# Cauchy Loss Function: Robustness Under Gaussian and Cauchy Noise

arXiv: https://arxiv.org/abs/2302.07238 · HTML: https://mlsanity.com/paper/2302.07238/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 22 references that are in the map.
- First posted on arXiv 14 Feb 2023.

## Builds on (most cited first, 2 of 2)

- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Robust subspace clustering by Cauchy loss function](https://mlsanity.com/paper/1904.12274/) (2019)

## Built on by (most cited first, 5 of 5)

- [Marginalized Bundle Adjustment: Multi-View Camera Pose from Monocular Depth Estimates](https://mlsanity.com/paper/2602.18906/) (2026)
- [On the Robustness of Kernel Ridge Regression Using the Cauchy Loss Function](https://mlsanity.com/paper/2503.20120/) (2025)
- [MEXA-CTP: Mode Experts Cross-Attention for Clinical Trial Outcome Prediction](https://mlsanity.com/paper/2501.06823/) (2025)
- [PRaDA: Projective Radial Distortion Averaging](https://mlsanity.com/paper/2504.16499/) (2025)
- [CLaDMoP: Learning Transferrable Models from Successful Clinical Trials via LLMs](https://mlsanity.com/paper/2505.18527/) (2025)

## Abstract (arXiv)

In supervised machine learning, the choice of loss function implicitly assumes a particular noise distribution over the data. For example, the frequently used mean squared error (MSE) loss assumes a Gaussian noise distribution. The choice of loss function during training and testing affects the performance of artificial neural networks (ANNs). It is known that MSE may yield substandard performance in the presence of outliers. The Cauchy loss function (CLF) assumes a Cauchy noise distribution, and is therefore potentially better suited for data with outliers. This papers aims to determine the extent of robustness and generalisability of the CLF as compared to MSE. CLF and MSE are assessed on a few handcrafted regression problems, and a real-world regression problem with artificially simulated outliers, in the context of ANN training. CLF yielded results that were either comparable to or better than the results yielded by MSE, with a few notable exceptions.