# Radial-Angular Geometry for Reliable Update Diagnosis in Noisy-Label Learning

arXiv: https://arxiv.org/abs/2605.17429 · HTML: https://mlsanity.com/paper/2605.17429/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 17 May 2026.

## Builds on (most cited first, 24 of 24)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Co-teaching: Robust Training of Deep Neural Networks with Extremely Noisy Labels](https://mlsanity.com/paper/1804.06872/) (2018)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach](https://mlsanity.com/paper/1609.03683/) (2016)
- [MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels](https://mlsanity.com/paper/1712.05055/) (2017)
- [Early-Learning Regularization Prevents Memorization of Noisy Labels](https://mlsanity.com/paper/2007.00151/) (2020)
- [How does Disagreement Help Generalization against Label Corruption?](https://mlsanity.com/paper/1901.04215/) (2019)
- [Unsupervised Label Noise Modeling and Loss Correction](https://mlsanity.com/paper/1904.11238/) (2019)
- [Training Deep Neural Networks on Noisy Labels with Bootstrapping](https://mlsanity.com/paper/1412.6596/) (2014)
- [An Investigation into Neural Net Optimization via Hessian Eigenvalue Density](https://mlsanity.com/paper/1901.10159/) (2019)
- [Limitations of the Empirical Fisher Approximation for Natural Gradient Descent](https://mlsanity.com/paper/1905.12558/) (2019)
- [Learning with Feature-Dependent Label Noise: A Progressive Approach](https://mlsanity.com/paper/2103.07756/) (2021)
- [UNICON: Combating Label Noise Through Uniform Selection and Contrastive Learning](https://mlsanity.com/paper/2203.14542/) (2022)
- [Catastrophic Fisher Explosion: Early Phase Fisher Matrix Impacts Generalization](https://mlsanity.com/paper/2012.14193/) (2020)
- [ProMix: Combating Label Noise via Maximizing Clean Sample Utility](https://mlsanity.com/paper/2207.10276/) (2022)
- [LongReMix: Robust Learning with High Confidence Samples in a Noisy Label Environment](https://mlsanity.com/paper/2103.04173/) (2021)
- [L2B: Learning to Bootstrap Robust Models for Combating Label Noise](https://mlsanity.com/paper/2202.04291/) (2022)
- [Handling Label Noise via Instance-Level Difficulty Modeling and Dynamic Optimization](https://mlsanity.com/paper/2505.00812/) (2025)
- [Enhancing Sample Selection Against Label Noise by Cutting Mislabeled Easy Examples](https://mlsanity.com/paper/2502.08227/) (2025)

## Abstract (arXiv)

Noisy-label methods often estimate sample reliability from forward-space signals such as loss, confidence, or entropy. These signals indicate whether a sample is difficult to predict, but they do not directly test whether its observed label induces a reliable parameter update. This gap matters because hard clean samples and mislabeled samples can have similar loss while inducing different updates. We recast reliability estimation as diagnosis of the observed-label update. The sample-wise empirical Fisher trace gives a backward-space measure of update energy: for the classifier layer, it factorizes into a prediction-residual term and a feature-sensitivity term, so it captures information beyond scalar loss. Trace, however, is still a radial magnitude signal and cannot decide whether a large update is useful or harmful. We therefore propose Relative Geometric Conflict (RGC), which compares the observed-label gradient with a reference gradient induced by an EMA teacher. The conflict term helps distinguish large but aligned hard-clean updates from large conflicting updates caused by corrupted labels. Across synthetic and real-world noisy-label benchmarks, RGC improves hard-clean preservation and accuracy under our evaluation protocol.