# Hubs and Hyperspheres: Reducing Hubness and Improving Transductive Few-shot Learning with Hyperspherical Embeddings

arXiv: https://arxiv.org/abs/2303.09352 · HTML: https://mlsanity.com/paper/2303.09352/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 45 references that are in the map.
- First posted on arXiv 16 Mar 2023.

## Builds on (most cited first, 26 of 26)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Meta-Learning for Semi-Supervised Few-Shot Classification](https://mlsanity.com/paper/1803.00676/) (2018)
- [Few-Shot Learning via Embedding Adaptation with Set-to-Set Functions](https://mlsanity.com/paper/1812.03664/) (2018)
- [SimpleShot: Revisiting Nearest-Neighbor Classification for Few-Shot Learning](https://mlsanity.com/paper/1911.04623/) (2019)
- [Charting the Right Manifold: Manifold Mixup for Few-shot Learning](https://mlsanity.com/paper/1907.12087/) (2019)
- [Pushing the Limits of Simple Pipelines for Few-Shot Learning: External Data and Fine-Tuning Make a Difference](https://mlsanity.com/paper/2204.07305/) (2022)
- [Edge-labeling Graph Neural Network for Few-shot Learning](https://mlsanity.com/paper/1905.01436/) (2019)
- [Infinite Mixture Prototypes for Few-Shot Learning](https://mlsanity.com/paper/1902.04552/) (2019)
- [Laplacian Regularized Few-Shot Learning](https://mlsanity.com/paper/2006.15486/) (2020)
- [Transductive Information Maximization For Few-Shot Learning](https://mlsanity.com/paper/2008.11297/) (2020)
- [Ridge Regression, Hubness, and Zero-Shot Learning](https://mlsanity.com/paper/1507.00825/) (2015)
- [Iterative label cleaning for transductive and semi-supervised few-shot learning](https://mlsanity.com/paper/2012.07962/) (2020)
- [Realistic Evaluation of Transductive Few-Shot Learning](https://mlsanity.com/paper/2204.11181/) (2022)
- [Transductive Few-Shot Classification on the Oblique Manifold](https://mlsanity.com/paper/2108.04009/) (2021)
- [Alleviating the Sample Selection Bias in Few-shot Learning by Removing Projection to the Centroid](https://mlsanity.com/paper/2210.16834/) (2022)
- [POODLE: Improving Few-shot Learning via Penalizing Out-of-Distribution Samples](https://mlsanity.com/paper/2206.04679/) (2022)
- [The Role of Global Labels in Few-Shot Classification and How to Infer Them](https://mlsanity.com/paper/2108.04055/) (2021)
- [CAD: Co-Adapting Discriminative Features for Improved Few-Shot Classification](https://mlsanity.com/paper/2203.13465/) (2022)
- [Powering Finetuning in Few-Shot Learning: Domain-Agnostic Bias Reduction with Selected Sampling](https://mlsanity.com/paper/2204.03749/) (2022)
- [VMF-SNE: Embedding for Spherical Data](https://mlsanity.com/paper/1507.08379/) (2015)

## Built on by (most cited first, 11 of 11)

- [Transductive Zero-Shot and Few-Shot CLIP](https://mlsanity.com/paper/2405.18437/) (2024)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Contrastive Tuning: A Little Help to Make Masked Autoencoders Forget](https://mlsanity.com/paper/2304.10520/) (2023)
- [Improving Open-world Continual Learning under the Constraints of Scarce Labeled Data](https://mlsanity.com/paper/2502.20974/) (2025)
- [Keep your distance: learning dispersed embeddings on mathbbSm](https://mlsanity.com/paper/2502.08231/) (2025)
- [Polaris: Coupled Orbital Polar Embeddings for Hierarchical Concept Learning](https://mlsanity.com/paper/2605.00265/) (2026)
- [Robust Transductive Few-shot Learning via Joint Message Passing and Prototype-based Soft-label Propagation](https://mlsanity.com/paper/2311.17096/) (2023)
- [Unbiased Max-Min Embedding Classification for Transductive Few-Shot Learning: Clustering and Classification Are All You Need](https://mlsanity.com/paper/2503.22193/) (2025)
- [HCFSLN: Adaptive Hyperbolic Few-Shot Learning for Multimodal Anxiety Detection](https://mlsanity.com/paper/2511.06988/) (2025)
- [Query-aware Hub Prototype Learning for Few-Shot 3D Point Cloud Semantic Segmentation](https://mlsanity.com/paper/2512.08253/) (2025)
- [Torus embeddings](https://mlsanity.com/paper/2603.03135/) (2026)

## Abstract (arXiv)

Distance-based classification is frequently used in transductive few-shot learning (FSL). However, due to the high-dimensionality of image representations, FSL classifiers are prone to suffer from the hubness problem, where a few points (hubs) occur frequently in multiple nearest neighbour lists of other points. Hubness negatively impacts distance-based classification when hubs from one class appear often among the nearest neighbors of points from another class, degrading the classifier's performance. To address the hubness problem in FSL, we first prove that hubness can be eliminated by distributing representations uniformly on the hypersphere. We then propose two new approaches to embed representations on the hypersphere, which we prove optimize a tradeoff between uniformity and local similarity preservation -- reducing hubness while retaining class structure. Our experiments show that the proposed methods reduce hubness, and significantly improves transductive FSL accuracy for a wide range of classifiers.