# Dirichlet-Based Prediction Calibration for Learning with Noisy Labels

arXiv: https://arxiv.org/abs/2401.07062 · HTML: https://mlsanity.com/paper/2401.07062/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 44 references that are in the map.
- First posted on arXiv 13 Jan 2024.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [WebVision Database: Visual Learning and Understanding from Web Data](https://mlsanity.com/paper/1708.02862/) (2017)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Learning with Noisy Labels Revisited: A Study Using Real-World Human Annotations](https://mlsanity.com/paper/2110.12088/) (2021)
- [Decoupling "when to update" from "how to update"](https://mlsanity.com/paper/1706.02613/) (2017)
- [Probabilistic End-to-end Noise Correction for Learning with Noisy Labels](https://mlsanity.com/paper/1903.07788/) (2019)
- [Understanding and Utilizing Deep Neural Networks Trained with Noisy Labels](https://mlsanity.com/paper/1905.05040/) (2019)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [Learning with Instance-Dependent Label Noise: A Sample Sieve Approach](https://mlsanity.com/paper/2010.02347/) (2020)
- [Active Bias: Training More Accurate Neural Networks by Emphasizing High Variance Samples](https://mlsanity.com/paper/1704.07433/) (2017)
- [Self-Adaptive Training: beyond Empirical Risk Minimization](https://mlsanity.com/paper/2002.10319/) (2020)
- [Robust Training under Label Noise by Over-parameterization](https://mlsanity.com/paper/2202.14026/) (2022)
- [Multi-Objective Interpolation Training for Robustness to Label Noise](https://mlsanity.com/paper/2012.04462/) (2020)
- [Joint Negative and Positive Learning for Noisy Labels](https://mlsanity.com/paper/2104.06574/) (2021)
- [Dirichlet-based Uncertainty Calibration for Active Domain Adaptation](https://mlsanity.com/paper/2302.13824/) (2023)
- [Noise-Robust Bidirectional Learning with Dynamic Sample Reweighting](https://mlsanity.com/paper/2209.01334/) (2022)

## Built on by (most cited first, 8 of 8)

- [Bidirectional Uncertainty-Based Active Learning for Open Set Annotation](https://mlsanity.com/paper/2402.15198/) (2024)
- [Rethinking Epistemic and Aleatoric Uncertainty for Active Open-Set Annotation: An Energy-Based Approach](https://mlsanity.com/paper/2502.19691/) (2025)
- [Sample Selection via Contrastive Fragmentation for Noisy Label Regression](https://mlsanity.com/paper/2502.17771/) (2025)
- [Label Calibration in Source Free Domain Adaptation](https://mlsanity.com/paper/2501.07072/) (2025)
- [Understanding and Mitigating the Bias in Sample Selection for Learning with Noisy Labels](https://mlsanity.com/paper/2401.13360/) (2024)
- [Revisiting Unknowns: Towards Effective and Efficient Open-Set Active Learning](https://mlsanity.com/paper/2603.07898/) (2026)
- [From Calibration to Refinement: Seeking Certainty via Probabilistic Evidence Propagation for Noisy-Label Person Re-Identification](https://mlsanity.com/paper/2602.23133/) (2026)
- [Prompt and Refinement: Asymmetric Mutual Learning for Infrared Small Target Detection with Noisy Labels](https://mlsanity.com/paper/2610.05918/) (2026)

## Abstract (arXiv)

Learning with noisy labels can significantly hinder the generalization performance of deep neural networks (DNNs). Existing approaches address this issue through loss correction or example selection methods. However, these methods often rely on the model's predictions obtained from the softmax function, which can be over-confident and unreliable. In this study, we identify the translation invariance of the softmax function as the underlying cause of this problem and propose the textitDirichlet-based Prediction Calibration (DPC) method as a solution. Our method introduces a calibrated softmax function that breaks the translation invariance by incorporating a suitable constant in the exponent term, enabling more reliable model predictions. To ensure stable model training, we leverage a Dirichlet distribution to assign probabilities to predicted labels and introduce a novel evidence deep learning (EDL) loss. The proposed loss function encourages positive and sufficiently large logits for the given label, while penalizing negative and small logits for other labels, leading to more distinct logits and facilitating better example selection based on a large-margin criterion. Through extensive experiments on diverse benchmark datasets, we demonstrate that DPC achieves state-of-the-art performance. The code is available at https://github.com/chenchenzong/DPC.