# Angular Visual Hardness

arXiv: https://arxiv.org/abs/1912.02279 · HTML: https://mlsanity.com/paper/1912.02279/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Dec 2019.

## Built on by (most cited first, 29 of 29)

- [Controlling Text-to-Image Diffusion by Orthogonal Finetuning](https://mlsanity.com/paper/2306.07280/) (2023)
- [Towards Principled Disentanglement for Domain Generalization](https://mlsanity.com/paper/2111.13839/) (2021)
- [von Mises-Fisher Loss: An Exploration of Embedding Geometries for Supervised Learning](https://mlsanity.com/paper/2103.15718/) (2021)
- [Learning with Hyperspherical Uniformity](https://mlsanity.com/paper/2103.01649/) (2021)
- [Taxonomy of Machine Learning Safety: A Survey and Primer](https://mlsanity.com/paper/2106.04823/) (2021)
- [SphereFace Revived: Unifying Hyperspherical Face Recognition](https://mlsanity.com/paper/2109.05565/) (2021)
- [A Geometric Perspective towards Neural Calibration via Sensitivity Decomposition](https://mlsanity.com/paper/2110.14577/) (2021)
- [Hyperspherical Consistency Regularization](https://mlsanity.com/paper/2206.00845/) (2022)
- [Continual Learning by Modeling Intra-Class Variation](https://mlsanity.com/paper/2210.05398/) (2022)
- [Iterative Teaching by Label Synthesis](https://mlsanity.com/paper/2110.14432/) (2021)
- [Recurrent Aligned Network for Generalized Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2403.05810/) (2024)
- [Discriminator-Free Generative Adversarial Attack](https://mlsanity.com/paper/2107.09225/) (2021)
- [Iterative Teaching by Data Hallucination](https://mlsanity.com/paper/2210.17467/) (2022)
- [Angular Gap: Reducing the Uncertainty of Image Difficulty through Model Calibration](https://mlsanity.com/paper/2207.08525/) (2022)
- [BoundaryFace: A mining framework with noise label self-correction for Face Recognition](https://mlsanity.com/paper/2210.04567/) (2022)
- [Data-Efficient Learning via Minimizing Hyperspherical Energy](https://mlsanity.com/paper/2206.15204/) (2022)
- [Hyperspherical Quantization: Toward Smaller and More Accurate Models](https://mlsanity.com/paper/2212.12653/) (2022)
- [IMEX-Reg: Implicit-Explicit Regularization in the Function Space for Continual Learning](https://mlsanity.com/paper/2404.18161/) (2024)
- [On The Distribution of Penultimate Activations of Classification Networks](https://mlsanity.com/paper/2107.01900/) (2021)
- [Orthogonal Concept Erasure for Diffusion Models](https://mlsanity.com/paper/2605.28902/) (2026)
- ["Understanding Robustness Lottery": A Geometric Visual Comparative Analysis of Neural Network Pruning Approaches](https://mlsanity.com/paper/2206.07918/) (2022)
- [Tilt and Average : Geometric Adjustment of the Last Layer for Recalibration](https://mlsanity.com/paper/2406.10017/) (2024)
- [Orthogonal Projection Subspace to Aggregate Online Prior-knowledge for Continual Test-time Adaptation](https://mlsanity.com/paper/2506.19022/) (2025)
- [Leveraging Angular Information Between Feature and Classifier for Long-tailed Learning: A Prediction Reformulation Approach](https://mlsanity.com/paper/2212.01565/) (2022)
- [Hyperspherical Loss-Aware Ternary Quantization](https://mlsanity.com/paper/2212.12649/) (2022)
- [Enhancing Robustness of Vision-Language Models through Orthogonality Learning and Self-Regularization](https://mlsanity.com/paper/2407.08374/) (2024)
- [Heterogeneous Federated Learning with Prototype Alignment and Upscaling](https://mlsanity.com/paper/2507.04310/) (2025)
- [Towards Imperceptible JPEG Image Hiding: Multi-range Representations-driven Adversarial Stego Generation](https://mlsanity.com/paper/2507.08343/) (2025)
- [LoCO: Low-rank Compositional Rotation Fine-tuning](https://mlsanity.com/paper/2605.15916/) (2026)

## Abstract (arXiv)

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.