# The Fisher-Rao Loss for Learning under Label Noise

arXiv: https://arxiv.org/abs/2210.16401 · HTML: https://mlsanity.com/paper/2210.16401/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 10 of 10)

- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Evaluation of Neural Architectures Trained with Square Loss vs Cross-Entropy in Classification Tasks](https://mlsanity.com/paper/2006.07322/) (2020)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [On Loss Functions for Deep Neural Networks in Classification](https://mlsanity.com/paper/1702.05659/) (2017)
- [Making Risk Minimization Tolerant to Label Noise](https://mlsanity.com/paper/1403.3610/) (2014)
- [Pulling back information geometry](https://mlsanity.com/paper/2106.05367/) (2021)
- [Igeood: An Information Geometry Approach to Out-of-Distribution Detection](https://mlsanity.com/paper/2203.07798/) (2022)
- [Adversarial Robustness via Fisher-Rao Regularization](https://mlsanity.com/paper/2106.06685/) (2021)

## Built on by (most cited first, 1 of 1)

- [A numerical approximation method for the Fisher-Rao distance between multivariate normal distributions](https://mlsanity.com/paper/2302.08175/) (2023)

## Abstract (arXiv)

Choosing a suitable loss function is essential when learning by empirical risk minimisation. In many practical cases, the datasets used for training a classifier may contain incorrect labels, which prompts the interest for using loss functions that are inherently robust to label noise. In this paper, we study the Fisher-Rao loss function, which emerges from the Fisher-Rao distance in the statistical manifold of discrete distributions. We derive an upper bound for the performance degradation in the presence of label noise, and analyse the learning speed of this loss. Comparing with other commonly used losses, we argue that the Fisher-Rao loss provides a natural trade-off between robustness and training dynamics. Numerical experiments with synthetic and MNIST datasets illustrate this performance.