# Variation-Bounded Loss for Noise-Tolerant Learning

arXiv: https://arxiv.org/abs/2511.12143 · HTML: https://mlsanity.com/paper/2511.12143/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2025.

## Built on by (most cited first, 2 of 2)

- [Can we Trust Unreliable Voxels? Exploring 3D Semantic Occupancy Prediction under Label Noise](https://mlsanity.com/paper/2603.06279/) (2026)
- [Robust Losses from Univariate Base Functions for Noisy-Label Learning](https://mlsanity.com/paper/2607.16768/) (2026)

## Abstract (arXiv)

Mitigating the negative impact of noisy labels has been aperennial issue in supervised learning. Robust loss functions have emerged as a prevalent solution to this problem. In this work, we introduce the Variation Ratio as a novel property related to the robustness of loss functions, and propose a new family of robust loss functions, termed Variation-Bounded Loss (VBL), which is characterized by a bounded variation ratio. We provide theoretical analyses of the variation ratio, proving that a smaller variation ratio would lead to better robustness. Furthermore, we reveal that the variation ratio provides a feasible method to relax the symmetric condition and offers a more concise path to achieve the asymmetric condition. Based on the variation ratio, we reformulate several commonly used loss functions into a variation-bounded form for practical applications. Positive experiments on various datasets exhibit the effectiveness and flexibility of our approach.