# SmoothOperator: Enhancing Representations for Fine-grained Open-set Recognition via Modulated Label Smoothing

arXiv: https://arxiv.org/abs/2610.00851 · HTML: https://mlsanity.com/paper/2610.00851/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 23 of 23)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Supervised Contrastive Learning](https://mlsanity.com/paper/2004.11362/) (2020)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Out-of-Distribution Detection with Deep Nearest Neighbors](https://mlsanity.com/paper/2204.06507/) (2022)
- [Towards Open Set Deep Networks](https://mlsanity.com/paper/1511.06233/) (2015)
- [Open-Set Recognition: a Good Closed-Set Classifier is All You Need?](https://mlsanity.com/paper/2110.06207/) (2021)
- [Recent Advances in Open Set Recognition: A Survey](https://mlsanity.com/paper/1811.08581/) (2018)
- [Reducing Network Agnostophobia](https://mlsanity.com/paper/1811.04110/) (2018)
- [Adversarial Reciprocal Points Learning for Open Set Recognition](https://mlsanity.com/paper/2103.00953/) (2021)
- [C2AE: Class Conditioned Auto-Encoder for Open-set Recognition](https://mlsanity.com/paper/1904.01198/) (2019)
- [OpenGAN: Open-Set Recognition via Open Data Generation](https://mlsanity.com/paper/2104.02939/) (2021)
- [Targeted Supervised Contrastive Learning for Long-Tailed Recognition](https://mlsanity.com/paper/2111.13998/) (2021)
- [Learning Placeholders for Open-Set Recognition](https://mlsanity.com/paper/2103.15086/) (2021)
- [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)
- [Nearest Neighbor Guidance for Out-of-Distribution Detection](https://mlsanity.com/paper/2309.14888/) (2023)
- [The Familiarity Hypothesis: Explaining the Behavior of Deep Open Set Methods](https://mlsanity.com/paper/2203.02486/) (2022)
- [Class-Specific Semantic Reconstruction for Open Set Recognition](https://mlsanity.com/paper/2207.02158/) (2022)
- [Exploring Diverse Representations for Open Set Recognition](https://mlsanity.com/paper/2401.06521/) (2024)

## Abstract (arXiv)

Open Set Recognition (OSR) aims to enable models to accurately classify known classes while rejecting samples from unseen classes. A key challenge in OSR lies in the inability to model the unbounded distribution of unknown classes during training, often leading to the misclassification of samples from these classes. Rather than modeling unknowns, recent work shapes the feature space so that known classes are compact and well separated, and spherical representation learning methods have achieved strong results this way. Label smoothing has been identified as one of the key drivers of this success, yet it applies the same coefficient to every training sample, regardless of how well each sample is already embedded. We show that the spherical representation learning objectives used in OSR share a single alignment--uniformity structure in which labels enter only through the alignment term. Label smoothing therefore acts as an alignment dial, and a fixed coefficient sets this dial to the same value for every sample. We propose a plug-in, SmoothOperator (SmoothOP), which sets the smoothing coefficient of each sample from its prominence, an embedding-space signal measuring how clearly the sample's own class stands out against its strongest competing class. Our method integrates into four existing spherical representation learning methods at minimal training overhead. SmoothOP assigns strong smoothing to samples with high prominence, which reduces their alignment and relaxes their pull. On the Semantic Shift Benchmark, SmoothOP-augmented variants generally outperform their base objectives across datasets, degrees of semantic shift, and OSR post-processors, with gains of up to 4.7% in AUROC, OSCR, and closed-set accuracy.