# On the Consistency of Max-Margin Losses

arXiv: https://arxiv.org/abs/2105.15069 · HTML: https://mlsanity.com/paper/2105.15069/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 33 references that are in the map.
- First posted on arXiv 31 May 2021.

## Builds on (most cited first, 3 of 3)

- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [An Embedding Framework for Consistent Polyhedral Surrogates](https://mlsanity.com/paper/1907.07330/) (2019)
- [Consistent Structured Prediction with Max-Min Margin Markov Networks](https://mlsanity.com/paper/2007.01012/) (2020)

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

- [A Universal Growth Rate for Learning with Smooth Surrogate Losses](https://mlsanity.com/paper/2405.05968/) (2024)
- [An Embedding Framework for the Design and Analysis of Consistent Polyhedral Surrogates](https://mlsanity.com/paper/2206.14707/) (2022)
- [Online Structured Prediction with Fenchel--Young Losses and Improved Surrogate Regret for Online Multiclass Classification with Logistic Loss](https://mlsanity.com/paper/2402.08180/) (2024)
- [On the inconsistency of separable losses for structured prediction](https://mlsanity.com/paper/2301.10810/) (2023)
- [Common Geodesics Do Not Guarantee Fisher Consistency of the Structured SVM: Minimal Counterexamples and a Tree-Metric Classification](https://mlsanity.com/paper/2608.27203/) (2026)

## Abstract (arXiv)

The foundational concept of Max-Margin in machine learning is ill-posed for output spaces with more than two labels such as in structured prediction. In this paper, we show that the Max-Margin loss can only be consistent to the classification task under highly restrictive assumptions on the discrete loss measuring the error between outputs. These conditions are satisfied by distances defined in tree graphs, for which we prove consistency, thus being the first losses shown to be consistent for Max-Margin beyond the binary setting. We finally address these limitations by correcting the concept of Max-Margin and introducing the Restricted-Max-Margin, where the maximization of the loss-augmented scores is maintained, but performed over a subset of the original domain. The resulting loss is also a generalization of the binary support vector machine and it is consistent under milder conditions on the discrete loss.