# On Classification-Calibration of Gamma-Phi Losses

arXiv: https://arxiv.org/abs/2302.07321 · HTML: https://mlsanity.com/paper/2302.07321/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 29 references that are in the map.
- First posted on arXiv 14 Feb 2023.

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

- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Robust Bi-Tempered Logistic Loss Based on Bregman Divergences](https://mlsanity.com/paper/1906.03361/) (2019)
- [Calibration and Consistency of Adversarial Surrogate Losses](https://mlsanity.com/paper/2104.09658/) (2021)
- [Convex Calibration Dimension for Multiclass Loss Matrices](https://mlsanity.com/paper/1408.2764/) (2014)
- [An Embedding Framework for Consistent Polyhedral Surrogates](https://mlsanity.com/paper/1907.07330/) (2019)
- [Multiclass Classification Calibration Functions](https://mlsanity.com/paper/1609.06385/) (2016)
- [Weston-Watkins Hinge Loss and Ordered Partitions](https://mlsanity.com/paper/2006.07346/) (2020)
- [Online Multiclass Boosting](https://mlsanity.com/paper/1702.07305/) (2017)
- [Astral Space: Convex Analysis at Infinity](https://mlsanity.com/paper/2205.03260/) (2022)
- [Online Agnostic Multiclass Boosting](https://mlsanity.com/paper/2205.15113/) (2022)

## Built on by (most cited first, 6 of 6)

- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [H-Consistency Guarantees for Regression](https://mlsanity.com/paper/2403.19480/) (2024)
- [Enhanced H-Consistency Bounds](https://mlsanity.com/paper/2407.13722/) (2024)
- [Adversarial Robustness in Two-Stage Learning-to-Defer: Algorithms and Guarantees](https://mlsanity.com/paper/2502.01027/) (2025)
- [Establishing Linear Surrogate Regret Bounds for Convex Smooth Losses via Convolutional Fenchel-Young Losses](https://mlsanity.com/paper/2505.09432/) (2025)
- [EnsLoss: Stochastic Calibrated Loss Ensembles for Preventing Overfitting in Classification](https://mlsanity.com/paper/2409.00908/) (2024)

## Abstract (arXiv)

Gamma-Phi losses constitute a family of multiclass classification loss functions that generalize the logistic and other common losses, and have found application in the boosting literature. We establish the first general sufficient condition for the classification-calibration (CC) of such losses. To our knowledge, this sufficient condition gives the first family of nonconvex multiclass surrogate losses for which CC has been fully justified. In addition, we show that a previously proposed sufficient condition is in fact not sufficient. This contribution highlights a technical issue that is important in the study of multiclass CC but has been neglected in prior work.