# Minimax Generalized Cross-Entropy

arXiv: https://arxiv.org/abs/2603.19874 · HTML: https://mlsanity.com/paper/2603.19874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Robust Loss Functions under Label Noise for Deep Neural Networks](https://mlsanity.com/paper/1712.09482/) (2017)
- [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)
- [Asymmetric Loss Functions for Learning with Noisy Labels](https://mlsanity.com/paper/2106.03110/) (2021)
- [A Tunable Loss Function for Robust Classification: Calibration, Landscape, and Generalization](https://mlsanity.com/paper/1906.02314/) (2019)
- [Robust Data Pruning under Label Noise via Maximizing Re-labeling Accuracy](https://mlsanity.com/paper/2311.01002/) (2023)
- [Generalized Maximum Entropy for Supervised Classification](https://mlsanity.com/paper/2007.05447/) (2020)
- [Minimax Classification with 0-1 Loss and Performance Guarantees](https://mlsanity.com/paper/2010.07964/) (2020)
- [Being Properly Improper](https://mlsanity.com/paper/2106.09920/) (2021)
- [Minimax risk classifiers with 0-1 loss](https://mlsanity.com/paper/2201.06487/) (2022)
- [MRCpy: A Library for Minimax Risk Classifiers](https://mlsanity.com/paper/2108.01952/) (2021)
- [On the alpha-loss Landscape in the Logistic Model](https://mlsanity.com/paper/2006.12406/) (2020)
- [Enhancing Noise-Robust Losses for Large-Scale Noisy Data Learning](https://mlsanity.com/paper/2306.05497/) (2023)
- [Consistent Robust Adversarial Prediction for General Multiclass Classification](https://mlsanity.com/paper/1812.07526/) (2018)

## Abstract (arXiv)

Loss functions play a central role in supervised classification. Cross-entropy (CE) is widely used, whereas the mean absolute error (MAE) loss can offer robustness but is difficult to optimize. Interpolating between the CE and MAE losses, generalized cross-entropy (GCE) has recently been introduced to provide a trade-off between optimization difficulty and robustness. Existing formulations of GCE result in a non-convex optimization over classification margins that is prone to underfitting, leading to poor performances with complex datasets. In this paper, we propose a minimax formulation of generalized cross-entropy (MGCE) that results in a convex optimization over classification margins. Moreover, we show that MGCEs can provide an upper bound on the classification error. The proposed bilevel convex optimization can be efficiently implemented using stochastic gradient computed via implicit differentiation. Using benchmark datasets, we show that MGCE achieves strong accuracy, faster convergence, and better calibration, especially in the presence of label noise.