# Variational Positive-incentive Noise: How Noise Benefits Models

arXiv: https://arxiv.org/abs/2306.07651 · HTML: https://mlsanity.com/paper/2306.07651/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 36 references that are in the map.
- First posted on arXiv 13 Jun 2023.

## Builds on (most cited first, 17 of 17)

- [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)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Representation Learning with Contrastive Predictive Coding](https://mlsanity.com/paper/1807.03748/) (2018)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Graph Information Bottleneck](https://mlsanity.com/paper/2010.12811/) (2020)
- [Learning Discrete Representations via Information Maximizing Self-Augmented Training](https://mlsanity.com/paper/1702.08720/) (2017)
- [Distributional Smoothing with Virtual Adversarial Training](https://mlsanity.com/paper/1507.00677/) (2015)
- [Positive-incentive Noise](https://mlsanity.com/paper/2212.09541/) (2022)

## Built on by (most cited first, 30 of 38)

- [Enhance Vision-Language Alignment with Noise](https://mlsanity.com/paper/2412.10817/) (2024)
- [Data Augmentation of Contrastive Learning is Estimating Positive-incentive Noise](https://mlsanity.com/paper/2408.09929/) (2024)
- [Learn Beneficial Noise as Graph Augmentation](https://mlsanity.com/paper/2505.19024/) (2025)
- [NFIG: Multi-Scale Autoregressive Image Generation via Frequency Ordering](https://mlsanity.com/paper/2503.07076/) (2025)
- [Adv-CPG: A Customized Portrait Generation Framework with Facial Adversarial Attacks](https://mlsanity.com/paper/2503.08269/) (2025)
- [Mixture of Noise for Pre-Trained Model-Based Class-Incremental Learning](https://mlsanity.com/paper/2509.16738/) (2025)
- [Object-AVEdit: An Object-level Audio-Visual Editing Model](https://mlsanity.com/paper/2510.00050/) (2025)
- [Integrating Reinforcement Learning with Visual Generative Models: Foundations and Advances](https://mlsanity.com/paper/2508.10316/) (2025)
- [Explore How to Inject Beneficial Noise in MLLMs](https://mlsanity.com/paper/2511.12917/) (2025)
- [MR-UIE: Multi-Perspective Reasoning with Reinforcement Learning for Universal Information Extraction](https://mlsanity.com/paper/2509.09082/) (2025)
- [Laytrol: Preserving Pretrained Knowledge in Layout Control for Multimodal Diffusion Transformers](https://mlsanity.com/paper/2511.07934/) (2025)
- [Unison: Harmonizing Motion, Speech, and Sound for Human-Centric Audio-Video Generation](https://mlsanity.com/paper/2605.08729/) (2026)
- [NoisyNN: Exploring the Impact of Information Entropy Change in Learning Systems](https://mlsanity.com/paper/2309.10625/) (2023)
- [InteractiveAvatar: Real-Time Streaming Video Generation for Consistent and Intent-Aware Avatars](https://mlsanity.com/paper/2606.22905/) (2026)
- [CNN2GNN: How to Bridge CNN with GNN](https://mlsanity.com/paper/2404.14822/) (2024)
- [AnchorFormer: Differentiable Anchor Attention for Efficient Vision Transformer](https://mlsanity.com/paper/2505.16463/) (2025)
- [TableZoomer: A Collaborative Agent Framework for Large-scale Table Question Answering](https://mlsanity.com/paper/2509.01312/) (2025)
- [Enhancing Neural Video Compression of Static Scenes with Positive-Incentive Noise](https://mlsanity.com/paper/2603.06095/) (2026)
- [SRAGAN: Saliency Regularized and Attended Generative Adversarial Network for Chinese Ink-wash Painting Style Transfer](https://mlsanity.com/paper/2404.15743/) (2024)
- [GRPO-RM: Fine-Tuning Representation Models via GRPO-Driven Reinforcement Learning](https://mlsanity.com/paper/2511.15256/) (2025)
- [Perturbation-Regularized Open-Vocabulary Remote Sensing Segmentation with Unified Multi-Domain Evaluation](https://mlsanity.com/paper/2604.15652/) (2026)
- [Data-Centric Long-Tailed Image Recognition](https://mlsanity.com/paper/2311.01744/) (2023)
- [Unveiling Hidden Vulnerabilities in Digital Human Generation via Adversarial Attacks](https://mlsanity.com/paper/2504.17457/) (2025)
- [ERF-BA-TFD+: A Multimodal Model for Audio-Visual Deepfake Detection](https://mlsanity.com/paper/2508.17282/) (2025)
- [ViewMask-1-to-3: Multi-View Consistent Image Generation via Multimodal Discrete Diffusion Models](https://mlsanity.com/paper/2512.14099/) (2025)
- [Safeguarding Text-to-Image Generative Models Against Unauthorized Knowledge Distillation](https://mlsanity.com/paper/2605.22060/) (2026)
- [Semantic-Aware Temporal Adaptation for UAV Anti-UAV Tracking](https://mlsanity.com/paper/2607.26511/) (2026)
- [Exploiting the Potential Supervision Information of Clean Samples in Partial Label Learning](https://mlsanity.com/paper/2505.09354/) (2025)
- [Real-Time Crowd Counting for Embedded Systems with Lightweight Architecture](https://mlsanity.com/paper/2510.13250/) (2025)
- [CoLM: Collaborative Large Models via A Client-Server Paradigm](https://mlsanity.com/paper/2511.06991/) (2025)

## Abstract (arXiv)

A large number of works aim to alleviate the impact of noise due to an underlying conventional assumption of the negative role of noise. However, some existing works show that the assumption does not always hold. In this paper, we investigate how to benefit the classical models by random noise under the framework of Positive-incentive Noise (Pi-Noise). Since the ideal objective of Pi-Noise is intractable, we propose to optimize its variational bound instead, namely variational Pi-Noise (VPN). With the variational inference, a VPN generator implemented by neural networks is designed for enhancing base models and simplifying the inference of base models, without changing the architecture of base models. Benefiting from the independent design of base models and VPN generators, the VPN generator can work with most existing models. From the experiments, it is shown that the proposed VPN generator can improve the base models. It is appealing that the trained variational VPN generator prefers to blur the irrelevant ingredients in complicated images, which meets our expectations.