# Introducing Fractional Classification Loss for Robust Learning with Noisy Labels

arXiv: https://arxiv.org/abs/2508.06346 · HTML: https://mlsanity.com/paper/2508.06346/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Builds on (most cited first, 17 of 17)

- [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)
- [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)
- [Symmetric Cross Entropy for Robust Learning with Noisy Labels](https://mlsanity.com/paper/1908.06112/) (2019)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Joint Optimization Framework for Learning with Noisy Labels](https://mlsanity.com/paper/1803.11364/) (2018)
- [Normalized Loss Functions for Deep Learning with Noisy Labels](https://mlsanity.com/paper/2006.13554/) (2020)
- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Dimensionality-Driven Learning with Noisy Labels](https://mlsanity.com/paper/1806.02612/) (2018)
- [Meta Label Correction for Noisy Label Learning](https://mlsanity.com/paper/1911.03809/) (2019)
- [Jo-SRC: A Contrastive Approach for Combating Noisy Labels](https://mlsanity.com/paper/2103.13029/) (2021)
- [Generalized Jensen-Shannon Divergence Loss for Learning with Noisy Labels](https://mlsanity.com/paper/2105.04522/) (2021)
- [SURE: SUrvey REcipes for building reliable and robust deep networks](https://mlsanity.com/paper/2403.00543/) (2024)
- [Lyapunov functions for nabla discrete fractional order systems](https://mlsanity.com/paper/1812.11368/) (2018)
- [Mitigating Label Noise on Graph via Topological Sample Selection](https://mlsanity.com/paper/2403.01942/) (2024)

## Built on by (most cited first, 2 of 2)

- [rSDNet: Unified Robust Neural Learning against Label Noise and Adversarial Attacks](https://mlsanity.com/paper/2603.17628/) (2026)
- [No Unique Minimizer, No Problem: On the Consistency of Robust Neural Classifiers](https://mlsanity.com/paper/2608.08489/) (2026)

## Abstract (arXiv)

Robust loss functions are crucial for training deep neural networks in the presence of label noise, yet existing approaches require extensive, dataset-specific hyperparameter tuning. In this work, we introduce Fractional Classification Loss (FCL), an adaptive robust loss that automatically calibrates its robustness to label noise during training. Built within the active-passive loss framework, FCL employs the fractional derivative of the Cross-Entropy (CE) loss as its active component and the Mean Absolute Error (MAE) as its passive loss component. With this formulation, we demonstrate that the fractional derivative order μ spans a family of loss functions that interpolate between MAE-like robustness and CE-like fast convergence. Furthermore, we integrate μ into the gradient-based optimization as a learnable parameter and automatically adjust it to optimize the trade-off between robustness and convergence speed. We reveal that FCL's unique property establishes a critical trade-off that enables the stable learning of μ: lower log penalties on difficult or mislabeled examples improve robustness but impose higher penalties on easy or clean data, reducing model confidence in them. Consequently, FCL can dynamically reshape its loss landscape to achieve effective classification performance under label noise. Extensive experiments on benchmark datasets show that FCL achieves state-of-the-art results without the need for manual hyperparameter tuning.