# One Positive Label is Sufficient: Single-Positive Multi-Label Learning with Label Enhancement

arXiv: https://arxiv.org/abs/2206.00517 · HTML: https://mlsanity.com/paper/2206.00517/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 47 references that are in the map.
- First posted on arXiv 1 Jun 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Multi-Label Image Recognition with Graph Convolutional Networks](https://mlsanity.com/paper/1904.03582/) (2019)
- [General Multi-label Image Classification with Transformers](https://mlsanity.com/paper/2011.14027/) (2020)
- [Learning a Deep ConvNet for Multi-label Classification with Partial Labels](https://mlsanity.com/paper/1902.09720/) (2019)
- [Progressive Identification of True Labels for Partial-Label Learning](https://mlsanity.com/paper/2002.08053/) (2020)
- [Provably Consistent Partial-Label Learning](https://mlsanity.com/paper/2007.08929/) (2020)
- [Implicit Reparameterization Gradients](https://mlsanity.com/paper/1805.08498/) (2018)
- [Multi-Label Learning from Single Positive Labels](https://mlsanity.com/paper/2106.09708/) (2021)
- [Cross-Modality Attention with Semantic Graph Embedding for Multi-Label Classification](https://mlsanity.com/paper/1912.07872/) (2019)
- [Large-scale Multi-label Learning with Missing Labels](https://mlsanity.com/paper/1307.5101/) (2013)
- [Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2110.12911/) (2021)
- [Multi-Label Learning with Global and Local Label Correlation](https://mlsanity.com/paper/1704.01415/) (2017)
- [Deep Multi-Species Embedding](https://mlsanity.com/paper/1609.09353/) (2016)
- [Expand Globally, Shrink Locally: Discriminant Multi-label Learning with Missing Labels](https://mlsanity.com/paper/2004.03951/) (2020)

## Built on by (most cited first, 22 of 22)

- [Progressive Purification for Instance-Dependent Partial Label Learning](https://mlsanity.com/paper/2206.00830/) (2022)
- [Boosting Single Positive Multi-label Classification with Generalized Robust Loss](https://mlsanity.com/paper/2405.03501/) (2024)
- [Deep Partial Multi-Label Learning with Graph Disambiguation](https://mlsanity.com/paper/2305.05882/) (2023)
- [Understanding Label Bias in Single Positive Multi-Label Learning](https://mlsanity.com/paper/2305.15584/) (2023)
- [Generalization Performance of Hypergraph Neural Networks](https://mlsanity.com/paper/2501.12554/) (2025)
- [Partial Feedback Online Learning](https://mlsanity.com/paper/2601.21462/) (2026)
- [Can Class-Priors Help Single-Positive Multi-Label Learning?](https://mlsanity.com/paper/2309.13886/) (2023)
- [Learning from True-False Labels via Multi-modal Prompt Retrieving](https://mlsanity.com/paper/2405.15228/) (2024)
- [More Reliable Pseudo-labels, Better Performance: A Generalized Approach to Single Positive Multi-label Learning](https://mlsanity.com/paper/2508.20381/) (2025)
- [Merlin L48 Spectrogram Dataset](https://mlsanity.com/paper/2511.00252/) (2025)
- [Pushing One Pair of Labels Apart Each Time in Multi-Label Learning: From Single Positive to Full Labels](https://mlsanity.com/paper/2302.14695/) (2023)
- [Scalable Label Distribution Learning for Multi-Label Classification](https://mlsanity.com/paper/2311.16556/) (2023)
- [Multi-label Learning from Privacy-Label](https://mlsanity.com/paper/2312.13312/) (2023)
- [Determined Multi-Label Learning via Similarity-Based Prompt](https://mlsanity.com/paper/2403.16482/) (2024)
- [A Survey on Incomplete Multi-label Learning: Recent Advances and Future Trends](https://mlsanity.com/paper/2406.06119/) (2024)
- [Probability-density-aware Semi-supervised Learning](https://mlsanity.com/paper/2412.17547/) (2024)
- [The Demon is in Ambiguity: Revisiting Situation Recognition with Single Positive Multi-Label Learning](https://mlsanity.com/paper/2508.21816/) (2025)
- [Least-Ambiguous Multi-Label Classifier](https://mlsanity.com/paper/2509.10689/) (2025)
- [Hyperbolic Structured Classification for Robust Single Positive Multi-label Learning](https://mlsanity.com/paper/2510.15296/) (2025)
- [Human-Corrected Labels Learning: Enhancing Labels Quality via Human Correction of VLMs Discrepancies](https://mlsanity.com/paper/2511.09063/) (2025)
- [Beyond "I cannot fulfill this request": Alleviating Rigid Rejection in LLMs via Label Enhancement](https://mlsanity.com/paper/2605.07883/) (2026)
- [When Semantically Consistent Encoding Meets View-Label Heterogeneity Modeling: A Unified Framework for Incomplete Multi-View Multi-Label Learning](https://mlsanity.com/paper/2609.07525/) (2026)

## Abstract (arXiv)

Multi-label learning (MLL) learns from the examples each associated with multiple labels simultaneously, where the high cost of annotating all relevant labels for each training example is challenging for real-world applications. To cope with the challenge, we investigate single-positive multi-label learning (SPMLL) where each example is annotated with only one relevant label, and show that one can successfully learn a theoretically grounded multi-label classifier for the problem. In this paper, a novel SPMLL method named SMILE, i.e., Single-positive MultI-label learning with Label Enhancement, is proposed. Specifically, an unbiased risk estimator is derived, which could be guaranteed to approximately converge to the optimal risk minimizer of fully supervised learning and shows that one positive label of each instance is sufficient to train the predictive model. Then, the corresponding empirical risk estimator is established via recovering the latent soft label as a label enhancement process, where the posterior density of the latent soft labels is approximate to the variational Beta density parameterized by an inference model. Experiments on benchmark datasets validate the effectiveness of the proposed method.