# Prototype Fission: Closing Set for Robust Open-set Semi-supervised Learning

arXiv: https://arxiv.org/abs/2308.15575 · HTML: https://mlsanity.com/paper/2308.15575/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 25 references that are in the map.
- First posted on arXiv 29 Aug 2023.

## Builds on (most cited first, 20 of 20)

- [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)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [End-to-End Semi-Supervised Object Detection with Soft Teacher](https://mlsanity.com/paper/2106.09018/) (2021)
- [Learning to Discover Novel Visual Categories via Deep Transfer Clustering](https://mlsanity.com/paper/1908.09884/) (2019)
- [Open-World Semi-Supervised Learning](https://mlsanity.com/paper/2102.03526/) (2021)
- [Adversarial Reciprocal Points Learning for Open Set Recognition](https://mlsanity.com/paper/2103.00953/) (2021)
- [Automatically Discovering and Learning New Visual Categories with Ranking Statistics](https://mlsanity.com/paper/2002.05714/) (2020)
- [Robust Classification with Convolutional Prototype Learning](https://mlsanity.com/paper/1805.03438/) (2018)
- [Learning Open Set Network with Discriminative Reciprocal Points](https://mlsanity.com/paper/2011.00178/) (2020)
- [Conditional Gaussian Distribution Learning for Open Set Recognition](https://mlsanity.com/paper/2003.08823/) (2020)
- [OpenMatch: Open-set Consistency Regularization for Semi-supervised Learning with Outliers](https://mlsanity.com/paper/2105.14148/) (2021)
- [Trash to Treasure: Harvesting OOD Data with Cross-Modal Matching for Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2108.05617/) (2021)
- [OpenLDN: Learning to Discover Novel Classes for Open-World Semi-Supervised Learning](https://mlsanity.com/paper/2207.02261/) (2022)
- [P-ODN: Prototype based Open Deep Network for Open Set Recognition](https://mlsanity.com/paper/1905.01851/) (2019)
- [PMAL: Open Set Recognition via Robust Prototype Mining](https://mlsanity.com/paper/2203.08569/) (2022)
- [OpenCoS: Contrastive Semi-supervised Learning for Handling Open-set Unlabeled Data](https://mlsanity.com/paper/2107.08943/) (2021)

## Built on by (most cited first, 1 of 1)

- [Evolving from Unknown to Known: Retentive Angular Representation Learning for Incremental Open Set Recognition](https://mlsanity.com/paper/2509.06570/) (2025)

## Abstract (arXiv)

Semi-supervised Learning (SSL) has been proven vulnerable to out-of-distribution (OOD) samples in realistic large-scale unsupervised datasets due to over-confident pseudo-labeling OODs as in-distribution (ID). A key underlying problem is class-wise latent space spreading from closed seen space to open unseen space, and the bias is further magnified in SSL's self-training loops. To close the ID distribution set so that OODs are better rejected for safe SSL, we propose Prototype Fission(PF) to divide class-wise latent spaces into compact sub-spaces by automatic fine-grained latent space mining, driven by coarse-grained labels only. Specifically, we form multiple unique learnable sub-class prototypes for each class, optimized towards both diversity and consistency. The Diversity Modeling term encourages samples to be clustered by one of the multiple sub-class prototypes, while the Consistency Modeling term clusters all samples of the same class to a global prototype. Instead of "opening set", i.e., modeling OOD distribution, Prototype Fission "closes set" and makes it hard for OOD samples to fit in sub-class latent space. Therefore, PF is compatible with existing methods for further performance gains. Extensive experiments validate the effectiveness of our method in open-set SSL settings in terms of successfully forming sub-classes, discriminating OODs from IDs and improving overall accuracy. Codes will be released.