# HyperSpaceX: Radial and Angular Exploration of HyperSpherical Dimensions

arXiv: https://arxiv.org/abs/2408.02494 · HTML: https://mlsanity.com/paper/2408.02494/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 38 references that are in the map.
- First posted on arXiv 5 Aug 2024.

## Builds on (most cited first, 19 of 19)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [CosFace: Large Margin Cosine Loss for Deep Face Recognition](https://mlsanity.com/paper/1801.09414/) (2018)
- [SphereFace: Deep Hypersphere Embedding for Face Recognition](https://mlsanity.com/paper/1704.08063/) (2017)
- [Learning Face Representation from Scratch](https://mlsanity.com/paper/1411.7923/) (2014)
- [Deep Metric Learning via Lifted Structured Feature Embedding](https://mlsanity.com/paper/1511.06452/) (2015)
- [Sampling Matters in Deep Embedding Learning](https://mlsanity.com/paper/1706.07567/) (2017)
- [Cross-Age LFW: A Database for Studying Cross-Age Face Recognition in Unconstrained Environments](https://mlsanity.com/paper/1708.08197/) (2017)
- [OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks](https://mlsanity.com/paper/1312.6229/) (2013)
- [Deep Learning Face Representation by Joint Identification-Verification](https://mlsanity.com/paper/1406.4773/) (2014)
- [Improved Residual Networks for Image and Video Recognition](https://mlsanity.com/paper/2004.04989/) (2020)
- [Orthogonal Projection Loss](https://mlsanity.com/paper/2103.14021/) (2021)
- [SphereFace2: Binary Classification is All You Need for Deep Face Recognition](https://mlsanity.com/paper/2108.01513/) (2021)
- [Git Loss for Deep Face Recognition](https://mlsanity.com/paper/1807.08512/) (2018)

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

- [Harmonizing Geometry and Uncertainty: Diffusion with Hyperspheres](https://mlsanity.com/paper/2506.10576/) (2025)
- [Impact of Regularization on Calibration and Robustness: from the Representation Space Perspective](https://mlsanity.com/paper/2410.03999/) (2024)

## Abstract (arXiv)

Traditional deep learning models rely on methods such as softmax cross-entropy and ArcFace loss for tasks like classification and face recognition. These methods mainly explore angular features in a hyperspherical space, often resulting in entangled inter-class features due to dense angular data across many classes. In this paper, a new field of feature exploration is proposed known as HyperSpaceX which enhances class discrimination by exploring both angular and radial dimensions in multi-hyperspherical spaces, facilitated by a novel DistArc loss. The proposed DistArc loss encompasses three feature arrangement components: two angular and one radial, enforcing intra-class binding and inter-class separation in multi-radial arrangement, improving feature discriminability. Evaluation of HyperSpaceX framework for the novel representation utilizes a proposed predictive measure that accounts for both angular and radial elements, providing a more comprehensive assessment of model accuracy beyond standard metrics. Experiments across seven object classification and six face recognition datasets demonstrate state-of-the-art (SoTA) results obtained from HyperSpaceX, achieving up to a 20% performance improvement on large-scale object datasets in lower dimensions and up to 6% gain in higher dimensions.