# Hyperspherical Consistency Regularization

arXiv: https://arxiv.org/abs/2206.00845 · HTML: https://mlsanity.com/paper/2206.00845/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 95 references that are in the map.
- First posted on arXiv 2 Jun 2022.

## Builds on (most cited first, 30 of 69)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Mask R-CNN](https://mlsanity.com/paper/1703.06870/) (2017)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Unsupervised Feature Learning via Non-Parametric Instance-level Discrimination](https://mlsanity.com/paper/1805.01978/) (2018)
- [Barlow Twins: Self-Supervised Learning via Redundancy Reduction](https://mlsanity.com/paper/2103.03230/) (2021)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [Context Encoders: Feature Learning by Inpainting](https://mlsanity.com/paper/1604.07379/) (2016)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Big Self-Supervised Models are Strong Semi-Supervised Learners](https://mlsanity.com/paper/2006.10029/) (2020)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)

## Built on by (most cited first, 16 of 16)

- [Temporal Attention Unit: Towards Efficient Spatiotemporal Predictive Learning](https://mlsanity.com/paper/2206.12126/) (2022)
- [PiFold: Toward effective and efficient protein inverse folding](https://mlsanity.com/paper/2209.12643/) (2022)
- [DealMVC: Dual Contrastive Calibration for Multi-view Clustering](https://mlsanity.com/paper/2308.09000/) (2023)
- [Latent SDEs on Homogeneous Spaces](https://mlsanity.com/paper/2306.16248/) (2023)
- [SemiReward: A General Reward Model for Semi-supervised Learning](https://mlsanity.com/paper/2310.03013/) (2023)
- [Enhancing Human-like Multi-Modal Reasoning: A New Challenging Dataset and Comprehensive Framework](https://mlsanity.com/paper/2307.12626/) (2023)
- [Cross-Gate MLP with Protein Complex Invariant Embedding is A One-Shot Antibody Designer](https://mlsanity.com/paper/2305.09480/) (2023)
- [PrefixMol: Target- and Chemistry-aware Molecule Design via Prefix Embedding](https://mlsanity.com/paper/2302.07120/) (2023)
- [PAID: Pairwise Angular-Invariant Decomposition for Continual Test-Time Adaptation](https://mlsanity.com/paper/2506.02453/) (2025)
- [Online Continual Learning via the Knowledge Invariant and Spread-out Properties](https://mlsanity.com/paper/2302.00858/) (2023)
- [Exploiting Label-Independent Regularization from Spatial Dependencies for Whole Slide Image Analysis](https://mlsanity.com/paper/2602.19487/) (2026)
- [PaperFit: Vision-in-the-Loop Typesetting Optimization for Scientific Documents](https://mlsanity.com/paper/2605.10341/) (2026)
- [Ontology-aware Network for Zero-shot Sketch-based Image Retrieval](https://mlsanity.com/paper/2302.10040/) (2023)
- [Beyond Self-Consistency: Loss-Balanced Perturbation-Based Regularization Improves Industrial-Scale Ads Ranking](https://mlsanity.com/paper/2502.18478/) (2025)
- [Dual Teacher-Student Learning for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/2505.11018/) (2025)
- [Heterogeneous Federated Learning with Prototype Alignment and Upscaling](https://mlsanity.com/paper/2507.04310/) (2025)

## Abstract (arXiv)

Recent advances in contrastive learning have enlightened diverse applications across various semi-supervised fields. Jointly training supervised learning and unsupervised learning with a shared feature encoder becomes a common scheme. Though it benefits from taking advantage of both feature-dependent information from self-supervised learning and label-dependent information from supervised learning, this scheme remains suffering from bias of the classifier. In this work, we systematically explore the relationship between self-supervised learning and supervised learning, and study how self-supervised learning helps robust data-efficient deep learning. We propose hyperspherical consistency regularization (HCR), a simple yet effective plug-and-play method, to regularize the classifier using feature-dependent information and thus avoid bias from labels. Specifically, HCR first projects logits from the classifier and feature projections from the projection head on the respective hypersphere, then it enforces data points on hyperspheres to have similar structures by minimizing binary cross entropy of pairwise distances' similarity metrics. Extensive experiments on semi-supervised and weakly-supervised learning demonstrate the effectiveness of our method, by showing superior performance with HCR.