LiNC: Lightweight Noise Correction via Per-Sample Trust and Gaussian Mixture Modeling

# Lightweight Noise Correction via Per-Sample Trust and Gaussian Mixture Modeling
Source: [https://arxiv.org/html/2608.04147](https://arxiv.org/html/2608.04147)
Abhishek Moturu Department of Computer Science University of Toronto The Hospital for Sick Children UHN KITE Research Institute T\-CAIREM Vector Institute moturuab@cs\.toronto\.edu &Babak Taati Department of Computer Science Institute of Biomedical Engineering University of Toronto Rehabilitation Sciences Institute UHN KITE Research Institute Vector Institute taati@cs\.toronto\.edu Anna Goldenberg∗ Department of Computer Science Department of Laboratory Medicine and Pathobiology University of Toronto The Hospital for Sick Children T\-CAIREM Vector Institute anna\.goldenberg@utoronto\.ca

###### Abstract

Label noise is common in medical imaging datasets due to factors such as inter\-rater variability, annotation errors, and ambiguous cases\. This can severely undermine the reliability and clinical effectiveness of machine learning models trained using those datasets\. To address this challenge, we introduce Lightweight Noise Correction \(LiNC\), which adds a single trainable trust parameter per training sample and learns when to use the observed label and when to defer to the model during a standard training loop\. The key idea is to train using a convex combination of the observed label and the model’s own predictive distribution, controlled by a per\-sample trust parameter\. We show that the gradient of this objective drives trust values in opposite directions for clean versus noisy samples in the early training phase, yielding separable trust distributions\. We use a 3\-component Gaussian Mixture Model over the trust values to separate them into clean, ambiguous, and noisy cases and then execute a short soft\-correction phase on the noisy cases and a final hard correction phase\. Experiments on ten 2D datasets from MedMNISTv2 under label noise of up to 50% show consistent gains in accuracy and strong mislabel detection\. LiNC adds negligible asymptotic overhead: the training\-time complexity remains dominated by the base network, with additional memory growing linearly with the size of the training set\.

## 1Introduction

Within healthcare, medical imaging is essential in supporting clinical tasks such as diagnosis, treatment planning, and disease monitoring\. Recent advancements in deep learning have significantly improved medical image analysis by automating the detection and classification of various medical conditions\. These advancements heavily depend on the availability of accurately labeled datasets\. Machine learning models tend to severely degrade in performance when trained on noisy data\. On the other hand, label noise is prevalent in healthcare datasets due to inconsistent annotations, human errors, and ambiguous findings during the annotation process\. Label noise can change the optimization landscape, hurt calibration, and amplify spurious correlations, if not properly addressed\[[10](https://arxiv.org/html/2608.04147#bib.bib81),[27](https://arxiv.org/html/2608.04147#bib.bib58),[28](https://arxiv.org/html/2608.04147#bib.bib79),[2](https://arxiv.org/html/2608.04147#bib.bib80),[8](https://arxiv.org/html/2608.04147#bib.bib16)\]\.

Many studies focus on learning with noisy labels in natural images\[[14](https://arxiv.org/html/2608.04147#bib.bib77),[9](https://arxiv.org/html/2608.04147#bib.bib76),[17](https://arxiv.org/html/2608.04147#bib.bib162),[13](https://arxiv.org/html/2608.04147#bib.bib72),[29](https://arxiv.org/html/2608.04147#bib.bib73),[23](https://arxiv.org/html/2608.04147#bib.bib71)\]\. However, medical imaging has additional constraints: clean validation sets are expensive, data distributions can shift, and practitioners may need interpretability into which training labels are unreliable\. Methods that require additional models, extensive hyperparameter tuning, or dataset\-specific or task\-specific thresholds are hard to justify in clinical workflows, which are often time\-constrained and resource\-constrained\.

We ask:*Can we get label correction and label noise signals essentially “for free” while keeping training close to standard fine\-tuning?*For this, we introduce LiNC, which uses a trainable trust parameterαi\\alpha\_\{i\}per sample that decides how much the model should trust the observed label versus its own predictive distribution\. Intuitively, if the model consistently assigns low probability to the observed label for a sample, the gradient pushesαi\\alpha\_\{i\}down, shifting supervision toward the model prediction and if the model assigns high probability to the observed label,αi\\alpha\_\{i\}increases, preserving supervision\. This produces a natural separation between clean and noisy samples without any access to true ground\-truth labels\.

#### Contributions\.

LiNC is a lightweight noise correction method that does not need more models, clean validation sets, or pruning, yet yields three concrete benefits:

- •We derive a simple expression for the per\-sample trust gradient,∂ℒ/∂αi\\partial\\mathcal\{L\}/\\partial\\alpha\_\{i\}, and show how it induces separability between clean and noisy labels\.
- •We use an unsupervised 3\-component GMM over trust values \(to separate noisy / ambiguous / clean samples\) to get threshold\-free separation and correction, inspired by GMM\-based separation in noisy\-label learning\[[13](https://arxiv.org/html/2608.04147#bib.bib72)\]\.
- •We add𝒪​\(N\)\\mathcal\{O\}\(N\)memory and a negligible constant\-factor compute cost, while producing per\-sample trust scores that can be used for dataset audits\.

![Refer to caption](https://arxiv.org/html/2608.04147v1/linc.png)Figure 1:Overview of LiNC\.The model produces a class\-probability vectorpip\_\{i\}for each training sample\. During soft warm\-up, LiNC jointly learns a per\-sample trust parameterαi\\alpha\_\{i\}and trains using the targetqi=\(1−αi\)​stopgrad⁡\(pi\)\+αi​ey~iq\_\{i\}=\(1\-\\alpha\_\{i\}\)\\operatorname\{stopgrad\}\(p\_\{i\}\)\+\\alpha\_\{i\}e\_\{\\tilde\{y\}\_\{i\}\}, which interpolates between the model prediction and the observed labely~i\\tilde\{y\}\_\{i\}\. A three\-component Gaussian mixture model \(3\-GMM\) is then fitted to the learned trust values, with components ordered by their means and interpreted as noisy, ambiguous, and clean\. Only samples with the lowest trust \(i\.e\. the noisy component\) are corrected: they first usepip\_\{i\}as a soft target and are subsequently assigned the hard labelarg⁡max⁡pi\\arg\\max p\_\{i\}for final training\. Clean and ambiguous samples are not relabeled, reducing the risk of over\-correcting borderline cases\. Dashed arrows indicate that the phase\-specific supervision is fed back into successive updates of the same model\.

## 2Related Work

Classical approaches assume the existence of a noise transition matrix, or an approximate one, and perform forward/backward loss correction\[[14](https://arxiv.org/html/2608.04147#bib.bib77)\]or explicitly learn a noise model\[[7](https://arxiv.org/html/2608.04147#bib.bib67)\]\. Robust loss functions aim to reduce sensitivity to incorrect labels without explicitly correcting them, e\.g\., generalized cross entropy\[[29](https://arxiv.org/html/2608.04147#bib.bib73)\], symmetric cross entropy\[[23](https://arxiv.org/html/2608.04147#bib.bib71)\], and robust losses\[[6](https://arxiv.org/html/2608.04147#bib.bib66)\]\. These methods are simple but do not directly provide an interpretable noise signal\.

Given the empirical observation that deep networks fit clean data before memorizing noise\[[2](https://arxiv.org/html/2608.04147#bib.bib80)\], Co\-teaching selects small\-loss samples using two networks\[[9](https://arxiv.org/html/2608.04147#bib.bib76)\]and DivideMix models losses with a GMM and treats training as semi\-supervised learning via MixMatch\[[13](https://arxiv.org/html/2608.04147#bib.bib72),[3](https://arxiv.org/html/2608.04147#bib.bib65)\]\. These methods can be effective but typically require multiple networks, excessive tuning, or additional losses\.

Pseudo\-labeling\[[12](https://arxiv.org/html/2608.04147#bib.bib164)\]and bootstrapping\[[17](https://arxiv.org/html/2608.04147#bib.bib162)\]blend observed labels with model predictions and progressive self label correction reduces confirmation bias\[[22](https://arxiv.org/html/2608.04147#bib.bib63),[24](https://arxiv.org/html/2608.04147#bib.bib59),[19](https://arxiv.org/html/2608.04147#bib.bib62)\]\. LiNC has similarities to bootstrapping, but is different in a very important way: trust is learned per sample rather than fixed globally, and we provide an explicit noise separation procedure that avoids hard\-coded thresholds\.

Several techniques estimate label quality post\-hoc using training dynamics \(AUM\[[16](https://arxiv.org/html/2608.04147#bib.bib51)\], forgetting events\[[21](https://arxiv.org/html/2608.04147#bib.bib22)\], DataMaps\[[20](https://arxiv.org/html/2608.04147#bib.bib20)\], EL2N/GraND\[[15](https://arxiv.org/html/2608.04147#bib.bib21)\], Data\-IQ\[[18](https://arxiv.org/html/2608.04147#bib.bib96)\], VoG\[[1](https://arxiv.org/html/2608.04147#bib.bib30)\], CNLCU\-S\[[25](https://arxiv.org/html/2608.04147#bib.bib23)\]\)\. LiNC produces an interpretable noise signal as a byproduct of training and directly uses it for correction\.

## 3Method

### 3\.1Problem Setup

Let𝒟=\{\(xi,y~i\)\}i=1N\\mathcal\{D\}=\\\{\(x\_\{i\},\\tilde\{y\}\_\{i\}\)\\\}\_\{i=1\}^\{N\}denote the training set, wherexi∈𝒳x\_\{i\}\\in\\mathcal\{X\}has potentially noisy observed labelsy~i∈\{1,…,C\}\\tilde\{y\}\_\{i\}\\in\\\{1,\\dots,C\\\}, whereCCis the number of classes,NNis the number of training samples\.

We train classifierfθf\_\{\\theta\}to output logitszi=fθ​\(xi\)z\_\{i\}=f\_\{\\theta\}\(x\_\{i\}\)\. Letpi=softmax​\(zi\)p\_\{i\}=\\mathrm\{softmax\}\(z\_\{i\}\)\. We introduce per\-sample trust parametersαi∈\(0,1\)\\alpha\_\{i\}\\in\(0,1\)\.

### 3\.2Trust\-based Supervision

For each sample, we form a soft target distribution as follows:

qi​\(αi\)=\(1−αi\)​stopgrad​\(pi\)\+αi​ey~i,q\_\{i\}\(\\alpha\_\{i\}\)=\(1\-\\alpha\_\{i\}\)\\mathrm\{stopgrad\}\(p\_\{i\}\)\+\\alpha\_\{i\}e\_\{\\tilde\{y\}\_\{i\}\},\(1\)whereey~ie\_\{\\tilde\{y\}\_\{i\}\}is the one\-hot vector for the observed label andstopgrad​\(⋅\)\\mathrm\{stopgrad\}\(\\cdot\)blocks gradients throughpip\_\{i\}when we are updatingαi\\alpha\_\{i\}\. Cross\-entropy loss with a soft target looks as follows:

ℒi​\(θ,αi\)=−∑c=1Cqi,c​\(αi\)​log⁡pi,c\.\\mathcal\{L\}\_\{i\}\(\\theta,\\alpha\_\{i\}\)=\-\\sum\_\{c=1\}^\{C\}q\_\{i,c\}\(\\alpha\_\{i\}\)\\log p\_\{i,c\}\.\(2\)This reduces to standard cross\-entropy, whenαi=1\\alpha\_\{i\}=1, and becomes self\-training, withpip\_\{i\}as the target, whenαi=0\\alpha\_\{i\}=0\.

### 3\.3Trust Gradient for Clean vs\. Noisy Labels

We now show that during the warmup, gradient descent pushesαi\\alpha\_\{i\}in opposite directions for clean vs\. mislabeled samples\.

###### Theorem 3\.1\(Sign of the trust gradient\)\.

For a fixed model output distributionpip\_\{i\}, the derivative of[2](https://arxiv.org/html/2608.04147#S3.E2)w\.r\.t\.αi\\alpha\_\{i\}is as follows:

∂ℒi∂αi=∑c=1Cpi,c​log⁡pi,c−log⁡pi,y~i\.\\frac\{\\partial\\mathcal\{L\}\_\{i\}\}\{\\partial\\alpha\_\{i\}\}=\\sum\_\{c=1\}^\{C\}p\_\{i,c\}\\,\\log p\_\{i,c\}\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\.\(3\)Hence, if the model agrees with the observed label, then∂ℒi/∂αi<0\\partial\\mathcal\{L\}\_\{i\}/\\partial\\alpha\_\{i\}<0and if the model disagrees with the observed label, then∂ℒi/∂αi\>0\\partial\\mathcal\{L\}\_\{i\}/\\partial\\alpha\_\{i\}\>0\.

###### Proof\.

Using[1](https://arxiv.org/html/2608.04147#S3.E1), expand[2](https://arxiv.org/html/2608.04147#S3.E2):ℒi=−\(1−αi\)​∑cpi,c​log⁡pi,c−αi​log⁡pi,y~i\.\\mathcal\{L\}\_\{i\}=\-\(1\-\\alpha\_\{i\}\)\\sum\_\{c\}p\_\{i,c\}\\log p\_\{i,c\}\-\\alpha\_\{i\}\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\. Differentiating w\.r\.t\.αi\\alpha\_\{i\}yields:∂ℒi∂αi=∑cpi,c​log⁡pi,c−log⁡pi,y~i\\frac\{\\partial\\mathcal\{L\}\_\{i\}\}\{\\partial\\alpha\_\{i\}\}=\\sum\_\{c\}p\_\{i,c\}\\,\\log p\_\{i,c\}\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\.

∂ℒi∂α=−log⁡pi,y~i⏟NLL of observed label−\(−∑cpi,c​log⁡pi,c⏟entropy​H​\(pi\)\)\\frac\{\\partial\\mathcal\{L\}\_\{i\}\}\{\\partial\\alpha\}=\\underbrace\{\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\}\_\{\\text\{NLL of observed label\}\}\-\\left\(\\underbrace\{\-\\sum\_\{c\}p\_\{i,c\}\\log p\_\{i,c\}\}\_\{\\text\{entropy \}H\(p\_\{i\}\)\}\\right\)\(4\)=−log⁡pi,y~i−H​\(pi\)\.=\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\-H\(p\_\{i\}\)\.\(5\)In early training, deep neural networks tend to learn the easier and cleaner patterns first before memorizing noise\[[2](https://arxiv.org/html/2608.04147#bib.bib80)\]\. As a result, for most clean samples the model assigns relatively high probability toy~i\\tilde\{y\}\_\{i\}, making−log⁡pi,y~i\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}small, and the inequality−log⁡pi,y~i<H​\(pi\)\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}<H\(p\_\{i\}\)holds, and for mislabeled samples,y~i\\tilde\{y\}\_\{i\}has a relatively low probability and−log⁡pi,y~i\>H​\(pi\)\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\>H\(p\_\{i\}\)\.

In other words, if the model agrees with the observed label, then we have−log⁡pi,y~i<H​\(pi\)⟹∂ℒi∂αi<0\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}<H\(p\_\{i\}\)\\implies\\frac\{\\partial\\mathcal\{L\}\_\{i\}\}\{\\partial\\alpha\_\{i\}\}<0andα\\alphaincreases toward11\. And if the model disagrees with the observed label, then we have−log⁡pi,y~i\>H​\(pi\)⟹∂ℒi∂αi\>0\-\\log p\_\{i,\\tilde\{y\}\_\{i\}\}\>H\(p\_\{i\}\)\\implies\\frac\{\\partial\\mathcal\{L\}\_\{i\}\}\{\\partial\\alpha\_\{i\}\}\>0andα\\alphadecreases toward0\. Therefore,αi\\alpha\_\{i\}becomes separable\. ∎

This is closely related to the small\-loss principle discussed by co\-teaching and mixture\-based methods\[[9](https://arxiv.org/html/2608.04147#bib.bib76),[13](https://arxiv.org/html/2608.04147#bib.bib72)\]\.

### 3\.4Separation of Clean vs\. Noisy Labels

Rather than picking a hard\-coded threshold forαi\\alpha\_\{i\}, we fit a 3\-component GMM to\{αi\}i=1N\\\{\\alpha\_\{i\}\\\}\_\{i=1\}^\{N\}after warmup\. The components are interpreted as*noisy*\(lowest mean\),*ambiguous*\(middle mean\), and*clean*\(highest mean\)\. We use the standard expectation–maximization algorithm to fit the GMM\[[4](https://arxiv.org/html/2608.04147#bib.bib61)\]and obtain samples belonging to the three clusters\.

We useK=3K=3to be the number of GMM components for the separation of the trust parameters to explicitly model ambiguous samples\. In preliminary experiments,K=2K=2tends to over\-correct borderline cases, i\.e\. corrupt many correct labels, whileK=3K=3yields a stable middle component to deal with ambiguous cases, similar to other mixture\-based methods\[[13](https://arxiv.org/html/2608.04147#bib.bib72)\]\.

### 3\.5Training Schedule

LiNC runs in three phases, as shown in Figure[1](https://arxiv.org/html/2608.04147#S1.F1):

- •Soft warmup:train using the soft target distribution \(Equation[1](https://arxiv.org/html/2608.04147#S3.E1)\) while performing manual gradient descent onαi\\alpha\_\{i\}\.
- •Soft correction:fit the GMM to find the “noisy”αi\\alpha\_\{i\}cluster \(lowest mean\) to train those corresponding samples using the model predictions, while the remaining samples continue to train using the soft target distribution \(Equation[1](https://arxiv.org/html/2608.04147#S3.E1)\)\.
- •Hard correction:correct the “noisy” labels by assigning them to be thearg⁡max\\arg\\maxof the model predictions and train using standard cross\-entropy\.

This makes LiNC cautious with borderline samples, whose labels may still be correct, while allowing it to confidently correct samples that are much more likely to be mislabeled\. This reduces unnecessary label changes without leaving clear label errors uncorrected\.

Algorithm 1Training with LiNC1:Input:training data

𝒟=\{\(xi,y~i\)\}i=1N\\mathcal\{D\}=\\\{\(x\_\{i\},\\tilde\{y\}\_\{i\}\)\\\}\_\{i=1\}^\{N\}, model

fθf\_\{\\theta\}, trust parameters

\{αi\}\\\{\\alpha\_\{i\}\\\},lr \(

ηα\\eta\_\{\\alpha\}\) and wd \(

λα\\lambda\_\{\\alpha\}\) for

\{αi\}\\\{\\alpha\_\{i\}\\\}, soft warmup epochs

ww, soft correction epochs

ss\.

2:Initialize:

αi=1\\alpha\_\{i\}=1
3:forepoch

=1=1to

EEdo

4:forminibatch

\(x,y~,idx\)\(x,\\tilde\{y\},\\mathrm\{idx\}\)do

5:

p←softmax​\(fθ​\(x\)\)p\\leftarrow\\mathrm\{softmax\}\(f\_\{\\theta\}\(x\)\)
6:

α←αidx\\alpha\\leftarrow\\alpha\_\{\\mathrm\{idx\}\}
7:ifepoch

≤w\\leq wthen

8:

q←\(1−α\)​stopgrad​\(p\)\+α​ey~q\\leftarrow\(1\-\\alpha\)\\,\\mathrm\{stopgrad\}\(p\)\+\\alpha\\,e\_\{\\tilde\{y\}\}
9:endif

10:if

w<epoch≤w\+sw<\\text\{epoch\}\\leq w\+sthen

11:

q←pq\\leftarrow pfor samples assigned to noisy GMM cluster

12:endif

13:if

epoch\>w\+s\\text\{epoch\}\>w\+sthen

14:

q←ey^q\\leftarrow e\_\{\\hat\{y\}\}where

y^=arg⁡max⁡p\\hat\{y\}=\\arg\\max p
15:endif

16:calculate loss

ℒ​\(θ,α\)=−∑q​\(α\)​log⁡p\\mathcal\{L\}\(\\theta,\\alpha\)=\-\\sum q\(\\alpha\)\\log p
17:update

θ\\thetausing optimizer step on

∇θℒ\\nabla\_\{\\theta\}\\mathcal\{L\}
18:ifepoch

≤w\+s\\leq w\+sthen

19:

αidx←αidx−ηα​\(∇αidxℒ\+λα​αidx\)\\alpha\_\{\\mathrm\{idx\}\}\\leftarrow\\alpha\_\{\\mathrm\{idx\}\}\-\\eta\_\{\\alpha\}\(\\nabla\_\{\\alpha\_\{\\mathrm\{idx\}\}\}\\mathcal\{L\}\+\\lambda\_\{\\alpha\}\\alpha\_\{\\mathrm\{idx\}\}\)
20:endif

21:endfor

22:ifepoch

=w=wthen

23:fit 3\-component GMM to

\{αi\}\\\{\\alpha\_\{i\}\\\}& identify noisy cluster \(lowest mean\)

24:endif

25:ifepoch

=w\+s=w\+sthen

26:for

xi∈𝒟x\_\{i\}\\in\\mathcal\{D\}, correct labels

y^i=arg⁡max⁡fθ​\(xi\)\\hat\{y\}\_\{i\}=\\arg\\max f\_\{\\theta\}\(x\_\{i\}\)for noisy cluster

27:freeze

αi\\alpha\_\{i\}
28:endif

29:endfor

30:Return:trained model

fθf\_\{\\theta\}and trust parameters

\{αi\}\\\{\\alpha\_\{i\}\\\}

### 3\.6Complexity: With vs\. Without LiNC

#### Runtime\.

LetEEbe the number of training epochs,BBbe batch size, andTfwd​\(B\)T\_\{\\text\{fwd\}\}\(B\)andTbwd​\(B\)T\_\{\\text\{bwd\}\}\(B\)denote the time required for one forward and backward pass on batch sizeBB, respectively\.

Standard training costsTbase=E⋅NB⋅\(Tfwd​\(B\)\+Tbwd​\(B\)\)T\_\{\\text\{base\}\}=E\\cdot\\frac\{N\}\{B\}\\cdot\(T\_\{\\text\{fwd\}\}\(B\)\+T\_\{\\text\{bwd\}\}\(B\)\)\. This gives us𝒪​\(E​N\)\\mathcal\{O\}\(EN\)runtime without LiNC\.

![Refer to caption](https://arxiv.org/html/2608.04147v1/organs10.png)

![Refer to caption](https://arxiv.org/html/2608.04147v1/organs20.png)

![Refer to caption](https://arxiv.org/html/2608.04147v1/organs30.png)

![Refer to caption](https://arxiv.org/html/2608.04147v1/organs40.png)

![Refer to caption](https://arxiv.org/html/2608.04147v1/organs50.png)

Figure 2:Empirical separability of trust valuesαi\\alpha\_\{i\}on OrganSMNIST under 10\-50% symmetric noise\. Green / pink are true clean / noisy subsets, respectively, and the dashed lines indicate GMM component means \(noisy / middle / clean\)\.LiNC adds 3 main additional operations for total timeTLiNC=Tbase\+w⋅NB⋅𝒪​\(B​C\)\+𝒪​\(N\)\+𝒪​\(N⋅Tfwd​\(1\)\)T\_\{\\text\{LiNC\}\}=T\_\{\\text\{base\}\}\+w\\cdot\\frac\{N\}\{B\}\\cdot\\mathcal\{O\}\(B\\,C\)\+\\mathcal\{O\}\(N\)\+\\mathcal\{O\}\(N\\cdot T\_\{\\text\{fwd\}\}\(1\)\), as follows:

1. 1\.line 11: formingqqcosts𝒪​\(B​C\)\\mathcal\{O\}\(B\\,C\),wwtimes\. Note thatw<Ew<E\.
2. 2\.line 23: EM onNNscalars withK=3K=3andIIiterations costs𝒪​\(N​K​I\)=𝒪​\(N\)\\mathcal\{O\}\(NKI\)=\\mathcal\{O\}\(N\)\.
3. 3\.line 26: computingy^\\hat\{y\}costs𝒪​\(N⋅Tfwd​\(1\)\)\\mathcal\{O\}\(N\\cdot T\_\{\\text\{fwd\}\}\(1\)\)\.

This again gives us𝒪​\(E​N\)\\mathcal\{O\}\(EN\)runtime with LiNC\.

#### Memory\.

Standard training stores model parameters:Mbase=𝒪​\(\|θ\|\)M\_\{\\text\{base\}\}=\\mathcal\{O\}\(\|\\theta\|\)\.

LiNC in addition storesNNtrust parameters:MLiNC=Mbase\+𝒪​\(N\)M\_\{\\text\{LiNC\}\}=M\_\{\\text\{base\}\}\+\\mathcal\{O\}\(N\), which is negligible\.

## 4Experimental Setup

Table 1:AUC comparison of several noise detection baselines on the OrganSMNIST dataset with 20% noise\.Table 2:Test top\-1 accuracy on MedMNISTv2 at 0% symmetric noise without LiNC\. Baseline results are from\[[26](https://arxiv.org/html/2608.04147#bib.bib93)\]\. Two best results are inbold, with ViT\-S/8\-224 consistently achieving very high accuracy\.Table 3:Test top\-1 accuracy under symmetric noise for 10 2D MedMNISTv2 datasets\. Standard training \(No LiNC\) and LiNC are evaluated at their Best and Last epochs\.### 4\.1Datasets and Noise Protocol

We evaluate on ten 2D datasets from MedMNISTv2\[[26](https://arxiv.org/html/2608.04147#bib.bib93)\]from varying domains including: PathMNIST, DermaMNIST, OCTMNIST, PneumoniaMNIST, BreastMNIST, BloodMNIST, TissueMNIST, OrganAMNIST, OrganCMNIST, and OrganSMNIST\. Following common noisy\-label evaluations\[[9](https://arxiv.org/html/2608.04147#bib.bib76),[13](https://arxiv.org/html/2608.04147#bib.bib72)\], we inject symmetric label noise at rates ofρ∈\{0\.1,0\.2,0\.3,0\.4,0\.5\}\\rho\\in\\\{0\.1,0\.2,0\.3,0\.4,0\.5\\\}by randomly replacing a fractionρ\\rhoof training labels with a uniformly sampled incorrect class\.

### 4\.2Model and Training

We finetune an ImageNet\-pretrained Vision Transformer\[[5](https://arxiv.org/html/2608.04147#bib.bib60)\]\(ViT\-S/8\-224, frozen everywhere except classifier head and last transformer block\) using Adam\[[11](https://arxiv.org/html/2608.04147#bib.bib3)\]for a total of 70 epochs, with batch size 128, learning rate5​e−45e\-4, and weight decay1​e−41e\-4, along with a MultiStepLR scheduler that reduces the learning rate by a factor of 0\.7 at 10, 20, 40, and 60 epochs\. We report the best test accuracy and last test accuracy\.

LiNC uses soft warmup forw=5w=5epochs, soft correction fors=5s=5epochs, and hard correction for the remainder\. Performance is relatively insensitive to the duration of the soft warmup and soft correction phases\. In practice, around 5–10 epochs for the soft phases was sufficient to obtain stable, competitive results\. The trust learning rateηα=1\\eta\_\{\\alpha\}=1, and trust weight decayλα=1​e−1\\lambda\_\{\\alpha\}=1e\-1\. All non\-LiNC hyperparameters are shared between baseline and LiNC\. The optimal hyperparameters without LiNC are still optimal with LiNC\.

### 4\.3Separation of Trust Parameters

Figure[2](https://arxiv.org/html/2608.04147#S3.F2)shows the empirical distributions of the learned trust parametersαi\\alpha\_\{i\}after the five\-epoch soft warm\-up on OrganSMNIST\. Across all evaluated noise rates, samples with clean observed labels are concentrated at higher trust values, whereas mislabeled samples tend to receive lower trust values\. This behavior is consistent with Theorem[3\.1](https://arxiv.org/html/2608.04147#S3.Thmtheorem1): early in training, the model is more likely to agree with correctly labeled examples and disagree with incorrectly labeled examples, causing their trust parameters to move in opposite directions\.

The separation remains visible as the symmetric noise rate increases from10%10\\%to50%50\\%\. At higher noise rates, the noisy distribution becomes broader and overlap near the boundary increases, but the low\-, middle\-, and high\-mean GMM components remain ordered\. The middle component provides a buffer between the two dominant modes, allowing LiNC to treat borderline samples as ambiguous rather than automatically correcting them\. This is particularly important in medical imaging, where disagreement with an observed label may reflect diagnostic difficulty rather than an annotation error\. By restricting correction to the lowest\-mean component, LiNC avoids imposing a binary clean/noisy decision on every uncertain example\.

Table[1](https://arxiv.org/html/2608.04147#S4.T1)provides a quantitative evaluation of this separation on OrganSMNIST with20%20\\%noise\. LiNC achieves an AUC of0\.98370\.9837, compared with0\.91260\.9126for VoG, the strongest competing method in this experiment\. This corresponds to an absolute improvement of0\.07110\.0711in AUC\. LiNC also substantially outperforms methods based on margins, forgetting events, losses, gradients, and other measures of sample difficulty\. These results indicate that a single scalar learned within the ordinary training loop can provide a highly informative signal of possible label corruption without requiring a clean reference set, a second model, or a predefined trust threshold\.

The magnitude ofαi\\alpha\_\{i\}should be interpreted as a model\- and training\-dependent trust score rather than as a probability that a label is correct\. In practice, the learned scores and GMM assignments can support two uses: selecting the lowest\-trust cases for correction during training and producing a ranked list of potentially problematic annotations for subsequent dataset review\.

![Refer to caption](https://arxiv.org/html/2608.04147v1/dermaplot.png)Figure 3:Test top\-1 accuracy over 70 epochs for DermaMNIST with 50% symmetric noise\. LiNC improves convergence and final accuracy compared to baseline training\.
### 4\.4Effect on Downstream Performance

Before introducing label noise, Table[2](https://arxiv.org/html/2608.04147#S4.T2)establishes that the selected ViT\-S/8\-224 model provides a strong reference model for the downstream experiments\. It achieves the highest listed test accuracy on seven of the ten MedMNISTv2 datasets and remains competitive on the other three\. The improvements in Table[3](https://arxiv.org/html/2608.04147#S4.T3)therefore do not arise from comparing LiNC with an intentionally weak architecture\. Moreover, LiNC and standard training use the same model, optimizer, learning\-rate schedule, augmentations, and non\-LiNC hyperparameters, isolating the effect of the proposed trust learning and correction procedure\.

Figure[3](https://arxiv.org/html/2608.04147#S4.F3)illustrates the training dynamics on DermaMNIST under50%50\\%symmetric noise\. Standard training initially reaches a test accuracy of0\.75290\.7529but subsequently deteriorates to0\.56460\.5646as training continues\. In contrast, LiNC reaches a higher best accuracy of0\.79340\.7934and maintains the same accuracy at the final epoch\. The resulting improvement is therefore4\.054\.05percentage points at the best epoch but22\.8822\.88percentage points at the last epoch\. This trajectory is consistent with the role of LiNC: the method preserves useful early learning while preventing the later optimization process from increasingly fitting corrupted targets\.

The same pattern appears across the ten datasets in Table[3](https://arxiv.org/html/2608.04147#S4.T3)\. Averaging across datasets, LiNC improves last\-epoch accuracy by2\.192\.19,7\.867\.86,12\.3112\.31,16\.9416\.94, and21\.4121\.41percentage points at noise rates of10%10\\%,20%20\\%,30%30\\%,40%40\\%, and50%50\\%, respectively\. Thus, the benefit grows monotonically as label corruption becomes more severe\. At50%50\\%noise, mean last\-epoch accuracy increases from0\.58820\.5882without LiNC to0\.80230\.8023with LiNC\. Improvements are not confined to a small subset of datasets: LiNC achieves higher last\-epoch accuracy in 49 of the 50 dataset\-noise combinations and higher best\-epoch accuracy in 42 of 50 combinations\.

There is a large difference between best\- and last\-epoch performance with and without LiNC\. Averaged over all 50 experimental conditions, the difference between best\- and last\-epoch accuracy is13\.1413\.14percentage points for standard training but only2\.312\.31percentage points for LiNC\. At50%50\\%noise, this degradation grows to23\.0623\.06points without LiNC, compared with only3\.563\.56points with LiNC\. LiNC stabilizes generalization after the model would otherwise begin memorizing corrupted labels\.

## 5Discussion

LiNC combines three simple mechanisms that address complementary aspects of noisy\-label learning\. First, the per\-sample trust parameter provides a direct, differentiable representation of the model’s agreement with each observed label\. Second, the three\-component GMM translates the resulting trust distribution into noisy, ambiguous, and clean groups without requiring a manually selected threshold or knowledge of the true noise rate\. Third, the staged correction schedule limits the risk of immediately reinforcing incorrect model predictions\. During soft correction, model outputs are used as distributions rather than hard class assignments and hard correction occurs only after this intermediate phase and only for samples assigned to the lowest\-trust component\.

The results suggest that LiNC is resistant to late\-stage memorization\. Improvements in best\-epoch accuracy are comparatively modest, averaging1\.311\.31percentage points across all conditions, whereas the average improvement at the last epoch is12\.1412\.14points\. This difference is expected from the method’s design\. Early in training, both approaches can learn predictive structure from the clean portion of the data\. Their behavior diverges later, when standard cross\-entropy continues to optimize against corrupted labels while LiNC has identified and replaced many of those targets\. The resulting stability is useful for model selection\.

LiNC has the asymptotic runtime of standard training and requires only𝒪​\(N\)\\mathcal\{O\}\(N\)additional memory for the trust parameters\. All trust updates occur within the same training loop, and the method does not require an ensemble, a second network, or a separate clean dataset\. The learned trust values also provide an auditable output\. For a medical dataset, low\-trust cases could be prioritized for expert re\-review, while cases assigned to the middle component could be examined as potentially ambiguous examples\.

There are some limitations to this method\. First, genuine clinical ambiguity may also lead multiple defensible labels to exist for the same case\. Under these conditions, the learned trust score may capture a combination of annotation reliability, sample difficulty, and model noise rather than label noise alone\. Evaluation on datasets with real\-world label errors and inter\-rater disagreement is therefore necessary\.

Second, the method depends on the early\-learning behavior underlying Theorem[3\.1](https://arxiv.org/html/2608.04147#S3.Thmtheorem1)\. A model can confidently disagree with a correct label or confidently agree with an incorrect label when the same systematic error is repeated throughout the dataset\. This risk may be greater for rare classes or underrepresented patient groups\. Future work should examine class\-conditional and subgroup\-specific trust distributions and measure whether correction rates or errors differ across clinically relevant groups\.

Third, a three\-component GMM will return three components even when the trust distribution contains little evidence of label corruption\. This limitation is most apparent when the dataset is completely clean, but it may also matter under low noise, as suggested by the PathMNIST result at10%10\\%\. Future work should extend to allow the model to abstain from hard correction, select the number of mixture components adaptively, or send low\-confidence cases to expert review\.

## 6Conclusion

We introduce LiNC, a lightweight method that learns a trust parameter for every training sample and uses the resulting distribution to separate noisy, ambiguous, and clean cases\. LiNC achieves an AUC of0\.98370\.9837for detecting corrupted labels in the evaluated OrganSMNIST setting and improves mean last\-epoch accuracy by21\.4121\.41percentage points across ten datasets at50%50\\%symmetric noise\. It also substantially reduces the deterioration between peak and final performance, demonstrating generalization benefits\. LiNC requires neither a clean validation set nor an additional model, preserves the asymptotic runtime of standard training, and adds only𝒪​\(N\)\\mathcal\{O\}\(N\)memory\. Its learned trust values provide both a mechanism for targeted correction and an interpretable signal for dataset auditing\. Future work should evaluate this framework under realistic, unknown noise processes and develop human\-review mechanisms for human\-model disagreement\.

## References

- \[1\]C\. Agarwal, D\. D’souza, and S\. Hooker\(2022\-06\-21\)Estimating example difficulty using variance of gradients\.arXiv\.External Links:2008\.11600Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[2\]D\. Arpit, S\. Jastrzębski, N\. Ballas, D\. Krueger, E\. Bengio, M\. S\. Kanwal, T\. Maharaj, A\. Fischer, A\. Courville, Y\. Bengio,et al\.\(2017\)A closer look at memorization in deep networks\.InInternational conference on machine learning,pp\. 233–242\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p1.1),[§2](https://arxiv.org/html/2608.04147#S2.p2.1),[§3\.3](https://arxiv.org/html/2608.04147#S3.SS3.1.p1.8)\.
- \[3\]D\. Berthelot, N\. Carlini, I\. Goodfellow, N\. Papernot, A\. Oliver, and C\. A\. Raffel\(2019\)Mixmatch: a holistic approach to semi\-supervised learning\.Advances in neural information processing systems32\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p2.1)\.
- \[4\]A\. P\. Dempster, N\. M\. Laird, and D\. B\. Rubin\(1977\)Maximum likelihood from incomplete data via the em algorithm\.Journal of the royal statistical society: series B \(methodological\)39\(1\),pp\. 1–22\.Cited by:[§3\.4](https://arxiv.org/html/2608.04147#S3.SS4.p1.2)\.
- \[5\]A\. Dosovitskiy, L\. Beyer, A\. Kolesnikov, D\. Weissenborn, X\. Zhai, T\. Unterthiner, M\. Dehghani, M\. Minderer, G\. Heigold, S\. Gelly,et al\.\(2020\)An image is worth 16x16 words: transformers for image recognition at scale\.arXiv preprint arXiv:2010\.11929\.Cited by:[§4\.2](https://arxiv.org/html/2608.04147#S4.SS2.p1.2)\.
- \[6\]A\. Ghosh, H\. Kumar, and P\. S\. Sastry\(2017\)Robust loss functions under label noise for deep neural networks\.InProceedings of the AAAI conference on artificial intelligence,Vol\.31\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p1.1)\.
- \[7\]J\. Goldberger and E\. Ben\-Reuven\(2017\)Training deep neural\-networks using a noise adaptation layer\.InInternational conference on learning representations,Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p1.1)\.
- \[8\]C\. Guo, G\. Pleiss, Y\. Sun, and K\. Q\. Weinberger\(2017\-08\-03\)On calibration of modern neural networks\.arXiv\.External Links:1706\.04599Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p1.1)\.
- \[9\]B\. Han, Q\. Yao, X\. Yu, G\. Niu, M\. Xu, W\. Hu, I\. Tsang, and M\. Sugiyama\(2018\)Co\-teaching: robust training of deep neural networks with extremely noisy labels\.Advances in neural information processing systems31\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p2.1),[§2](https://arxiv.org/html/2608.04147#S2.p2.1),[§3\.3](https://arxiv.org/html/2608.04147#S3.SS3.p2.1),[§4\.1](https://arxiv.org/html/2608.04147#S4.SS1.p1.2)\.
- \[10\]D\. Karimi, H\. Dou, S\. K\. Warfield, and A\. Gholipour\(2020\)Deep learning with noisy labels: exploring techniques and remedies in medical image analysis\.Medical image analysis65,pp\. 101759\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p1.1)\.
- \[11\]D\. P\. Kingma\(2014\)Adam: a method for stochastic optimization\.arXiv preprint arXiv:1412\.6980\.Cited by:[§4\.2](https://arxiv.org/html/2608.04147#S4.SS2.p1.2)\.
- \[12\]D\. Leeet al\.\(2013\)Pseudo\-label: the simple and efficient semi\-supervised learning method for deep neural networks\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p3.1)\.
- \[13\]J\. Li, R\. Socher, and S\. C\. Hoi\(2020\)Dividemix: learning with noisy labels as semi\-supervised learning\.arXiv preprint arXiv:2002\.07394\.Cited by:[2nd item](https://arxiv.org/html/2608.04147#S1.I1.i2.p1.1),[§1](https://arxiv.org/html/2608.04147#S1.p2.1),[§2](https://arxiv.org/html/2608.04147#S2.p2.1),[§3\.3](https://arxiv.org/html/2608.04147#S3.SS3.p2.1),[§3\.4](https://arxiv.org/html/2608.04147#S3.SS4.p2.3),[§4\.1](https://arxiv.org/html/2608.04147#S4.SS1.p1.2)\.
- \[14\]G\. Patrini, A\. Rozza, A\. Krishna Menon, R\. Nock, and L\. Qu\(2017\)Making deep neural networks robust to label noise: a loss correction approach\.InProceedings of the IEEE conference on computer vision and pattern recognition,pp\. 1944–1952\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p2.1),[§2](https://arxiv.org/html/2608.04147#S2.p1.1)\.
- \[15\]M\. Paul, S\. Ganguli, and G\. K\. Dziugaite\(2023\-03\-28\)Deep learning on a data diet: finding important examples early in training\.arXiv\.External Links:2107\.07075Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[16\]G\. Pleiss, T\. Zhang, E\. Elenberg, and K\. Q\. Weinberger\(2020\)Identifying mislabeled data using the area under the margin ranking\.InAdvances in Neural Information Processing Systems,H\. Larochelle, M\. Ranzato, R\. Hadsell, M\.F\. Balcan, and H\. Lin \(Eds\.\),Vol\.33,pp\. 17044–17056\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[17\]S\. Reed, H\. Lee, D\. Anguelov, C\. Szegedy, D\. Erhan, and A\. Rabinovich\(2014\)Training deep neural networks on noisy labels with bootstrapping\.arXiv preprint arXiv:1412\.6596\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p2.1),[§2](https://arxiv.org/html/2608.04147#S2.p3.1)\.
- \[18\]N\. Seedat, F\. Imrie, and M\. v\. d\. Schaar\(2024\-03\-07\)Dissecting sample hardness: a fine\-grained analysis of hardness characterization methods for data\-centric AI\.arXiv\.External Links:2403\.04551Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[19\]H\. Song, M\. Kim, and J\. Lee\(2019\)Selfie: refurbishing unclean samples for robust deep learning\.InInternational conference on machine learning,pp\. 5907–5915\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p3.1)\.
- \[20\]S\. Swayamdipta, R\. Schwartz, N\. Lourie, Y\. Wang, H\. Hajishirzi, N\. A\. Smith, and Y\. Choi\(2020\-10\-15\)Dataset cartography: mapping and diagnosing datasets with training dynamics\.arXiv\.External Links:2009\.10795Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[21\]M\. Toneva, A\. Sordoni, R\. T\. d\. Combes, A\. Trischler, Y\. Bengio, and G\. J\. Gordon\(2019\-11\-15\)An empirical study of example forgetting during deep neural network learning\.arXiv\.External Links:1812\.05159Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[22\]X\. Wang, Y\. Hua, E\. Kodirov, D\. A\. Clifton, and N\. M\. Robertson\(2021\)Proselflc: progressive self label correction for training robust deep neural networks\.InProceedings of the IEEE/CVF conference on computer vision and pattern recognition,pp\. 752–761\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p3.1)\.
- \[23\]Y\. Wang, X\. Ma, Z\. Chen, Y\. Luo, J\. Yi, and J\. Bailey\(2019\)Symmetric cross entropy for robust learning with noisy labels\.InProceedings of the IEEE/CVF international conference on computer vision,pp\. 322–330\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p2.1),[§2](https://arxiv.org/html/2608.04147#S2.p1.1)\.
- \[24\]H\. Wei, L\. Feng, X\. Chen, and B\. An\(2020\)Combating noisy labels by agreement: a joint training method with co\-regularization\.InProceedings of the IEEE/CVF conference on computer vision and pattern recognition,pp\. 13726–13735\.Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p3.1)\.
- \[25\]X\. Xia, T\. Liu, B\. Han, M\. Gong, J\. Yu, G\. Niu, and M\. Sugiyama\(2021\-06\-01\)Sample selection with uncertainty of losses for learning with noisy labels\.arXiv\.External Links:2106\.00445Cited by:[§2](https://arxiv.org/html/2608.04147#S2.p4.1)\.
- \[26\]J\. Yang, R\. Shi, D\. Wei, Z\. Liu, L\. Zhao, B\. Ke, H\. Pfister, and B\. Ni\(2023\)MedMNIST v2\-a large\-scale lightweight benchmark for 2d and 3d biomedical image classification\.Scientific Data10\(1\),pp\. 41\.Cited by:[§4\.1](https://arxiv.org/html/2608.04147#S4.SS1.p1.2),[Table 2](https://arxiv.org/html/2608.04147#S4.T2),[Table 2](https://arxiv.org/html/2608.04147#S4.T2.10.2)\.
- \[27\]C\. Zhang, S\. Bengio, M\. Hardt, B\. Recht, and O\. Vinyals\(2016\)Understanding deep learning requires rethinking generalization\.arXiv preprint arXiv:1611\.03530\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p1.1)\.
- \[28\]C\. Zhang, S\. Bengio, M\. Hardt, B\. Recht, and O\. Vinyals\(2021\)Understanding deep learning \(still\) requires rethinking generalization\.Communications of the ACM64\(3\),pp\. 107–115\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p1.1)\.
- \[29\]Z\. Zhang and M\. Sabuncu\(2018\)Generalized cross entropy loss for training deep neural networks with noisy labels\.Advances in neural information processing systems31\.Cited by:[§1](https://arxiv.org/html/2608.04147#S1.p2.1),[§2](https://arxiv.org/html/2608.04147#S2.p1.1)\.