# DINO as a von Mises-Fisher mixture model

arXiv: https://arxiv.org/abs/2405.10939 · HTML: https://mlsanity.com/paper/2405.10939/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 49 of its 69 references that are in the map.
- First posted on arXiv 17 May 2024.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 49)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Exploring Simple Siamese Representation Learning](https://mlsanity.com/paper/2011.10566/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [BEiT: BERT Pre-Training of Image Transformers](https://mlsanity.com/paper/2106.08254/) (2021)
- [Improved Baselines with Momentum Contrastive Learning](https://mlsanity.com/paper/2003.04297/) (2020)
- [Describing Textures in the Wild](https://mlsanity.com/paper/1311.3618/) (2013)
- [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)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [An Empirical Study of Training Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.02057/) (2021)
- [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)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Colorful Image Colorization](https://mlsanity.com/paper/1603.08511/) (2016)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Deep Clustering for Unsupervised Learning of Visual Features](https://mlsanity.com/paper/1807.05520/) (2018)
- [The 2017 DAVIS Challenge on Video Object Segmentation](https://mlsanity.com/paper/1704.00675/) (2017)
- [Self-Supervised Learning of Pretext-Invariant Representations](https://mlsanity.com/paper/1912.01991/) (2019)
- [Prototypical Contrastive Learning of Unsupervised Representations](https://mlsanity.com/paper/2005.04966/) (2020)

## Built on by (most cited first, 15 of 15)

- [Collapse-Proof Non-Contrastive Self-Supervised Learning](https://mlsanity.com/paper/2410.04959/) (2024)
- [On Partial Prototype Collapse in the DINO Family of Self-Supervised Methods](https://mlsanity.com/paper/2410.14060/) (2024)
- [Your Classifier Can Be Secretly a Likelihood-Based OOD Detector](https://mlsanity.com/paper/2408.04851/) (2024)
- [Self-Supervised Syllable Discovery Based on Speaker-Disentangled HuBERT](https://mlsanity.com/paper/2409.10103/) (2024)
- [S3PT: Scene Semantics and Structure Guided Clustering to Boost Self-Supervised Pre-Training for Autonomous Driving](https://mlsanity.com/paper/2410.23085/) (2024)
- [CleverDistiller: Simple and Spatially Consistent Cross-modal Distillation](https://mlsanity.com/paper/2503.09878/) (2025)
- [Distribution Guidance Network for Weakly Supervised Point Cloud Semantic Segmentation](https://mlsanity.com/paper/2410.08091/) (2024)
- [QUEST: A robust attention formulation using query-modulated spherical attention](https://mlsanity.com/paper/2604.00199/) (2026)
- [Probabilistic Contrastive Learning with Explicit Concentration on the Hypersphere](https://mlsanity.com/paper/2405.16460/) (2024)
- [Divergence-Based Similarity Function for Multi-View Contrastive Learning](https://mlsanity.com/paper/2507.06560/) (2025)
- [Understanding Ice Crystal Habit Diversity with Self-Supervised Learning](https://mlsanity.com/paper/2509.07688/) (2025)
- [Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation](https://mlsanity.com/paper/2509.19903/) (2025)
- [Why Prototypes Collapse: Diagnosing and Preventing Partial Collapse in Prototypical Self-Supervised Learning](https://mlsanity.com/paper/2510.20108/) (2025)
- [An Information Theoretic Framework for Graph Novelty Generation via Latent Mixture Modeling](https://mlsanity.com/paper/2606.19770/) (2026)
- [Von Mises-Fisher Mixture Model with Dynamic Shrinkage for Realistic Test-Time Transduction](https://mlsanity.com/paper/2607.15851/) (2026)

## Abstract (arXiv)

Self-distillation methods using Siamese networks are popular for self-supervised pre-training. DINO is one such method based on a cross-entropy loss between K-dimensional probability vectors, obtained by applying a softmax function to the dot product between representations and learnt prototypes. Given the fact that the learned representations are L2-normalized, we show that DINO and its derivatives, such as iBOT, can be interpreted as a mixture model of von Mises-Fisher components. With this interpretation, DINO assumes equal precision for all components when the prototypes are also L2-normalized. Using this insight we propose DINO-vMF, that adds appropriate normalization constants when computing the cluster assignment probabilities. Unlike DINO, DINO-vMF is stable also for the larger ViT-Base model with unnormalized prototypes. We show that the added flexibility of the mixture model is beneficial in terms of better image representations. The DINO-vMF pre-trained model consistently performs better than DINO on a range of downstream tasks. We obtain similar improvements for iBOT-vMF vs iBOT and thereby show the relevance of our proposed modification also for other methods derived from DINO.