# AMC-Loss: Angular Margin Contrastive Loss for Improved Explainability in Image Classification

arXiv: https://arxiv.org/abs/2004.09805 · HTML: https://mlsanity.com/paper/2004.09805/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2020.

## Built on by (most cited first, 14 of 14)

- [FedTGP: Trainable Global Prototypes with Adaptive-Margin-Enhanced Contrastive Learning for Data and Model Heterogeneity in Federated Learning](https://mlsanity.com/paper/2401.03230/) (2024)
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- [Leveraging Angular Distributions for Improved Knowledge Distillation](https://mlsanity.com/paper/2302.14130/) (2023)
- [Learnable Adaptive Cosine Estimator (LACE) for Image Classification](https://mlsanity.com/paper/2110.05324/) (2021)
- [Mutual Contrastive Low-rank Learning to Disentangle Whole Slide Image Representations for Glioma Grading](https://mlsanity.com/paper/2203.04013/) (2022)
- [Graph Your Own Prompt](https://mlsanity.com/paper/2509.23373/) (2025)
- [Regression Metric Loss: Learning a Semantic Representation Space for Medical Images](https://mlsanity.com/paper/2207.05231/) (2022)
- [Learning Time-Series Representations by Hierarchical Uniformity-Tolerance Latent Balancing](https://mlsanity.com/paper/2510.01658/) (2025)
- [Label Geometry Aware Discriminator for Conditional Generative Networks](https://mlsanity.com/paper/2105.05501/) (2021)
- [Adaptive Sparse Softmax: An Effective and Efficient Softmax Variant](https://mlsanity.com/paper/2508.03175/) (2025)
- [Are Emotions Arranged in a Circle? Geometric Analysis of Emotion Representations via Hyperspherical Contrastive Learning](https://mlsanity.com/paper/2601.06575/) (2026)
- [Rethinking the Harmonic Loss via Non-Euclidean Distance Layers](https://mlsanity.com/paper/2603.10225/) (2026)

## Abstract (arXiv)

Deep-learning architectures for classification problems involve the cross-entropy loss sometimes assisted with auxiliary loss functions like center loss, contrastive loss and triplet loss. These auxiliary loss functions facilitate better discrimination between the different classes of interest. However, recent studies hint at the fact that these loss functions do not take into account the intrinsic angular distribution exhibited by the low-level and high-level feature representations. This results in less compactness between samples from the same class and unclear boundary separations between data clusters of different classes. In this paper, we address this issue by proposing the use of geometric constraints, rooted in Riemannian geometry. Specifically, we propose Angular Margin Contrastive Loss (AMC-Loss), a new loss function to be used along with the traditional cross-entropy loss. The AMC-Loss employs the discriminative angular distance metric that is equivalent to geodesic distance on a hypersphere manifold such that it can serve a clear geometric interpretation. We demonstrate the effectiveness of AMC-Loss by providing quantitative and qualitative results. We find that although the proposed geometrically constrained loss-function improves quantitative results modestly, it has a qualitatively surprisingly beneficial effect on increasing the interpretability of deep-net decisions as seen by the visual explanations generated by techniques such as the Grad-CAM. Our code is available at https://github.com/hchoi71/AMC-Loss.