# Beyond Tsybakov: Model Margin Noise and H-Consistency Bounds

arXiv: https://arxiv.org/abs/2511.15816 · HTML: https://mlsanity.com/paper/2511.15816/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 41 references that are in the map.
- First posted on arXiv 19 Nov 2025.

## Builds on (most cited first, 12 of 12)

- [Principled Approaches for Learning to Defer with Multiple Experts](https://mlsanity.com/paper/2310.14774/) (2023)
- [Predictor-Rejector Multi-Class Abstention: Theoretical Analysis and Algorithms](https://mlsanity.com/paper/2310.14772/) (2023)
- [Theoretically Grounded Loss Functions and Algorithms for Score-Based Multi-Class Abstention](https://mlsanity.com/paper/2310.14770/) (2023)
- [Realizable H-Consistent and Bayes-Consistent Loss Functions for Learning to Defer](https://mlsanity.com/paper/2407.13732/) (2024)
- [A Universal Growth Rate for Learning with Smooth Surrogate Losses](https://mlsanity.com/paper/2405.05968/) (2024)
- [Cardinality-Aware Set Prediction and Top-k Classification](https://mlsanity.com/paper/2407.07140/) (2024)
- [Multi-Label Learning with Stronger Consistency Guarantees](https://mlsanity.com/paper/2407.13746/) (2024)
- [An Embedding Framework for Consistent Polyhedral Surrogates](https://mlsanity.com/paper/1907.07330/) (2019)
- [Mastering Multiple-Expert Routing: Realizable H-Consistency and Strong Guarantees for Learning to Defer](https://mlsanity.com/paper/2506.20650/) (2025)
- [Surrogate Regret Bounds for Polyhedral Losses](https://mlsanity.com/paper/2110.14031/) (2021)
- [Balancing the Scales: A Theoretical and Algorithmic Framework for Learning from Imbalanced Data](https://mlsanity.com/paper/2502.10381/) (2025)
- [Binary Excess Risk for Smooth Convex Surrogates](https://mlsanity.com/paper/1402.1792/) (2014)

## Built on by (most cited first, 7 of 7)

- [Improved Balanced Classification with Theoretically Grounded Loss Functions](https://mlsanity.com/paper/2512.23947/) (2025)
- [Principled Algorithms for Optimizing Generalized Metrics in Binary Classification](https://mlsanity.com/paper/2512.23133/) (2025)
- [A Theoretical Framework for Modular Learning of Robust Generative Models](https://mlsanity.com/paper/2602.17554/) (2026)
- [Optimized Deferral for Imbalanced Settings](https://mlsanity.com/paper/2604.27723/) (2026)
- [Linear-Core Surrogates: Smooth Loss Functions with Linear Rates for Classification and Structured Prediction](https://mlsanity.com/paper/2604.27742/) (2026)
- [Online Learning-to-Defer with Varying Experts](https://mlsanity.com/paper/2605.12340/) (2026)
- [Principled Algorithms for Optimizing Generalized Metrics in Multi-Label Learning](https://mlsanity.com/paper/2605.28767/) (2026)

## Abstract (arXiv)

We introduce a new low-noise condition for classification, the Model Margin Noise (MM noise) assumption, and derive enhanced H-consistency bounds under this condition. MM noise is weaker than Tsybakov noise condition: it is implied by Tsybakov noise condition but can hold even when Tsybakov fails, because it depends on the discrepancy between a given hypothesis and the Bayes-classifier rather than on the intrinsic distributional minimal margin (see Figure 1 for an illustration of an explicit example). This hypothesis-dependent assumption yields enhanced H-consistency bounds for both binary and multi-class classification. Our results extend the enhanced H-consistency bounds of Mao, Mohri, and Zhong (2025a) with the same favorable exponents but under a weaker assumption than the Tsybakov noise condition; they interpolate smoothly between linear and square-root regimes for intermediate noise levels. We also instantiate these bounds for common surrogate loss families and provide illustrative tables.