event Number
Dog
Dog
Augmentaation
(n 9.)
( 96
(e 80
Imagg
Strong Augmentation
Nolay Dataset (x).
(1n
Mixture
Unilize Wrong Event
<(w:)
Phase 1: Cbtain Prior Knowledge
Phase Robust Model Adaptation
Figure 3: Illustration of the proposed IDO framework. The training process is divided into two stages. In the first stage, prior knowledge, i.c. coarse distribution of wrong event, is obtained, and a base model that owns basic discrimination capability is captured. In the second stage, robust noise learning performed. By using BMM, we obtain both cleanliness and difficulty information for individual samples, enabling instance- level dynamic optimization. The sample's wrong event information and the model's 's classification capability mutually benefit each other, leading to high improvement.
where (.), T2(-) are the posterior probabilities of B1, B2, and e(.) is the difficulty coefficient in [5 We will give the formation of each loss function in detail in the following subsection. After each epoch of robust training, we also update the wrong event information for each sample. With more accurate model output, the clean and noisy distribution gradually separate. In this way, both the model and the wrong event information become more accurate. The stage 2 process is illustrated in the right side of Fig
4.2 Analysis of loss function
For instance z, two-view augmentation generates weak view " and strong view x [39 40). For clean distribution Bi, we utilize the typical cross-entropy loss for both views, leading to the loss term Le:
Lc (x 9) + Loe (x
where fee cross-entropy loss in Eq 7 For noisy distribution B2, we compute the linear average of the model outputs from the two views to obtain robust pseudo-label replace y;:
f(x,) = 1 ((=)))
(10)
which leads to the loss term Lys controlled by confidence coefficient:
Lx = c f(x;) lzg(f( ===(:::)))cc==m((((())))
(11)
To optimize the difficult samples, aim enhance the feature extraction capability of the model w.r.t these samples, as their labels and model outputs are often inaccurate. Specifically, we encourage the outputs of the two views be close possible, and we use LSTM measure this similarity:
LSIM (f(=;)) f(x)))²
(12)
LST.M is the squared error (SE) between the two predictions. We use LSTM to increase the loss weight difficult samples. This encourages the model to focus more on learning from these samples, thereby achieving more robust feature extraction and classification capabilities.

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Table 1: Comparison with state-of-the-an LNL algorithms in test accuracy (%) on CIFAR-100 and Ima-eNete datasets.
Methods
Architecture
CIFAR-100
Tiny-ImageNet
Sym. %
Sym. 40%
Sym. 60%
Asym. 40%
Inst. 40%
Sym. 20%
Sym. 50%
Inst. 40%
Standard
RN-50
75. 15:
59.41=0.84
41.12=1.35 33
53.42+1. 14
58.84=122 2.33
68, 08.84+0.51 51
45.92+1 1,02
53.72+1. 18
SCE
RN
05.21
69.37=0.65
55.25=0071
67.04:0.81
69.73=0.41 57.1820.68
58.6240.63
67.36200.9
TURN
RN-50
80.7020..38 38
78.6810.44
73.36.0.53
69.4910.69
69.8220.993
70.21 59
67.5220.81
65.61=1.01
ELR
RN
80.97=0..1
78.22s0.45
73.97=0.55
75.61+0.31
79.77=0.45
70.54=0:51
64.25=0.47
75.62=0..8
CoL
83.1540.35
81.7620.40 40
79.22.00.59
73.6040.61
80.1820.49
70.92:0063
67.3840,78
72.71=1.02
DMix
RN-50
84.27+0.26
83.08+0.31 31
80.69+0.33 36
66.60+0.89 89
81.37=0.40 40
73.61 36
41
73.39::0:48
UNICON
RN-50
84.12:0.29 29
83,20s0.25
82.24 76.7740.39
75.61=0.47
73.43:0.56
74.71=0.49
DISC
RN-50
83.68:0.36
82.25 40
12:0.51
77.12+0. 44
82.2620.22 28
75.73=0.44 42
74.63:0.57
75.79H0.22 26
DeFT
CLIP-RN-50
84.32+0:21
82.96:60.50
79.92 79.92=0.74
69.9240.81
82. $2.50=0. 19
76.81-40 19
73.92:0.37
74.16400335
IDO
RN-50
85.0820..21
K3.7750.23
81.4220.27
78.1720018
03.84:0.20
78.571:..25
75.4210.29
77.4022.3
SCE
VIT-B
01.26:2.20
90.3840.22 29
87.42:0.377
73.4610.77
83 62222.4444
87.51=0.27
86. 1240.32
83, 13.2210.51
TURN
ViT-B
91.01=0.21
89.75=0.33
88.61=0.55 35
85.1220.25
84.67s0.30
86.74=0.3 31
75. 37:3224
83,72:0.36
ELR
VIT-B
91.52+0 16
90.43+0. 19
89. 74:04+020 20
84 06.6240..2 23
91 1..42.0..0 16
87 37.2220025 29
86.51 14
80. 07.92=0.22 26
DeFT
CLIP-VIT-B
13.1130.13
91.23 01.23+0.17 17
89,42:00 25
72. 96966608) 81
87 27.64=0.22
89.04=0:22 22
72.93=0.66 62
85. 15.26=0033
IDO
92.67=0.09
92.36+0.13
91.45=0.13
89.65+0.12
92.24=0.15
91.25=0.15
90.21=0014
90.32+0.19
5
Experiments
5.1 Experimental settings
Synthetic Datasets. We begin by evaluating the performance of IDO on three popular image
classification benchmarks (CIFAR-10, CIFAR-100 41 and Tiny-ImageNet 42) using synthetic datasets with varying types and ratios of noisy labels. For a noise transition matrix T E [0. 1 Tiy represents the probability of a ground-truth label being flipped to a corrupted label y =
we introduce three common types of label noise: 1) Symmetric Noise [6 17]: with noise rate 7) and K-class image classification task, we define T.j = * for x j. where the true labels are replaced with random labels. 2) Asymmetric Noise: Tiş = p(y jly i). which is designed to mimic the structure of real-world label noise. The labels are only replaced by similar classes. 3) Instance-dependent Noise [43] Tsp = plù = jly = i, 2), which represents a more realistic scenario that considers the influence of instance æ in the label corruption process.
Following previous works [T [S]
Following previous works 25 we conduct experiments on CIFAR- 100 with symmetric noise ratio r E (0.2, 0.4, 0.6), asymmetric noise ratio r = 0.4 and instance noise ratio 0.4, and on Tiny-ImageNet with symmetric noise ratio r E f0.2, and instance noise ratio r = 0.4.
Real-World Datasets. We further investigate the performance of IDO on three real- world noisy label datasets: 1) CIONR- [4] (r R 0.4): A variant of CIFAR- 100 with real-world human annotations collected from Amazon Mechanical Turk. 2) Clothing IM [5] (r R 0.385): A large- scale dataset consisting of I million clothing images across categories, collected from online shopping websites. 3) Web [1 (r 0.2): A dataset using 1,000 classes from ImageNet ILSVRCI2, containing 2.4 million images crawled from Flickr and Google. Following previous works 13 [2]. we conduct experiments the top 50 classes of the Google image subset.
Architecture and baselines. Using pre-trained models for roise-robust training can improve training 12 13). In our experiments, we primarily utilize two widely adopted pre-trained models: ViT-B/16 and ResNet-50. For ResNet-50, we compare IDO with state-of of-the--rttee art LNL
quality (28] 46
algorithms, including one-stage methods SCE 47), DivideMix (DMix) [17, ELR (8. Co-learning
(CoL)) 24), UNICON [66), DISC [I] and two-stage methods TURN 12 and DEFT [3. For
ViT-B/16, we compare IDO with SCF, ELR, TURN and DEFT. Scalability analysis (see Table 3) shows DMix and UNICON require 4x more time and 3x more memory, limiting scalability and making comprehensive comparisons real-world datasets, we also compare with some state-of-the-an methods including LongReMix (48) and ProMix 44 The results of the baseline are reproduced by using the open-sourced code.
ViT-B/16 impractical. To verify the effectiveness of IDO on
We run epochs for stage one to obtain the prior knowledge about wrong event for each sample, and run 10 epochs for stage two to fully robust train the pre-trained model. For two-stage baselines, we run 5 epochs for stage one and run 10 epochs for stage two to fully train the model. For one-stage baselines, we run 15 epochs to fully train the model. All experiment results are the averages of five random runs on a single A 1000 80G GPU. For detailed hyperparameter settings about the optimizer, datasct and baseline, please refer to Appendix B
Implementation. Following setting in 12 13
7

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Table 2: Comparison with state-of-the-arr LNL algorithms in test aceuracy (%) CIFAR-10ON, M.othing1M, WebVision dataset. The best results are highlighted in bold. Results marked with an
asterisk (*) are from 13
Method
Architecture
CIFAR-100N
ClothingIM-R ClothingIM-F
Web
Standard
ResNer-50
$6.71
67.52
69.85
77.84
SCE
ResNet-50
61.42
69.65
71.83
78.35
TURN
ResNet-50
69.54
68.32
72.98
79.28
DeFT
CLIP-ResNet-00
65.53
70,46
73.38
76.62
ELR
ResNet-50
69.25
70.52
73.10
80.16
CoL.
ResNet-50
71.29
72.04
73.09
80,96
DMx
ResNer-50
72.91
72.23
74.56
81.72
UNICON
ResNet-50
73.12
72.44
74.25
82.48
DISC
ResNet-50
73.33
72.15
74.27
82,69
IDO
ResNet-50
73.58
72.65
74.85
82.92
SCE
VIT-16/B
76.45
69.52
73.13
83.25
TURN
ViT-16/B
78.12
70.31
73.89
83.44
ELR
VIT VTF-16/B
72.23
UNICON
CLIP-VIT-16/B
77.76
70.40
84.63
CLIP-VIT-IGR VIT-16/B
74.09
70.65
84,96
ProMix
CLIP-VIT VIT-
76.07
70.79
84.55
DeFT*
CLIP VIT-16/B 16/B
79.12
72.59
85,21
IDO
VIT-16/B
81.36
73.04
74.99
86.03
5.2 Performance for noisy label learning
Overall performance on synthetic datasets. Table demonstrates that IDO consistently outperforms competing methods in CIFAR 100 and Tiny-ImageNet with an average accuracy 1,4%, achieving state-of-the-ar performance on both large and small models. IDO outperforms DMix and UNICON especially in non-symmetric noise through its instance-level modeling. DeFT generally performs well non-asymmetric noise, but faces challenges in resource-constrained scenarios due its dependence on CLIP. DISC and ELR achieve good performance in non-symmetric noise but show limitation in symmetric noise, due to inadequate correction for symmetric noise. While existing methods struggle in some noise cases, IDO is able to handle different noise levels and types more effectively by difficulty modeling and dynamic optimization. Results of CIFAR- 10 are Appendix
E.4
Overall performance on real-world datasets. Table 2
demonstrates that IDO consistently outper- forms competing methods in three real-world datasets with average accuracy of 0.7% both large and small models. DeFT achieves promising results with dual-prompt technique but faces challenges in fine-graing grained classification tasks, such as Clothing IM. DMix and UNICON achieve competitive results in three datasets through dual-network subset partitioning, but with slower training efficiency and limitations scalability. In challenging real-world noisy scenarios, loss regularization methods, i.e. SCE and ELR, do not perform well because they do not attempt to modify the noisy labels.
5.3 Further analysis
We also conduct extensive experiments to validate the superiority of the wrong event metric, the effectiveness, efficiency, and scalability of the proposed optimization framework.
Dynamic loss VS. byperparametter-assed methods. Existing methods introduce extra hyperparam- eters, such as coefficients of loss terms, cutoff threshold for grouping the samples and momentum coefficient, which are hard to tune. demonstrate the advantages dynamic loss, we conducted experiments comparing IDO with two classic algorithms, ELR and DMix. We adjusted the hyper- parameters of them to compare with IDO. The results in Table 7 and Table iindicatee that the value of the hyperparameters for ELR and DMix greatly affects the performance. Besides, the optimal parameters vary across different noise types and ratios, while IDO achieves the best results without hyperparameter tuning. For detailed information, please refer Ao A
Efficiency and scalability of IDO. Existing methods have two drawbacks: high memory demand and low computing efficiency. For instance, DMix and UNICON train two networks simultaneously. which consumes a large amount memory and limits scalability. Moreover, each sample requires to feed-forward computations, resulting in low efficiency. IDO, in contrast, only requires training single network using wrong event metric, which can scaled to larger models. Additionally, each sample only needs two forward computations (two-views), achieving higher efficiency. Fig shows

---

Table 4: Comparison of noise modeling ability across metrics at training time in phase 1, using pre-trained ResNet50 CIFAR-100 The training duration for phase is set to 6 epochs. The " no- tation indicates cases where BMM fails provide adequate fitting, due to all samples being assigned an identical metric value of O.
Table 3: Comparison of methods scalability, running DMix, UNICON and IDO on CIFAR- 100 Inst. 40% noise with larger models on the A100 80GB GPU with batch size of 64. We record the accuracy, average per epoch time (s) and the maximum GPU memory consump- tion (GB).
Noise
Sym.
Inst. 40%
Model
VIT-B/16
ConyNeXi-B
Epoch
2
Metric
Acc.
Time
Mom.
Time
Single Loss
80.2
81.1
79.5
76.3
78.2
76.9
74.6
68.8
DMix
89.5
1596
31.8
88.5
3197
57.4
Loss
79.9
80.9
79.3
77.8
UNICON
90.5
2628
45.2
89.9
4183
78.9
FKL
71.8
73.2
78.2
72.9
75.2
80.2
IDO
91.9
458
14.8
90.8
785
24.7
FE
65.8
71.9
75.8
67.0
73.2
81.7
Wirong Fvent
80.9
81.5
that IDO achieves state-of-the-art performance while achieving high efficiency, Table 3 shows IDO 4x faster and x less memory than DMix and UNICON large models, with better performance on average. For detailed training time analysis, please refer Appendix
Wrong event VS. other metrics. We adjust the BMM fitting distributions of different metrics to compare their performance in noise modeling. We change the duration of stage evaluate the metrics at different training stages. The results are presented in Table 4 Loss shows optimal performance in the early stage, but the optimal point hard identify; Even worse, the per- formance rapidly degrades in later stages due to noise overfitting. While the EMA-loss (Expo- nential Moving Average) mitigates noise overfit- ting in later training phases, it limits the capacity during the initial phase, creating a trade-off be- tween strly-stage and late-stage. The visualiza- tion about the clean sample selection ability of loss and wrong event in Appendix C.4 Both forgetting event (FE) and First k-epoch Learn- ing (FKL.) show their noise modeling capabili- ties after the model begins overfit the noise.
Accuracy(55
Epoch
86
84
500
Tinia per Epoch (5)
Accuracy (%)
82
80
200
DMix
DeFT
UNICON
COL
Figure 4: Comparison with state-of-the-art LNL algorithms in effectiveness and efficiency, using pre-trained ResNet50 on the A A100 80GB GPU and CIFAR- 100 dataset with 20% symmetric noise.
However, these metrics need to accumulate over time to show differences, resulting in suboptimal per- formance in the early stages. Overall, wrong event exhibits superior noise modeling capabilities in all training stages. The experiment results match our theoretical analysis in Secciiion 3.2 confirming the effectiveness of wrong event in identifying noise. More analysis on metrics is in Appendix
Table 5: Ablation studies on the loss modules are conducted using ResNet50 under three different noise settings on CIFAR100
Modules
CIFAR100
Le
Ex
LSIM Sym. 60%
Asym. 40%
Inst. 40 %
75.1
57.7
70.5
79.5
70.4
77.3
78.2
72.0
80.3
81.4
78.2
83.7
The effect of different loss terms. Our loss function consists of three components: Le, Lv and LSIM, modeling clean samples, noisy samples, and difficult samples, respectively. Our ablation experiments demonstrate that all three components contribute to improving the model performance (see Table We observe that L, achieves higher improvement for symmetric noise, leveraging the accuracy of model output to improve classification performance, while L.T.M shows greater improvements for asymmetric and instance noise, improving the model's ability learn from difficult samples by imposing consistency predictions. More exploratory experiments in Appendix E

---

Table 6: Comparison of dynamic weight c(w) against fixed-weighting methods CIFAR-100
Weighting Method
Sym. 60%
Asym. 40%
Inst. 40%
Withoul c
79.5
70.4
77.3
Fixed 0.25
81.3
76.5
83,3
Fixed 0.5
80.8
77.5
82.4
Fixed c
80.3
76.8
82.8
Dynamic c
81.4
78.2
83.8
The behavior of the difficulty-basee weighting, IDO relies more heavily consistency learning under difficult conditions. We conducted experiments comparing our dynamic weight <(w) against fxed-weighting methods (See Table
(6). The result supports our core hypothesis, much like the principle behind Focal Loss [4]. showing that a weighting term to expand the loss difficult data necessary and better than treating all samples the same. We consider that for easy data, cross-entropy loss serves as a more direct and effective learning signal than consistency loss while consistency loss serves effective learning signal for difficult data. Dropping and fixing the difficulty coefficient both decrease the performance. More exploratory experiments are in Appendix E
6
Limitations and broader impact
6.1 Limitations
Wrong event becomes suboptimal when the noise ratio becomes extremely high, i.e., more than 90%, because the distribution of wrong event will become extreme imbalance and the model struggles to converge. However, we do not suppose this will restrict the practical application ability of IDO, as real-world noise rates are often between 8.0% and 38.5% [50). far from extreme scenarios. However, designing lightweight and highly scalable framework that remains competitive under extreme noise ratio is an important challenge for the community.
6.2 Broader Impact
Our research on label-noise learning contributes to building trustworthy machine learning systems. particularly in scenarios where high-quality annotations are costly or subjective (e.g., medical imaging diagnosis, social media content moderation). Consequently, as this method develops in effectiveness and scalability, the requirement for large-scale human- aannant- data might decrease, potentially contributing to a rise in unemployment among data annotation professionals.
7 Conclusion
In this work, we introduce IDO, a novel framework that tackles noisy labels through fine-grained, instance-level optimization. Our approach is centered on the wrong event metric, a simple yet highly stable measure of sample cleanliness and difficulty that remains effective throughout training, even post-overfittig. By modeling this metric with a Beta Mixture Model, IDO uses dynamic loss function that eliminates the need for manual hyperparameter tuning. Experiments confirm that IDO sets a new state-of-the-art in accuracy while being significantly more efficient and scalable than previous methods, offering practical and robust solution for real-world noisy label learning.
Acknowledgments
Chengliang Chai supported by National Key Research and Development Program of China (2024YFC3388000) NSFC (62472031), Beijing Nova Program, Baidu202402) and Huawei. Ye Yuan is supported by Beijing Natural Science Foundation (L241101)) the National Key R&D Program of China (Grant No. F222222B200000) and the NSFC (Grant Nos. 61932004, 62225203, U21 A20516), Guoren Wang supported by the NSFC (62427808. U2001211), the Liaoning Revitalization Talents Program (Grant No. No.XLLC2204003 Yuping Wang is supported by the NSFC (U23A20297, U23A20317). Lei Cao is supported by the NSF(DB123377544) and
Open Fund (CCF.
Amazon Research Awards.
10

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-Supplementary Material-
This supplementary material provides additional analysis and explanation of our paper, "Handling
Label Noise via Instance-Level Difficulty Modeling and Dynamic Optimization ", which were not included in the main manuscript due to page constraints.
First of all, for the readers' better understanding, we describe the main content of the appendix. Appendix A details the sensitive analysis of two SOTA methods, including detailed parameter setting. Appendix B outlines the characteristics of each dataset and implementation details of learning rate, optimizer, baseline. Appendix C provides extensive theoretical and experimental analysis of wrong event for further analysis. In Appendix D, we illustrate the training time analysis.
A Sensitivity analysis of parameter configurations in two SOTA methods
In this section, we conduct comprchensive experiments on two advanced algorithms, ELR and DMix [17), to investigate the sensitivity of manually fixed parameters. Our analysis focuses key hyperparameters including the subset division threshold, loss term weights, momentum averaging coefficients, among others.
A.1 Analysis and experiments of ELR
ELR algorithm incorporates two crucial hyperparameters: the regularization term weight À and the temporal ensembling momentum coefficient B. Table 7 demonstrates the parameter sensitivity of ELR, showing that the performance is significantly influenced by parameter choices and comparison with the result of IDO. The parameter settings recommended for training from seratch in the original paper, where the authors recommend 3 = 0.7, X = 3 for symmetric noise on CIFARIO0 and 3 3= 0.9, À for asymmetric noise on CIFAR-100. However, parameter settings undergo significant shifts in pretrained settings. Optimal performance is achieved when 3 E [0.3, 0.5]. À E [3, 5). demonstrating that optimal hyperparameters vary across different models and datasets, necessitating careful parameter tuning. Our proposed method IDO effectively addresses this challenge through dynamically weighted optimization.
Table 7: Hyperparameter sensitivity of ELR, utilizing pre-trained ResNet50 on the CIFARIOS 100 dataset with three noise settings. The default values are set À = 3 and 3 0.7. Each time, parameter perturbed while others are set to default. We consider the value ranges X E {0, 1, 3, 5, 7, 103 and B E {0.1, 0.3, 0.5, 0.7, 0.9, 0.99]. following original paper [8].
Hyperparameter
regularization term weight
momentum coefficient 8
IDO
Noise Dataset
3
7
10
0.1
0.3
0.7
0.9
0.99
CIFAR- 100 Sym. 60%
41.1
41.7
73.9
75.9
46.4
1.0
12.2
75.9
77.1
73.9
51.3
42.9
81.0
CIFAR-106 100 Inst. 40%
58.8
56.0
79.7
82.9
69.5
25.0
49.9
82.9
82.6
79.7
67.3
59.4
83.6
CIFAR-IOON 61.0
61.6
69.2
62.7
56.1
70.7
69.2
65.3
62.1
73.6
A.2 Analysis and experiments of DivideMix
DivideMix algorithm incorporates three crucial hyperparameters: the unsupervised loss term weight Au. GMM threshold for subset partitioning and beta distribution parameter of Mixup (5I).
Table 8 demonstrates the parameter sensitivity of DivideMix, showing that the performance is
significantly influenced by parameter choices and comparison with IDO's result. The parameter settings recommended for training from scratch in the original paper, where the authors recommend A, 25, r E [0.5, 0.6) a 4 for symmetric noise on CIFAR 100 and X 0, 0.5, 4 for asymmetric noise on 100. However, parameter settings undergo significant shifts in pretrained settings. Optimal performance achieved when X,, E [50, 150). E [0.1, 0.5) shows that optimal hyperparameters vary between different models and data sets, which requires careful parameter tuning. Our proposed method IDO effectively addresses this challenge through dynamically weighted optimization.
15

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Table 8: Hyperparameter sensitivity of DivideMix, utilizing pre-trained ResNet50 the CIFARI00 dataset with three noise settings. The default values are set as Xu = 50, r = 0.5 and a = 4. Each time, one parameter is perturbed while others are set to default. We consider the value ranges of A E {0, 25, 50, 150). 7 E {0.1, 0.3, 0.5, 0.7, 0.9} and a E {0.5, 1, 2, 4} following original paper
Hyperparameter
Cu term weight A
GMM threshold
Mixup purameter a
IDO
Noise Dataset
0
25
150
0.1
0.3
0.5
0.7
0.9
2
4
CIFAR- 100 Sym. 60%
80.7
79.3
79.9
80.8
81.1
80.5
79.6
67.4
29.8
80.9
79.7
79.2
78.0
81.0
110 Inst. 40%
79.7
79.9
81.9
81.1
80.3
79.3
79.7
78.1
70.5
79.8
81.1
82.3
81.3
83.6
CIFAR- 100 Asym, 40%
63.2
63.6
66.6
67.9
63.8
65.3
66.6
65.9
57.6
60.3
62.1
66.4
66.6
77.8
B Additional implementation details
Regarding the hyperparameterss the model. In our experiments, we primarily utilized pre-trained ResNet-50, 16B and ConvNeXt-B models, both of which were obtained by calling the PyTorch timm library. For the pre-training hyperparameters of the model, we adhered to the settings used in prior work 12 13, as detailed in Table 9 One-stage baselines follow the setting in stage 2.
Table 9: Optimizer configurations for different models and stages.
Phase
Stage 1
Stage 2
Configuration
VTT-B/16
ResNet-50
ConyNeXt-B
VIT-B/16
ResNet-50
ConyNeXI-B
Optimizer
SGD
AdamW
AdamW
SGD
AdamW
AdamW
Learning Rate
1 x 10
1 10-3
1 x 10
I x 10-2
1 10-3
1 10
Weight Decay
1 x 10-5
1x 10-5
1 101
1 x 10-5
10-5
1 10
Scheduler
No LP
No
No
Cosine
Cosine
Cosine
Strategies
FFT
LP
FFT
FFT
FFT
Regarding the details of the datasets. The model quality was determined by the accuracy on the test set at the last epoch. For synthetic datasets, added noise to the entire training set and used the test set to evaluate performance. CIFAR 100 consists of 100 classes, with 50,000 training images and 10,000 test images, and we set the batch size to 128. Tiny- ImageNet contains 200 classes, with 100,000 training images and 10,000 test images, and we also set the batch size to 128.
For real-world datasets, we only used the noisy datasets and did not utilize the clean subsets provided by the datasets. Clothing M is a class-imbalanced dataset, and we sample class-balanced subsets each time, with batch size of 64 and 1,000 iterations. Clothing M-F means using fixed subset during training, used in 1K 12. Clothing MM- M-R means sampling random subset per epoch, used in [I] In Clothing M-R, we calculate wrong event for the subset every 100 iterations. CIFAR 100N is identical to CIFAR100 except for its real-world noisy labels. For WebVision, we used the first 50 classes, which include 66000 training images and 2,500 test images, and we set the batch size to 128.
Regarding the hyperparameters of the baselines. The baseline results were generated under consistent experimental settings using publicly available code. The hyperparameters were configured according to the recommendations outlined in the original papers.
SCE [47] is a robust noise-tolerant loss function with two hyperparameters, a and 3. The original paper suggests that large may lead overfitting, while a small can mitigate overfitting but slow down convergence. Therefore, the authors recommend using a small a and a large 3 to replace existing loss functions. Since pre-trained models converge faster, we adopted the configuration proposed in the original paper to suppress overfitting to noise, setting a = 0.1, = 1.
ELR [8] introduces regularization term to the loss function, leveraging the correct predictions of noisy samples during early learning to achieve roiue-robust learning with two hyperparameters, and B. The authors recommend hyperparameter settings of CIFAR 100, Clothing IM and Web Vision, with À = 3, B = 0.7. We applied the same settings across these datasets. For CIFAR10ON and Tiny-emageNet, adopted the same configuration used for CIFAR100.
DivideMix 17 a co-training-bass based label correction method that introduces five key hyperparame- ters: number of MixMatch views M, temperature of sharpen labels T,, mixup parameter a, GMM
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Throughout
30000
Chee Date
1101
8000
700
Know Doper Outr
Figure 5: The baseline model ResNet- 18 trained on CIFAR-10 40% asymmetric noise for 100 epochs. We show the loss distributions (the first row) and wrong event distribution (the second row) during training. The four columns, (a) (b) (c) (d), represent the distributions at epoch 10, 50, 100 and the entire training phase. In (d), the heavy lines represent the median value and the shaded areas the interquartile ranges, respectively. It is clear that wrong event can clearly separate noisy data and clean data, even if the model fits noise.
threshold r and unsupervised loss term coefficient A. We followed the original paper's settings, for most experiments, setting M 2, 0.5, = 4, T= 0.5, and X = 50.
Co-learning [24] is a method combining supervised learning and self-supervised learning, with Laup Lint + Latr. All the coefficients of loss terms are set following the original paper.
label correction method that combines supervised learning, supiriuper learning and contrastive learning. There are seven main parameters mentioned: unsupervised loss coefficient λu. regularization coefficient Xy, contrastive loss coefficient Ac filter coefficient т, adjustment threshold d₂ and mixup coefficient a. Following the original paper, we set Ac = 0.025, A, = 30, A, = 1, 1, = 0.7, T = 5 and a =
UNICON 16 is a co-training-
DISC [1] is method which dynamically selects and corrects dataset. Four main hyperparameters are mentioned: warm-up period T,, coefficient of the hard-set loss Ay. momentum coefficient À and positive offset value Following the pre-trained model setting in the original paper, we set To 1, 0.7, Au- = 0.2 and o = 0.3.
TURN 12) is a method which firstly uses noise-robust loss function to obtain a clean set with LP, and FFT the model on the clean set. The main hyperparameter is the GMM threshold r. Following the original paper, we set 0.6 in all experiments.
DeFT 13 is CLiP-based method which used dual prompts CLIP obtain clean set with parameter-efficient fine-tuning (PEFT), and FFT the pre-trained downstream model on the clean set. The heavy reliance CLIP significantly limits the method's applicability in computational resource-constrained scenarios.
Regarding the hyperpapameters of BMM. Since IDO relies on priors, all experiments default that (1, 2), (2, 1). The EM algorithm will update the parameters to the appropriate values.
C More analysis of wrong event
C.1 More empirical observations of wrong event
We show comparison between wrong event and loss under symmetric noise (see Fig We also conduct experiments under instance noise, and asymmetric noise to verify that wrong event outperforms the loss across all types of noise. 3 and Fig comparison between wrong event and loss under asymmetric noise and instance noise, respectively. The experiment results reveal that in more challenging noisy environments, the model tends to rapidly fit the loss of noisy samples, resulting in compromised accuracy and stability of the provided modeling information. In contrast,
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Epech
Eoach
Eoach
Henry Moar
Lea DoAderies
34000
3403
Ore Dete
12:00
Oran Dex
Cren men Wiong Leee
bolo Dara
3400
300
1003
1203
280
103
(5)
(c)
(40
Figure 6: The baseline model is ResNet-18 trained on CIFAR-I0 with 50% instance noise for 100 epochs. We show the loss distributions (the first row) and wrong event distribution (the second row) during training. The four columns, (a) (b) (c) (d), represent the distributions epoch 10, 50, 100 and the entire training phase. In (d), the heavy lines represent the median value and the shaded areas are the interquartile ranges, respectively. It is clear that wrong event can clearly separate noisy data and clean data, even if the model fits noise.
wrong event metric maintains its capability to deliver robust modeling information about sample cleanliness and difficulty.
C.2 Analysis on the change rate between wrong event and loss
We provide an analysis about the change rate between wrong event and loss. The loss change rate 87 [_ +oo in every epoch T' with unbounded limits and frequently unpredictable mutations. A usually seen phenomenon named forgetting event [19] (last epoch right, this epoch wrong) can cause the probability of given label to plummet from high probability (e.g. 0.9) to a small probability (c.g. ~ 0.1). causing the loss to skyrocket and the relative change to become enormous. This can happen randomly and repeatedly for all samples.
However, for wrong event, the change rate needs more discussion. Firstly, we have w wi + o,+ 6T+1 E {0,1) and wff" [o...., T), meaning the wrong event value is monotonically increasing. The change rate is 6T w! We analyze this in two distinct cases:
The "0 to 1" Transition: When a sample is misclassified for the very first time, w/f transitions from 0 to 1. At this point, the relative change ō is not defined. This is singular, one-time event for any given sample, marking its initial entry into the set "ever-misclassifeed" samples.
All Subsequent Changes (wf 2 1)): For every subsequent misclassification, the denominator wff"
67 is at least 1. The relative change is w. This value is strictly bounded within the range [0,1] far smaller than the change rate of loss. More importantly, as the model continues misclassify sample, w/ increases, causing the maximum possible relative change to decrease. The metric is therefore self-stabilizing.
The relative change of wrong event well-behaved, bounded, and self stabilztai after a single initial event. Conversely, the relative change of loss is unbounded and perpetually susceptible to explosive volatility. This fundamental difference in their rate of change is why wrong event serves as a far more reliable and stable signal for modeling sample characteristies in noisy environments.
This analysis provides a strong theoretical basis for the empirical stability we observed in Figure 7 In experiments, the values of loss and wrong not in the same range. We normalize metric values and track the range of value changes during training (1,) = 115 1, |wj w/ and
Max Change argmax (6.), Avg Change = N Σn= ò,. The result is in Figure Loss variance
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is near the size of the dataset, confirming that loss has no bound. Wrong event variance decreases over training. Besides, due to the mutation loss, the mean change larger than wrong event. Experiment results confirm the theoretical analysis regardless of pre-training or not.
1.0
1.0
0.8
0.8
Variance
0.6
Veriance
change
Max Charge Aug Change
Max Change
Seg Charge
0.4
0.2
0.2
0.0
0.0
Epoch
Epoch
(a) Variance over epochs on pre-training setting
(b) Variance over epochs on random initialized setting
Figure 7: Variance comparison between loss and wrong event (WE). We test random pre-trained ResNet-50 on CIFAR- 100 Inst. 40% noise (left) and random initialized ResNet-18 on CIFAR- 10 Inst. 40% noise (right).
C.3 More discussion about different metrics
Researchers have proposed some metrics trying to replace loss because loss is easy to fit noise, such as forgetting event [1), fluctuation event (52), first k-epoch learning [20]. All of them are based on
forgetting. In all the following equations, the symbol y; is used to denote the model prediction of sample (2i, Vi) at epoch Forgetting event (FE) defined as
T 1 1
forgetting event,
-
(y) + vt)
which counts how many times model forgets prediction of given labels. Fluctuation event is defined as
fluctuation event, = (3/ = y ) A (Th + )
where 1 S 12. First k-epoch learning (fkl) is defined as
fkl; = arg = J.
(T. = - -
e
which records the epoch when a sample has been predicted to its given label for consecutive k epochs for the first time.
We group all three metrics into forgetting- based metrics (FBM). All metrics extract the statistical information to assist noise modeling, but are still different. Notably, FBM needs time to remember the given label, because the model needs time fit the given label, especially when the label is noisy while wrong event needn't t. This difference makes FBM spend pretty longer time accumulating statisties. Considering easy noisy data for example, ground-truie -ruth of easy noisy data is consistently predicted, so the model cannot remember noisy labels. Easy noisy data's wrong event would increase rapidly, but FBM would be constant value. Thus, FBM cannot distinguish easy noisy data in early stage, needing more training time and thus the scalability limited, while wrong event has good modeling ability during training phase. Table 4 also shows that loss-based metrics perform well in early stage but decrease over training, and FBM such FE and fkl perform poorly in early stage but increase over training, needing more training time. While wrong event perform well during the entire training phase, showing effectiveness and efficiency.
early stage, model learns correctly and
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1.0
0.8
True Postive Ralte
0.6
Thue Postive
60.6
0.4
0.4
Lamaan SMUCaT 53:
Whong Duend (pach 29 (AC
(hong Event: loech 114---000
0.2
0.2
Spech JAA
Wore Event: 13 (KUCed.00
8.0
0.2
0.4
0.6
0.8
1.0
8.0
0.2
0.4
0.6 Rate
0.8
Posttive
Figure 8: The AUC-ROC curves of loss and wrong event. The experiment conducted with random initialized ResNet-18 on CIFAR-10 (left) and pre-trained ResNet-50 on CIFAR-100 (right) under I0st.40% noise, The curves show the dynamic selection eurves over epochs. We visualize the ability of clean sample selection in early, midterm and later training stages. The curves show that wrong event has a larger AUC value than loss and show good performance during the whole training phase, which represents better ability of clean sample selection.
C.4 Selection ability between wrong event and loss
Table shows that wrong event outperforms loss in test accuracy. To further compare their clean sample selection ability, we calculate F-score along with precision and recall, AUC along with accuracy and precision under pre-training and random initialized settings. (Table 10 and Table 1] show the F-score, Table 12 and Table 13 show the AUC value and Figure 8jshows the AUC-ROC curves during training. All results indicate that wrong event is better than loss selecting clean samples. Wrong event clearly model the noise during the whole training phase, while loss only performs well in early stage. In conclusion, wrong event is a simple but effective metric to select clean samples, which can capture noise well even if the model has fitted the noise.
Table 10: The precision, recall, F-score of loss and wrong event. The experiment is conducted with random initialized ResNet18 on CIFARI 10 under Inst.40% noise. We set three thresholds to calculate F-score.
Threshold
Epoch
10
10
60
F-score
0.49
0.38
0.29
0.34
0.29
0.20
0.00
0.00
0.00
Loss
Precision
0.62
0.76
0.79
0.71
0.79
0.75
0.92
0.90
0.60
Recall
0.41
0.25
0.18
0.23
0.18
0.11
0.00
0.00
F-score
0.60
0.67
0.70
0.63
0.70
0.72
0.70
0.79
0.76
Wrong Event
Precision
0.43
0.51
0.46
Recall
0.99
0.99
0.99
0.99
0.99
0.99
0.77
0.71
0.65
Table 11: The precision, recall, F-score of loss and wrong event. The experiment is conducted with pre-trained ResNet-50 on CIFARI00 under Inst.40% noise. We set three thresholds to calculate F-score.
Threshold
Epoch
5
20
30
20
30
20
30
F-score
0.77
0.84
0.56
0.83
0.61
0.04
0.05
0.01
0.00
Precision
Recall
1.00
0.96
0.87
0.85
0.45
0.02
0.02
0.00
0.00
F-score
0.76
0.85
0.84
0.85
0.90
0.92
0.87
0.92
0.88
Wrong Precision
0.62
Recall
1.00
0.97
0.99
0.99
0.98
0.96
0.93
0.92
0.81
D Training time analysis
We analyze the training time of IDO to understand its efficiency. Results in Figure 4 show that IDO is faster than all baselines. For IDO itself, the running time x BMM fitting forward propogation.
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Table 12: AUC value of wrong event and loss with random initialized ResNet-18 under different noise types and levels on CIFAR-10 10 (left) and CIFAR-100 (right). Higher AUC value indicates better clean sample selection ability.
Noise
Sym 611
Asym. 40%
Inst. 40%
Noise
Sym. 60%
Asym, 40%6
Inst. 40%
Epach
20
66
100
20
50
100
20
60
100
Epoch
20
60
100
20
60
100
20
60
100
Loss
0.15
0.30
0.63
01.00
0..64
0.58
0.84
0.65
0.59
Loss
0.85
(1.6))
0.60
0.62
0.56
0.55
0.79
0.61
0.59
Wrong Event
0.96
0.98
0.97
0.94
0.94
0.92
0.94
0.95
0.94
Wrong Event
0.57
0.92
0.91
0.72
0.75
0.74
0.86
0.88
0.88
Table 13: AUC value of wrong event and loss with pre-trained ResNet- 50 under different noise types
and levels on 100. Higher AUC value indicates better clean sample selection ability.
Noise
Sym. 60%
Asym, 40%
Inst. 40%
Epoch
25
Loss
0.96
0.88
0.74
0.66
0.63
0.50
0.84
0.75
0.67
Wrong Event
0.97
0.98
0.98
0.76
0.80
0.79
0.93
0.95
0.94
In Table 14 state-of-the-arr art methods which leverage probabilistic model, using single Nvidia A100 80GB GPU,
we compare the total training time of IDO on CIFAR-100 Inst,40% noise with several
IDO is faster than M-correction and DivideMix which involve multiple forward propagation and fitting iterations. In Table 14 we also break down the computation time for each operation in IDO. Results show that BMM efficient, only 4.6s per epoch, which is 3.8% of the total training time, Moreover, results show that wrong event-based BMM in IDO is faster than loss-based BMM/GMM in M-correction and DivideMix. The reason that the robustness of wrong event helps to reduce the fitting iteration rounds and require no reinitialization significantly in successive epochs, needing more fitting rounds and reinitialization in each epoch. In the open-sourced code, IDO only iterates few rounds based the last BMM (1 iteration per round, no reinitialization), while M-correction and DivideMix need many rounds and reinitialization (10 GMM iterations in DivideMix. 20 BMM iterations M-correction) to handle loss mutation.
time. While loss often varies
Table 14: Comparison methods using probabilistic model on CIFAR-100 with Inst. 40% Noise
Method
Accuracy| ())
Per Epoch Time(s)
Per Epoch Fitting Time(s)
MBCo)))ctionBBMM))
78.9
399
14.7
DivideMixGGMM)
81.3
457
19.5
IDO(BMM)
83.7
121
4.6
E More exploratory experiments
In this section, conduct more exploratory experiments, hoping offer more insight and inspiration to the readers and community.
E.1 Base model vs. initial model
After Stage we already have information about clean, noisy and hard samples. interesting to think that it is better to train the model from the base model or directly from the initial model. Since the base model has already been trained on corrupted samples, retraining from the initial model might lead to better performance.
Table 15: Comparison of initial model and base model on CIFAR-100 with different noise types
Start Model
Sym. 60%
Asym. 40%
Inst. 40%
Initial Model
80.1
77.1 78.0
83.3
Base Model
81.5
83.7
We run experiments to verify this. Results are in Table 15 Overall, base model yields better results. Its advantage is high when handling Sym. noise as symmetric noise is harder to and easy to detect. The difference is smaller when handling Asym./Inst. noise as the model fits these noise more casily,
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decreasing the performance. Within the relatively limited training time, using the base model can more quickly achieve better performance.
E.2 Wrong event loss accumulation
As the single epoch loss is easy to fit noise, it is interesting to think whether accumulated loss can prevent fitting noise. We have conducted new experiments compare accumulated loss and wrong event. We get two observations from the results in Table 16
Table 16: Comparison of wrong event and accumulated loss on CIFAR-100 with various noise types
Noise
Sym. 60%
Asym. 40%
Inst. 40%
Single Loss BMM
71.9
72.6
Accumulated Loss GMM
79.2
74.5
77.9
Accumulated Loss + BMM
80.1
75.9
79.1
Wrong event + BMM
81.2
78.3
83.4
1. Accumulated loss performs better than single loss because accumulation prevents fitting noise, but the variance increases linearly when summing i.i.d. data. Besides, accidental sample forgetting can have a significant impact on the accumulated loss, increasing the variance. Thus, the distribution of loss sum flatter than that of wrong event, which blurs the classification boundaries, making more data misclassified which drops the performance.
BMM performs better than GMM. In [77, the authors point that GMM does not fit well Asym. noise. Therefore, BMM, which shows stronger fitting ability, performs better.
E.3 Synthetic dataset vs. real world dataset
We find that IDO and all baselines achieve smaller improvement on real-world datasets compared to synthetic datasets as shown in Table and Table 2 which is worth further discussion.
We first analyze the difference between wealdworld noise and synthetic noise. [12] [53] pointed out that real world noise usually lies closer the decision boundary than synthetic noise, which harder to detect. In other words, it is easier to fit as boundary cases, slightly changing the decision boundary and thus results in less degradation of model performance than synthetic noise which will significantly change the decision boundary after fitted. As the degradation become smaller, the improvement space from w/ label noise to w/o label noise for algorithms is smaller.
E.4 Strong algorithm collapse in CIFAR-10
The experiment result for CIFAR-10 is in Table 17 IDO still outperforms baselines. It is surprising to see performance drop outside of UNICON, competitive algorithm in other datasets, showing that the variation of the hyperparameters across datasets and models easily decrease the model performance. This indicates high tuning cost and performance drop for hyperparameter-basee methods in real world scenarios.
Table 17: Comparison with ffte-of-the--e LNL algorithms in accuracy (%) on CIFAR-10.
Noise
Architecture
Sym. 20%
Sym. 40 %
Sym. 60%
Asym. 40%
Inst. 40
Standard
ResNer-50
93.2%
92.3%
88.2% 2%
91.1%
90.9%
UNICON
ResNet-50
94.8%
93.2%
92.5%
93.5%
93.9%
ResNet-50
95.8 8%
95.1
95.0%
94.8%
DeFT
CLIP-ResNet-50
96.9%
96.6%
95.7%
93.8%
95.1%
DivideMix
ResNet-50
97.1%
96.8%
96.3%
93.1%
96.0%
DISC
ResNet-50
96.8%
96.5%
95.5%
95.2%
96.5%
IDO
ResNet-50
97.3%
96.9%
96.5%
95.3%
96.6%
E.5 Including more baselines
We include InstanceGM 54 and NAI.
55 as our two more baselines in new experiments on
CIFAR- 100 (see Table 18
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Table 18: Comparison of more baselines CIFAR-100 with various noise types
Method
Sym. 60%
Asym. 40%
Inst. 40%
Standard
41.1
53.4
58.8
InstanceGM
80.5
76.3
83.1
NAL
80.9
77.6
81.3
IDO
81.4
78.2
83.8
The results show that while InstanceGi is strong in its target setting (instance noise), it underperforms in symmetric and asymmetric noise because InstanceGM too cautious in judging noise which leads to insufficient label correction. NAL performs well but is slightly behind IDO, particularly in the most challenging instance-dependent scenario. IDO demonstrates consistently state-of-the-art performance across all three settings.
E.6 Experiments broader noise levels
To thoroughly evaluate IDO's robustness and practical applicability, we agree that testing on a wider range of noise levels is erucial. We have conducted new experiments CIFAR-100 using the pretrained ResNet-50 with more noise levels (See Table 19h. For symmetric noise, a high noise ratio of 80% added. For asymmetric noise, 20% and 45% are added. For instance-dependent noise, 20% and 60% are added. Besides, a noise-free (0%) baseline is included.
Table 19: Performance comparison of broader noise levels
Method
Sym. 0%
Sym. 80%
Asym. 20%
Asym. 45%
Inst. 20%
Inst. 60%
Standard UNICON
82.8%
35,2%
68.5%
46.2%
70.4%
31.6%
84.8%
64.0%
83.5%
73.2%
84.9%
58.2%
DeFT
85.1% %
57.6%
78.9%
65.2%
82.4%
56.5%
IDO
85.8%
62.5%
85.4%
74.1 %
85.1 %
60.8 %
These results demonstrate that IDO maintains significant performance advantage across wide spectrum of noise types and levels, including the challenging 45% asymmetric noise and 60% instance- dependent noise scenario. This confirms the robustness of our approach, even under conditions far more extreme than the 8%-38.5% noise typically found in real-world datasets [50]. Impressively, IDO also achieves the best performance in the noise-free (0%) setting, showing it does not degrade performance on clean data.
As discussed in our limitations, performance degradation is only observed at extremely high noise ratio of 80%, which is expected due to the severe imbalance the wrong event distribution that affects the BMM and model convergence. We believe these new results comprehensively address the concern about robustness and practical applicability.
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Reviews:
[{"review_id": "lwBnkHU76F", "reviewer": "Reviewer_hZpr", "summary": "This paper proposes a two-stage framework, IDO (Instance-level Difficulty Modeling and Dynamic Optimization), for robust training on noisy labeled data. It introduces wrong event, a metric counting incorrect predictions per sample, which effectively distinguishes clean, noisy, and hard samples throughout training. Experiments on synthetic and real-world datasets show that IDO outperforms state-of-the-art methods in accuracy, efficiency, and scalability.", "questions": "1. How does the method perform when class boundaries are highly entangled? \n\n2. Similar to question 1, additional experiments across a wider range of noise levels—especially under instance-dependent noise—would strengthen the paper. These results would offer a more realistic understanding of the method’s robustness and practical applicability. \n\n3. According to Table 5, the similarity loss seems to have a larger effect in more challenging noise settings (e.g., Asym. 40%, Inst. 40%). Does this imply that the method relies more heavily on consistency learning under difficult conditions? What happens if the difficulty score is fixed to a high value—i.e., treating all samples as difficult? Is it desirable for easy samples to receive a low weight for similarity loss? A deeper analysis of the behavior of the difficulty-based weighting would be helpful.\n\n4. Including more baselines, such as InstanceGM, would provide a more comprehensive comparison and help contextualize the proposed method’s performance more clearly.\n  - Garg, Arpit, et al. \"Instance-dependent noisy label learning via graphical modelling.\" Proceedings of the IEEE/CVF winter conference on applications of computer vision. 2023.", "limitations": "As the paper mentioned, the situation with a high noise ratio differs from the actual data environment, but analyzing performance will help in evaluating the robustness of the methodology.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The method is well-motivated and empirically sound. The paper is clearly written, with thorough explanations, visualizations, and ablation studies. In addition, the proposed approach is thoughtfully designed to reduce reliance on hyperparameter tuning.\n\nHowever, the paper does not sufficiently discuss potential failure cases, such as performance under a wider range of noise levels, especially in instance-dependent noise settings. Moreover, although obtaining prior knowledge in Stage 1 is crucial—particularly in capturing the label wave number—there is a lack of detailed analysis on its impact and sensitivity.", "was_revised": true, "final_justification": "The authors have provided a detailed and thoughtful rebuttal with substantial additional experiments and analyses. Their responses addressed the main concerns raised in my initial review, particularly regarding robustness under diverse noise conditions, the sensitivity of Stage 1, and the behavior of the difficulty-based weighting mechanism. The inclusion of additional baselines such as InstanceGM and NAL also strengthened the empirical evaluation.\n\nBased on the updated understanding, I have raised my score to borderline accept. I look forward to seeing the revised version reflect these improvements.", "rebuttal": "**Overall Response:**\n\nWe sincerely thank you for your detailed and constructive feedback. Your insightful questions have helped us to further strengthen the paper. We have conducted several new experiments based on your suggestions and are confident that incorporating these results and discussions will significantly improve the final manuscript. Below, we address each of your points in detail.\n\n**Question 1:** The paper does not sufficiently discuss potential failure cases, such as performance under a wider range of noise levels, especially in instance-dependent noise settings and high noise ratio settings. More experiments help to evaluate the robustness and practical applicability of the method.\n\n**Response:** \n\nThank you for this excellent suggestion. To thoroughly evaluate IDO's robustness and practical applicability, we agree that testing on a wider range of noise levels is crucial. We have conducted 6 new experiments on CIFAR-100 using the pretrained ResNet-50 with more noise levels. For symmetric noise, a high noise ratio of 80\\% is added. For asymmetric noise, 20\\% and 45\\% are added. For instance-dependent noise, 20\\% and 60\\% are added. Besides, a noise-free (0\\%) baseline is included. The results summarized below.\n\n| Methods | Sym. 0\\% | Sym. 80\\% | Asym. 20\\% | Asym. 45\\% | Inst. 20\\% | Inst. 60\\% |\n|-|-|-|-|-|-|-|\n| Standard | 82.8\\% | 35.2\\% | 68.5\\% | 46.2\\% | 70.4\\% | 31.6\\% |\n| UNICON   | 84.8\\% | **64.0\\%** | 83.5\\% | 73.2\\% | 84.9\\% | 58.2\\% |\n| DeFT     | 85.1\\% | 57.6\\% | 78.9\\% | 65.2\\% | 82.4\\% | 56.5\\% |\n| **IDO**  | **85.8\\%** | 62.5\\% | **85.4\\%** | **74.1\\%** | **85.1\\%** | **60.8\\%** |\n\nThese results demonstrate that **IDO maintains a significant performance advantage across a wide spectrum of noise types and levels**, including the challenging 45% asymmetric noise and 60% instance-dependent noise scenario. This confirms the robustness of our approach, even under conditions far more extreme than the 8%–38.5% noise typically found in real-world datasets [1]. Impressively, IDO also achieves the best performance in the noise-free (0%) setting, showing it does not degrade performance on clean data.\n\nAs we discussed in our limitations (line 670), performance degradation is only observed at an extremely high noise ratio of 80%, which is expected due to the severe imbalance in the wrong event distribution that affects the BMM and model convergence. We believe these new results comprehensively address the concern about robustness and practical applicability.\n\n**Question 2:** Although obtaining prior knowledge in Stage 1 is crucial—particularly in capturing the label wave number—, there is a lack of detailed analysis on its impact and sensitivity.\n\n**Response:** \n\nWe appreciate the reviewer's focus on the criticality of Stage 1. We agree that its impact and sensitivity are vital for the framework. In our original manuscript (Table 4), we investigate how the duration of Stage 1 could influence capturing the label wave number and then influence the final performance.\n\nFor the reviewer's convenience, we summarize that Table 4 shows our method's final performance remains consistently high, regardless of whether Stage 1 fits noise—across early (1/2 epochs), middle (4 epochs), or late (8 epochs) training stage—demonstrating robustness throughout. This demonstrates that **our framework, especially obtaining the prior knowledge, is not sensitive to the exact stopping point of Stage 1**. This robustness is also supported by the original Label Wave paper [2] with experiments on various noise settings and datasets, which established its stability.\n\nTo make this point clearer for the reader, we will add a dedicated paragraph in the final manuscript to explicitly discuss the sensitivity and impact of Stage 1, referencing these findings.\n\n**Question 3:** How does the method perform when class boundaries are highly entangled?\n\n**Response:** \n\nThis is a very insightful question. Highly entangled class boundaries are precisely the challenge posed by asymmetric, instance-dependent, and real-world noise. Our framework handles this through two parts: 1. The wrong event metric helps identify these hard examples, which tend to have fluctuating predictions and thus cluster in the middle of the wrong event distribution. 2. The difficulty coefficient $ϵ(w)$ and consistency loss $L_{SIM}$ then dynamically up-weights the consistency loss $L_{SIM}$ for these specific samples. \n\nThis forces the model to learn more robust and consistent representations for samples near the decision boundary, effectively disentangling them. As demonstrated in our new experiments for Question 1, IDO's superior performance under 45% asymmetric and 60% instance-dependent noise directly demonstrates its effectiveness in handling such entangled boundaries.\n\n**Question 4:** The similarity loss seems to have a larger effect in more challenging noise settings. Does this imply that the method relies more heavily on consistency learning under difficult conditions? What happens if the difficulty score is fixed to a high value—i.e., treating all samples as difficult? Is it desirable for easy samples to receive a low weight for similarity loss? A deeper analysis of the behavior of the difficulty-based weighting would be helpful.\n\n**Response:** \n\nWe appreciate the reviewer's sharp observation and agree that this is a crucial aspect of our method. Your intuition is correct: **IDO relies more heavily on consistency learning under difficult conditions.** To analyze the behavior of the difficulty-based weighting, we conducted 4 new experiments comparing our dynamic weight $ϵ(w)$ against several fixed-weighting methods.\n\n\n| Weighting Method| Sym. 60% | Asym. 40% | Inst. 40% |\n|-|-|-|-|\n| Without $ϵ$=0    | 79.5     | 70.4      | 77.3      |\n| Fixed $ϵ$=0.25   | 81.3     | 76.5      | 83.3      |\n| Fixed $ϵ$=0.5    | 80.8     | 77.5      | 82.4      |\n| Fixed $ϵ$=1      | 80.3     | 76.8      | 82.8      |\n| Dynamic $ϵ$       | **81.4**     | **78.2**      | **83.8**      |\n\n\nThe result shows that **dynamic weighting > fixed weighting > drop the loss term**, and the performance shows no clear correlation with fixed value of difficulty coefficients. This supports our core hypothesis, much like the principle behind Focal Loss [3]: $F(p)=-(1-p)^γlog(p)$, showing that a weighting term to expand the loss of difficult data is really necessary and better than treating all samples the same. We consider that for easy data, cross-entropy loss serves as a more direct and effective learning signal than consistency loss while consistency loss $L_{SIM}$ serves as a effective learning signal for difficult data. Dropping and fixing the difficulty coefficient $ϵ$ both decrease the performance.\n\n\n**Question 5:** Including more baselines, such as InstanceGM [4], would provide a more comprehensive comparison and help contextualize the proposed method’s performance more clearly.\n\n\n**Response:** \n\nThanks for providing related works! We agree that comparing with more recent works is important. We include InstanceGM [4] and NAL [5] as our two more baselines in 3 new experiments on CIFAR-100. \n\n| Methods  | Sym. 60% | Asym. 40% | Inst. 40% |\n| ------------ | ------------ | ------------- | ------------- |\n| Standard | 41.1       | 53.4        | 58.8       |\n| InstanceGM     | 80.5      | 76.3        | 83.1       |\n| NAL     | 80.9      | 77.6        | 81.3       |\n| IDO     | **81.4**        | **78.2**         | **83.8**         |\n\nThe results show that while InstanceGM is strong in its target setting (instance noise), it underperforms in symmetric and asymmetric noise because InstanceGM is too cautious in judging noise which leads to insufficient label correction. NAL performs well but is slightly behind IDO, particularly in the most challenging instance-dependent scenario. IDO demonstrates consistently state-of-the-art performance across all three settings. We will include a more comprehensive comparison with InstanceGM and NAL in our revised manuscript.\n\nOnce again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your valuable comments again. Thanks and looking forward to your reply!\n\n[1] Learning from noisy labels with deep neural networks:  A survey. CoRR'20.\n\n[2] Early stopping against label noise without validation data. ICLR'20.\n\n[3] Focal Loss for Dense Object Detection. ICCV'17.\n\n[4] Instance-dependent noisy label learning via graphical modelling.CVPR'23.\n\n[5] Noise attention learning: Enhancing noise robustness by gradient scaling. NeurIPS'22."}, {"review_id": "6wqwtnztJt", "reviewer": "Reviewer_2oRY", "summary": "This paper addresses the problem of Learning with Noisy Labels (LNL) by introducing both a metric, Wrong Event, and a framework, Instance-level Difficulty Modeling and Dynamic Optimization (IDO), and custom loss function. The main contribution is the development and usage of the Wrong Event metric. The Wrong Event metric is an indicator of label cleanliness (whether a label is correct or not), and is computed as the cumulative sum (over epochs) that a given training example is incorrectly classified, as per its as-labelled class. The idea is that easy & noisy samples will consistently be incorrectly predicted and thus have a high Wrong Event score, and that difficult & noisy (or clean) samples will have a medium Wrong Event score. With this insight, the Wrong Event metric feeds into the IDO framework as a parameter from which cleanliness and difficulty (at the per-sample-level) are estimated (using a two-component beta mixture model). The IDO framework itself works in two stages (first stage is used to generate prior distributions for the Wrong Event distributions, and the second is for actual robust model training, making use of the custom loss function and Wrong Event metric). The paper evaluates its method on several synthetically corrupted datasets (CIFAR-10, CIFAR-100, Tiny ImageNet), and real-world noisy datasets (CIFAR-100N, Clothing1M, WebVision), with compelling results. Thought classification accuracy is only marginally improved vs. existing LNL methods, the improvements seem to persist across all datasets and rates of label noise.", "questions": "- My interpretation was that the main contribution is the Wrong Event metric; however, a rather elaborate framework (and loss function) are also developed here. What is the main takeaway here? Is it this metric (such that other creative frameworks may be used) or the framework (whereby other creative metrics may be used) that is the main contribution?\n- Why does the method use only 10 or 15 epochs when the earlier figures show 100 epochs? Does the intuition described in the earlier figures still hold in this case?\n- What is the meaning of f() in your paper? Is this the model? What does f() output - the list of predicted probabilities or the predicted class?", "limitations": "- No error bars even though the checklist answers item 7 as \"Yes\". \n- Limitations and Broader Impacts are discussed in Appendix F according to justification in checklist item 2. However, as reviewer, I am not obligated to review the appendices. It is my understanding that limitations should be discussed in the main paper.", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 1, "significance": 3, "originality": 4, "strengths_and_weaknesses": "Quality:\n\n-\tThe paper seems  to be technically sound, but some claims are not well supported:\n  - “wrong event can clearly separate noisy and clean data at all training stages” – unclear how this is demonstrated, can this be shown in fig 2, can this work after just one epoch, is there evidence for fitting to noisy samples?;  \n  - comparing the variance of loss vs wrong event – these have different units, do you mean relative variance?; \n  - line 129 “with their outcomes frequently flipping between similar classes” – it would be nice to see evidence of this, and would most of these flipped-between classes not also be incorrect?; \n  - line 205 “With more accurate model output, the clean and noisy distribution gradually separate.” – is this true in terms of being able to discern which distribution a sample is from? Please demonstrate.\n-  L_{SIM} is only the squared error (you need to do this over all samples to get MSE). Because of how it is used in the overall training objective (8), this is NOT MSE.\n-\tResults are from 5 random trials, but only means are reported. Please include error bars (std).\n-\tMethods are appropriate, several datasets with several types of label noise (symm, asymm, instance-dept) are used.\n-\tAuthors have not touched on weaknesses of their work\n\n\nClarity:\n\n-\tI found this paper difficult to read, follow, and understand. I spent considerable time to carefully read this paper to the best of my ability. There are several notational issues that lead to difficulties in understanding: \n  - Line 115 says f() is a model. Does f output a list of predicted probabilities or does it output the predicted class directly? In Eq (1), it seems that f(x) outputs a categorical label (should this be argmax of f?). In Eq (10), the output from f on two augmentations is averaged, but how can we average two categories (should the output be lists of probabilities?)? Also in Eq (10), it would seem that f is defined recursively based on the right hand side of the equation (is the left hand side the definition of f, or is it just a new pseudo-label and should be given a new variable). In Eq (11), it is unclear how the mathematical operations are performed on either a categorical or list of predicted probabilities output from f (is log evaluated on all probs of all classes?). \n  - Is noise rate given a variable of \\mu or r?\n-\tIssues with Figures: \n  - Fig 2 axes - Why is horizontal axis \"Loss / Wrong event Distribution\", What is the horizontal axis meant to be?, In (d), why is the vertical axis on the right?; \n  - Fig 2 - says Mean but caption says median, which is it?; \n  - Fig 4 - Why use line chart here? The methods on the horizontal axis are categorical and not interpolatable. Is the vertical axis meant to be number of examples, or accuracy?\n-\tMinor grammatical issues are found throughout (use of singular vs plural, “Following setting in [12,13].”, etc.) are distracting.\n\n\nSignificance:\n\n-\tThis paper improves upon existing LNL work in a meaningful way, given the comprehensive outperformance of existing methods on all datasets and noise rates.\n\n\nOriginality:\n\n-\tThis paper is original in its presentation of the Wrong Event metric, framework, and multi-part custom loss function.", "was_revised": true, "final_justification": "The authors have responded to all my concerns, most prominent of which was from the 'Clarity' category. I have left my original review but increased my rating from 4 to 5. See my response to rebuttal for more context.", "rebuttal": "**Overall Response:**\n\nWe sincerely thank you for your detailed and constructive feedback. Your insightful questions have helped us to further strengthen the paper. We have conducted several new experiments based on your suggestions and are confident that incorporating these results and discussions will significantly improve the final manuscript. Below, we address each of your points in detail.\n\n**Question 1**: On the evidence for the claim that \"wrong event can clearly separate noisy and clean data at all training stages.\"\n\n**Response**: \n\nWe appreciate your question regarding this core claim. Fig.2,5,6,8 (visualizations of histogram and AUC-ROC curves) and Tab.9,10,11,12 (calculations of precision, recall, F-score and AUC) show that wrong event can clearly separate noisy and clean data at all training stages with pretrained or randomly initialized models. For the extremely early training stage, i.e., one epoch, Tab.4 shows that wrong event can achieve the accuracy of 80.2% same as loss. \n\n**Question 2**: On the comparison of variance between Loss and Wrong Event, and their different units.\n\n**Response**: \n\nYes, we are comparing the relative variance. The loss $l$ and wrong event $w$ are not in the same range. We normalize the two metrics and track the range of value changes during training. As shown in Fig. 7, the experimental results show that the range of loss has no clear upper bound, confirming its instability, and the range of wrong event converges as training progresses, demonstrating superior stability. Furthermore, due to loss mutations, the mean change of loss is also larger than that of wrong event.\n\n**Question 3**: On providing evidence for \"outcomes frequently flipping between similar classes\" for hard samples.\n\n**Response**: \n\nThanks for this question! This characteristic of hard samples is widely recognized in the field and has been demonstrated in several prior works. Previous papers [1][2][3][4][5][10] have shown that the hard sample predictions frequently flipping between similar classes by visualizing the learned representations using t-SNE 2D embeddings, giving the confusion matrix of prediction and labels or giving the statistic information about softmax outputs of certain samples, such as chiffon/shirt, windbreaker/jacket, 1/7, deer/horse, whale/dolphin and etc. In our single-label classification task, although these classes may be semantically related, the sample officially belongs to only one correct class. Therefore, such \"flipping\" is still considered a misclassification. We will add these citations to the manuscript to support this point.\n\n**Question 4**: On demonstrating the process of \"the clean and noisy distribution gradually separate.\"\n\n**Response**: \n\nThank you for the valuable question. We can empirically illustrate the process as follows. At initialization, wrong event value for all samples is 0. During early training, the model learns correct patterns, its predictions for clean samples tend to match the given labels, so their wrong event values grow slowly or not at all. Conversely, for noisy samples, the model's prediction based on true features mismatches the given noisy label, causing their wrong event values to increase steadily. This differential growth progressively separates the distributions of clean and noisy samples, making it easier to distinguish which distribution a sample is from. Even if the model later memorizes the entire dataset, the wrong event values are \"frozen\" at their current, separated states, thus preserving the established distinguishability.\n\n**Question 5**: On the correction that $L_{SIM}$ is squared error, not MSE.\n\n**Response**: \n\nWe really appreciate your attention to detail. $L_{SIM}$ is indeed the per-sample squared error, not MSE. We will correct it in the manuscript.\n\n**Question 6**: On issues with figures and grammar.\n\n**Response**: \n\nThanks for your attention to detail. For Fig.2, we will clarify that the horizontal axis represents the \"Value of Wrong Event / Loss,\" move the y-axis of subplot (d) back to the left, and confirm that the figure reports the median, not the mean. For Fig.4, we will replace the line chart with a more appropriate format and clarify the y-axis as accuracy(%). We will correct all the issues with figures and grammar in the final manuscript.\n\n**Question 7**: On including error bars (std) for experimental results.\n\n**Response**: \n\nThanks for your concerns! Reporting statistical significance is crucial for demonstrating robustness. We show some error bars in the CIFAR-100 experiment as follows\n\n| Methods   | Sym. 60%      | Asym. 40%     | Inst. 40%     |\n|-|-|-|-|\n| Standard  | 41.08±0.87%   | 53.42±0.95%   | 58.79±0.77%   |\n| DivideMix | 80.66±0.55%   | 66.62±0.56%   | 81.27±0.48%   |\n| ELR       | 73.94±0.74%   | 75.61±0.63%   | 79.70±0.59%   |\n| DeFT      | 79.91±0.43%   | 69.94±0.80%   | 82.51±0.40%   |\n| IDO       | **81.44±0.51%**   | **78.20±0.44%**   | **83.82±0.51%**   |\n\nWe will include the error bars (std) for all experiments in the revised manuscript to report the statistical significance and robustness of our 5-run experiments.\n\n**Question 8**: On discussing the weaknesses/limitations of our work in the main paper.\n\n**Response**: \n\nThanks for suggestions! We run 6 new experiments under a wider range of noise levels in the three noise types to verify IDO's robustness and potential weakness. For Sym. noise, 80% is added. For Asym. noise, 20% and 45% are added. For Inst. noise, 20% and 60%. Besides, a noise-free (0 %) baseline is included. All the experiments use ResNet-50 to train on CIFAR-100 following the implements in the paper. \n\n\n| Methods | Sym. 0% | Sym. 80% | Asym. 20% | Asym. 45% | Inst. 20\\% | Inst. 60\\% |\n|-|-|-|-|-|-|-|\n| Standard | 82.8% | 35.2\\% | 68.5\\% | 46.2\\% | 70.4\\% | 31.6\\% |\n| UNICON   | 84.8\\% | **64.0\\%** | 83.5\\% | 73.2\\% | 84.9\\% | 58.2\\% |\n| DeFT     | 85.1\\% | 57.6\\% | 78.9\\% | 65.2\\% | 82.4\\% | 56.5\\% |\n| **IDO**  | **85.8\\%** | 62.5\\% | **85.4\\%** | **74.1\\%** | **85.1\\%** | **60.8\\%** |\n\nThe results show that **IDO performs well and robustly within a noise range that far exceeds the 8 %–38.5 % observed in real-world datasets** [6]. Degradation only appears under extremely high noise ratios—rare in practice—because, as discussed in line 670, the highly imbalanced wrong event distribution prevents BMM and model from converging. We will move the \"Limitations\" section from the appendix to the main paper.\n\n**Question 9**: What is the meaning of f() and noise rate in the paper? \n\n**Response**: \n\nThanks for pointing it out! We apologize for the confusing terminology on f(). f() is the softmax probability of model output. We will explicitly define the output of the function f(⋅) in different contexts **(predicted class $\\text{argmax } f()$ vs. softmax probabilities $f()$)** to remove all ambiguity in Equations (1), (10), and (11). Noise rate $r$ is a given number in each task.\n\n**Question 10**: On clarifying whether the main contribution is the Wrong Event metric or the IDO framework.\n\n**Response**: \n\nThank you for the question that helped us clarify our core contribution. **We regard the two components as an inseparable and mutually reinforcing system that together forms our main contribution.** Current frameworks suffer from high computational costs, heavy hyperparameter tuning and corase-grained optimization, which our lightweight, hyperparameter-free IDO framework is designed to address. The dynamic loss coefficients of IDO relies on robust noise modeling, but existing metrics loss[7], EMA-loss[8], FE[9], FKL[10] have known limitations (Line 76, 296, 584). We therefore introduce wrong event, which supplies accurate noise-modeling information at no extra computational cost. While wrong event could in principle be plugged into other frameworks and IDO could adopt alternative metrics, the two components are designed to complement each other and achieve optimal performance when used jointly.\n\n**Question 11**: On the question of why the method uses 10/15 epochs vs. 100 epochs shown in figures.\n\n**Response**: \n\nThank you for this detailed observation. The difference in epoch numbers stems from the model initialization settings: Fig.2 show 100 epochs for randomly initialized ResNet-18 models, and method uses 10 or 15 epochs for pretrained ResNet-50 models. For randomly initialized models, the visualizations of histogram and AUC-ROC curves are in **Fig.2,5,6,8**, and calculations of precision, recall, F1-score and AUC are in **Tab.9,11**. For pretrain models, visualizations are in **Fig.8**, and calculations are in **Tab.10,12**. The results confirm that the core intuition behind our framework is effective in both scenarios.\n\nOnce again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. Thanks and looking forward to your reply!\n\n[1] Symmetric Cross Entropy for Robust Learning With Noisy Labels. ICCV'19\n\n[2] Beyond Class-Conditional Assumption: A Primary Attempt to Combat Instance-Dependent Label Noise. AAAI'21 \n\n[3] Learning from Massive Noisy Labeled Data for Image Classification. CVPR'15\n\n[4] Beyond Synthetic Noise: Deep Learning on Controlled Noisy Labels. ICML'20\n\n[5] Tripartite: Tackle Noisy Labels by a More Precise Partition. arXiv'22\n\n[6] Learning from noisy labels with deep neural networks: A survey. CoRR'20\n\n[7] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR'20\n\n[8] Robust Curriculum Learning: from clean label detection to noisy label self-correction. ICLR'21\n\n[9] An Empirical Study of Example Forgetting During Deep Neural Network Learning. ICLR'19\n\n[10] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples. ICCV'23"}, {"review_id": "2HsSdt0N00", "reviewer": "Reviewer_pBv4", "summary": "The paper studies the problem of label noise learning in the lense of empirical observation. In particular, the paper proposes a metric, coined as *wrong event*, which count the number of times the model mispredict the given label after each training epoch. Such a newly-observed metric has a profound impact in identifying the clean, noisy and difficult samples. That distincs the proposed method with previous methods which may lump both the noisy and difficult samples together. Based on the *wrong event* metric, a mixture of 2 Beta distributions is inferred to divide samples into two groups, each with their own nature (i.e., clean or noisy) and their difficulty. These factors are then taken into account to design a loss function consisting of three components: clean loss, noisy loss and consistency loss between two different data augmentations. Empirical evaluation achieves state-of-the-art results compared to previous methods in several benchmarks.", "questions": "My main concern is the limited theoretical justification and analysis on the proposed metric *wrong event*. In its current form, it is unclear how that would result in something clean, or noisy with their own difficulty. At the end of the day, such a metric largely depends on the model used to estimate it. Then, if the model is bias, the metric is also bias, rendering its ineffectiveness.", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 1, "clarity": 2, "significance": 1, "originality": 2, "strengths_and_weaknesses": "## Strengths\n- The motivation of separating or weighting noisy and difficult samples is sound. It is actually the main weakness of the majority methods in label noise learning, which often rely on small loss hypothesis. Tackling such a problem is one of the major strengths of the paper.\n- The paper proposes a simple metric to quantify both the cleanness and difficulty of each training samples. This metric has empirically shown working well in practice.\n\n## Weaknesses\nThe paper is mainly a pure-observation based approach. There is limited justification for what is proposed in the paper, and in particular the *wrong event*. Although it has been demonstrated through several empirical results, it is unclear whether the metric is effectiveness in identifying label noise. In addition, despite being claimed with theoretical analysis, such an analysis is mostly incorrect and very limited to shed any insights into the proposed *wrong event*.\n\nThe claim of the theoretical analysis at line 132 and in the Appendix C2: $\\frac{w\\_{i}^{T + 1} - w_{i}^{T}}{w_{i}^{T}} \\in [0, 1/T]$ is incorrect. The left hand side term should be in $[0, +\\infty]$. A slightly similar concern on the loss. Since the loss is positive, $\\frac{l\\_{i}^{T + 1} - l_{i}^{T}}{l_{i}^{T}} \\in (-\\infty, +\\infty)$.", "was_revised": true, "final_justification": "The authors acknowledge the flaw in the theoretical analysis presented in Appendix C2. Since the flaw does not affect much of the conclusion from the paper, I update my rating accordingly.", "rebuttal": "**Overall Response:**\n\nWe sincerely thank you for your critical and insightful review. Your insightful questions have helped us to further strengthen the paper. We have conducted several new experiments based on your suggestions and are confident that incorporating these results and discussions will significantly improve the final manuscript. Below, we address each of your points in detail.\n\n**Question 1:** The paper is mainly a pure-observation based approach with limited justification for what is proposed in the paper, and in particular the wrong event. \n\n**Response:** \n\nThank you for the incisive and critical feedback. **We fully acknowledge that wrong event is a mainly empirical, observation-driven metric and totally agree with the reviewer that a rigorous theoretical analysis provides the most comprehensive understanding of a method. We view this as a valuable direction for our future work.** \n\nNevertheless, we respectfully argue that in deep learning, providing extensive, consistent evidence for a novel metric and framework's superiority constitutes a significant contribution in its own right. Empirical, observation-driven research approach is a characteristic shared by many successful methods in Learning with Noisy Labels (LNL). The **small loss hypothesis** [1] as you mentioned and the **memorization effect hypothesis** [2] are mainly proposed with an empirical, observation-driven research approach. The metrics used to model noise such as **loss[3], ema-loss[4], forgetting event(FE)[5], fluctuation event[6], first k-epoch learning(fkl)[7] and label wave[8]** are also mainly proposed with an empirical, observation-driven research approach. \n\nIn our original manuscript, our validation in the manuscript goes far beyond simple observation. We demonstrate the superiority of wrong event not only through state-of-the-art accuracy on six diverse benchmarks (**Tables 1, 2**) but also through direct, multi-faceted comparisons against other metrics:\n\nNoise Modeling Ability (**Table 4**): We show wrong event achieves superior final accuracy, demonstrating its robust modeling capability across all training phases (early, middle and late stages).\n\nStability and Robustness (**Fig. 7**): We analyze the change range of normalized metrics, proving that wrong event is significantly more stable than loss.\n\nClean Sample Selection (**Fig. 2,5,6,8, Tables 9-12**): We provide a comprehensive comparison against loss using visualizations of histograms and AUC-ROC curves and calculations of precision, recall, F1-score, and AUC. These results confirm the superior selection ability of wrong event across different training strategies (from-scratch and pre-trained) and throughout all training phases (early, middle and late stages).\n\nWe believe our method, backed by this extensive evidence, offers valuable insights to the community. We will explicitly state the lack of a formal convergence proof as a limitation in the revised manuscript, highlighting it as a promising avenue for future theoretical research.\n\n**We believe that our method can offer insights for the community on this field, and we will included the limitation of lacking rigorous theoretical analysis such as full theoretical proof of convergence in the revised paper, leaving a promising future work.**\n\n**Question 2:** It is unclear whether the metric is effective in identifying label noise, because such a metric largely depends on the model used to estimate it. Then, if the model is bias, the metric is also bias, rendering its ineffectiveness.\n\n**Response:**\n\nThis is an excellent point, and we acknowledge your valid concern regarding the interplay between the metric and potential model bias. We designed our experimental protocol specifically to test this.\n\nOur method was validated on **six diverse synthetic and real-world benchmarks** (CIFAR-10/100, Tiny-ImageNet, CIFAR-100N, Clothing1M and WebVision), across **various noise types** (symmetric, asymmetric, instance-dependent and real world noise), **architectures** (ResNet18/50, ViT, ConvNeXt) and **training strategy** (from-scratch / pretrained). IDO consistently outperforms state-of-the-art methods in these varied settings, demonstrating the generalizability and robustness of our approach. \n\nMore directly, our analyses in Figures 4, 8 and Tables 9-12 demonstrate the metric's resilience to model state and bias:\n\n**Robustness to Model State:** wrong event maintains its discriminative power in early, middle, and late training stages, regardless of whether the model is underfitting or has begun overfitting (i.e., become biased by) the noisy labels.\n\n**Robustness to Model Initialization:** The metric performs effectively in both randomly initialized and powerful pre-trained settings, showing it is not dependent on a strong initial model.\n\nExtensive experiments demonstrate the consistent efficacy of wrong event across diverse settings, particularly its robustness to various models. This comprehensive evidence demonstrates that **wrong event is not fragilely dependent on a perfectly unbiased model but is a robust metric across a wide spectrum of practical conditions**. We hope this fully addresses your concern.\n\n\n**Question 3:** The claim of the theoretical analysis at line 132 and in the Appendix C2: $\\frac{w_i^{T+1}-w_i^{T}}{w_i^T}\\in[0,\\frac{1}{T}]$ is incorrect. The left hand side term should be in $[0,+\\infty]$ . A slightly similar concern on the loss. Since the loss is positive, $\\frac{l_i^{T+1}-l_i^{T}}{l_i^T}\\in[-\\infty,+\\infty]$.\n\n**Response:**\n\nWe sincerely apologize for this error and are very grateful for your sharp attention to detail. This was an oversight on our part. We have thoroughly re-examined this point and provide a corrected, more rigorous analysis below.\n\nThe change rate of loss is indeed $\\frac{l_i^{T+1}-l_i^{T}}{l_i^T}\\in[-\\infty,+\\infty]$ in every epoch $T$ with unbounded limits and frequently unpredictable mutations. A usually seen phenomenon named forgetting event [5] (last epoch right, this epoch wrong) can cause the probability of given label to plummet from a high probability (e.g. ~0.9) to a small probability (e.g. ~0.1), causing the loss to skyrocket and the relative change to become enormous. This can happen randomly and repeatedly for all the samples.\n\nHowever, for wrong event, the change rate needs more discussion. Firstly, we have $w_i^{T+1}=w_i^T+\\delta_i^{T+1},\\delta_i^{T+1}\\in\\{0,1\\} \\text{ and } w_i^T\\in [0,\\dots,T]$, meaning the wrong event value is monotonically increasing. The change rate is $\\frac{\\delta_i^{T+1}}{w_i^T}$. We analyze this in two distinct cases:\n\n**The \"0 to 1\" Transition:** You are correct to identify the unique case where the metric's stability might be questioned. When a sample is misclassified for the very first time, $w_i^T$ transitions from 0 to 1. At this point, the relative change $\\frac{1}{0}$ is undefined. This is a singular, one-time event for any given sample, marking its initial entry into the set of \"ever-misclassified\" samples. \n\n**All Subsequent Changes ($w_i^T \\geq 1$):** For every subsequent misclassification, the denominator $w_i^T$ is at least 1. The relative change is  $\\frac{\\delta_i^{T+1}}{w_i^T}$. **This value is strictly bounded within the range [0,1]** far smaller than the change rate of loss. More importantly, as the model continues to misclassify a sample, $w_i$ increases, causing the maximum possible relative change ($\\frac{1}{w_i^T}$) to decrease. The metric is therefore self-stabilizing.\n\nThis analysis provides a strong theoretical basis for the empirical stability we observed in Figure 7. The relative change of wrong event is well-behaved, bounded, and self-stabilizing after a single initial event. Conversely, the relative change of loss is unbounded and perpetually susceptible to explosive volatility. This fundamental difference in their rate of change is why wrong event serves as a far more reliable and stable signal for modeling sample characteristics in noisy environments.\n\n**We thank you again for pushing us to analyze our metric's stability more deeply. We will completely revise this section in the manuscript to reflect this rigorous and correct analysis.**\n\nOnce again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. Thanks and looking forward to your reply!\n\n[1] Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels. NIPS'18\n\n[2] A closer look at memorization in deep networks. ICML'17\n\n[3] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR'20\n\n[4] Robust Curriculum Learning: from clean label detection to noisy label self-correction. ICLR'21\n\n[5] An Empirical Study of Example Forgetting During Deep Neural Network Learning. ICLR'19\n\n[6] Self-filtering: A noise-aware sample selection for label noise with confidence penalization. ECCV'22.\n\n[7] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples. ICCV'23"}, {"review_id": "JHVaw1c5vi", "reviewer": "Reviewer_HFBm", "summary": "This paper proposes IDO (Instance-level Difficulty Modeling and Dynamic Optimization), a two-stage training framework for learning with noisy labels. The core contribution is a novel metric called “wrong event”, which tracks the frequency of model misclassification during training to distinguish clean, noisy, and hard samples without requiring extra hyperparameters. A Beta Mixture Model (BMM) is fitted to the distribution of wrong event scores to probabilistically model both sample cleanliness and difficulty. The method dynamically adjusts loss contributions based on these measures, achieving strong generalization performance while being computationally efficient and scalable.", "questions": "In the caption of Figure 2, the authors mentioned \"Since wrong events are monotonically increasing based on historical statistics instead of current model prediction, when model overfits the dataset, wrong event values for all samples do not change, rather than converging to zero as loss values typically do.\". It is not clear about what is the \"wrong event values\". Why when wrong events are monotonically increasing, wrong event values do not change?", "limitations": "The authors didn't compare the results with very recent work defencing against label noises, e.g., \"Noise attention learning: Enhancing noise robustness by gradient scaling, NeurIPS 2022\",", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\nThe paper proposes instance-level dynamic loss weighting that captures both sample difficulty and label cleanliness. It\navoids the extensive hyperparameter tuning required by prior methods like DivideMix or ELR and provides clear theoretical rationale and empirical validation for the stability of the proposed metric.\n\nWeeknesses: \nIn the first stage of this framework, the paper assumes that \"prior knowledge, i.e., coarse distribution of wrong event, is obtained\". However,  the prior knowledge cannot be easily obtained in reality.\n\n In this paper, the performance improvement may be from different components/terms of the loss function. Ablation Study is missing.", "was_revised": true, "final_justification": "The authors have provided ablation study and add additional references, making the clarify better. I've increased clarification score. But after carefully considering authors arguments, my concern is still that the novelty and significance haven't been changed much. So I maintain the overall score.", "rebuttal": "**Overall Response:**\n\nWe sincerely thank the reviewer for their insightful feedback and detailed comments. We have carefully studied your questions and, based on your suggestions, have conducted additional analysis and experiments. We are confident that incorporating these discussions and new results will significantly strengthen the final manuscript.\n\n**Question 1:** In the first stage of this framework, the paper assumes that \"prior knowledge, i.e., coarse distribution of wrong event, is obtained\". However, the prior knowledge cannot be easily obtained in reality.\n\n**Response:** \n\nThanks for your concerns! We apologize for the confusing terminology on \"prior knowledge\". We would like to clarify that this \"prior knowledge\" is **not assumed or required beforehand**, but is **generated internally during Stage 1 of our framework**. It specifically refers to the initial wrong event statistics gathered during Stage 1, which are then used to initialize the dynamic optimization in Stage 2. Our method does not require any pre-existing knowledge of the dataset-specific characteristics. The results on real world noisy datasets such as CIFAR-100N, Webvision and Clothing1M also show the practical applicability of our method in reality. We will add a more precise description to \"prior knowledge\" in the revision manuscript to avoid misunderstanding.\n\n\n\n**Question 2:**  The performance improvement may be from different components/terms of the loss function. Ablation Study is missing.\n\n**Response:** \n\nWe completely agree that a thorough ablation study is essential for understanding the source of performance improvements. We included these studies in our original submission and appreciate the opportunity to highlight their findings here. The performance gains from IDO stem from two main contributions:\n\n**First, Comprehensive Loss Function:** As you noted, our three-part loss function models clean, noisy, and difficult samples respectively. Our ablation study in **Table 5** demonstrates that each component— $L_{C}$, $L_{N}$, and $L_{SIM}$ —contributes positively to the final performance, and removing any of them leads to a drop in accuracy.\n\n**Second, Superiority of the wrong event Metric:** Our proposed wrong event metric provides more accurate and stable information for noise modeling than other metrics. The ablation study in **Table 4** compares wrong event against Single Loss [1], EMA Loss [2], Forgetting Event (FE) [3] , and First k-epoch Learning (FkL) [4]. The results show that wrong event consistently outperforms these other metrics across different training stages. \n\nWe will ensure these key ablation results are more prominently signposted in the revised manuscript.\n\n**Question 3:** In Figure 2, the authors mentioned \"Since wrong events are monotonically increasing based on historical statistics instead of current model prediction, when model overfits the dataset, wrong event values for all samples do not change, rather than converging to zero as loss values typically do.\". It is not clear about what the \"wrong event values\" is. Why, when wrong events are monotonically increasing, wrong event values do not change?\n\n**Response:** \n\nThank you for this question. We agree the original phrasing in the Figure 2 caption was a bit confusing and appreciate the chance to clarify. Specifically, **the wrong event value of a sample is the number of disagreement between the prediction and the given label during training.** At each epoch, the wrong event value of a sample either stays the same (if the prediction matches the given label) or increments by one (if they differ), so the wrong event values are monotonically increasing. As the model overfits, almost memorizing all the given labels,  **the wrong event value of each sample nearly *stabilizes* (stops increasing), unlike the loss which converges to zero.** This attribute preserves the discriminative power of wrong event distribution at overfitting phase.\n\nWe will revise the caption in Figure 2 to make this explanation clearer.\n\n**Question 4:** The authors didn't compare the results with \"Noise attention learning: Enhancing noise robustness by gradient scaling, NeurIPS 2022\".\n\n**Response:** \n\nThanks for providing related works! We agree that comparing with more recent works is important. We include InstanceGM [5] and NAL [6] as our two more baselines in 3 new experiments on CIFAR-100. \n\n| Methods    | Sym. 60% | Asym. 40% | Inst. 40% |\n| ---------- | -------- | --------- | --------- |\n| Standard   | 41.1     | 53.4      | 58.8      |\n| InstanceGM | 80.5     | 76.3      | 83.1      |\n| NAL        | 80.9     | 77.6      | 81.3      |\n| IDO        | **81.4** | **78.2**  | **83.8**  |\n\nThe results show that while InstanceGM is strong in its target setting (instance noise), it underperforms in symmetric and asymmetric noise because InstanceGM is too cautious in judging noise which leads to insufficient label correction. NAL performs well but is slightly behind IDO, particularly in the most challenging instance-dependent scenario. IDO demonstrates consistently state-of-the-art performance across all three settings. We will include a more comprehensive comparison with InstanceGM and NAL in our revised manuscript.\n\nOnce again, we thank you for your valuable and insightful feedback, which has significantly improved our work. We sincerely hope that our analysis and experiments can address your confusion and questions, providing a clearer understanding of our work. If you have any questions about our paper, please feel free to point out and we will try to address it as soon as possible. We would like to express our sincere gratitude for your valuable comments again. Thanks and looking forward to your reply!\n\n[1] DivideMix: Learning with Noisy Labels as Semi-supervised Learning. ICLR'20\n\n[2] Robust Curriculum Learning: from clean label detection to noisy label self-correction. ICLR'21.\n\n[3] An Empirical Study of Example Forgetting During Deep Neural Network Learning. ICLR'19.\n\n[4] Late Stopping: Avoiding Confidently Learning from Mislabeled Examples. ICCV'23.\n\n[5] Noise attention learning: Enhancing noise robustness by gradient scaling. NeurIPS'22.\n\n[6] Instance-dependent noisy label learning via graphical modelling.CVPR'23."}]

Author rebuttal:

Meta-review: The paper tackles the problem of learning with noisy labels. It devises a two-stage process to first identify samples that are clean, noisy, or difficult, and secondly trains a noise-robust loss-reweighted model given the information from the first stage. It shows improved performance over a large set of baselines across various benchmark datasets. 

Four expert reviewers evaluated the paper. They found the approach well-motivated, and some found the paper clearly-written with several illustrations. They particularly appreciated the simple "difficulty metric" and the hyperparameter-free design. They also had concerns regarding lacking a wider range of (instance-dependent) benchmarks, potential error in the equations in the appendix, and missing ablation studies and related works. 

The authors provided a thorough rebuttal to the criticisms that was attended to by all the reviewers. Reviewers further discussed the rebuttal with the authors iteratively. The discussion led to all reviewers leaning towards acceptance.

The AC believes there is no outstanding major issue with the paper and therefore defers to the unanimous suggestion of the reviewers and suggests acceptance.
Decision: Accept (poster)