# Positive-incentive Noise

arXiv: https://arxiv.org/abs/2212.09541 · HTML: https://mlsanity.com/paper/2212.09541/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 19 Dec 2022.

## Builds on (most cited first, 3 of 3)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Matrix Completion via Non-Convex Relaxation and Adaptive Correlation Learning](https://mlsanity.com/paper/2203.02189/) (2022)

## Built on by (most cited first, 30 of 39)

- [On the Design Fundamentals of Diffusion Models: A Survey](https://mlsanity.com/paper/2306.04542/) (2023)
- [AI Flow: Perspectives, Scenarios, and Approaches](https://mlsanity.com/paper/2506.12479/) (2025)
- [Variational Positive-incentive Noise: How Noise Benefits Models](https://mlsanity.com/paper/2306.07651/) (2023)
- [Multi-granularity Correspondence Learning from Long-term Noisy Videos](https://mlsanity.com/paper/2401.16702/) (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)
- [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)
- [Complex Mixer for MedMNIST Classification Decathlon](https://mlsanity.com/paper/2304.10054/) (2023)
- [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)
- [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)
- [Adaptive Layerwise Perturbation: Unifying Off-Policy Corrections for LLM RL](https://mlsanity.com/paper/2603.19470/) (2026)
- [Class-Aware Prototype Learning with Negative Contrast for Test-Time Adaptation of Vision-Language Models](https://mlsanity.com/paper/2510.19802/) (2025)
- [GRPO-RM: Fine-Tuning Representation Models via GRPO-Driven Reinforcement Learning](https://mlsanity.com/paper/2511.15256/) (2025)
- [Generative Transmission: Rethinking Computation, Bandwidth, and Memory in Communication](https://mlsanity.com/paper/2607.17482/) (2026)
- [Data-Centric Long-Tailed Image Recognition](https://mlsanity.com/paper/2311.01744/) (2023)
- [Structuring the Processing Frameworks for Data Stream Evaluation and Application](https://mlsanity.com/paper/2411.06799/) (2024)
- [Unveiling Hidden Vulnerabilities in Digital Human Generation via Adversarial Attacks](https://mlsanity.com/paper/2504.17457/) (2025)
- [Representation Discrepancy Bridging Method for Remote Sensing Image-Text Retrieval](https://mlsanity.com/paper/2505.16756/) (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)
- [Semantic-Aware Temporal Adaptation for UAV Anti-UAV Tracking](https://mlsanity.com/paper/2607.26511/) (2026)
- [Leveraging Noisy Manual Labels as Useful Information: An Information Fusion Approach for Enhanced Variable Selection in Penalized Logistic Regression](https://mlsanity.com/paper/2504.16585/) (2025)
- [Real-Time Crowd Counting for Embedded Systems with Lightweight Architecture](https://mlsanity.com/paper/2510.13250/) (2025)

## Abstract (arXiv)

Noise is conventionally viewed as a severe problem in diverse fields, e.g., engineering, learning systems. However, this paper aims to investigate whether the conventional proposition always holds. It begins with the definition of task entropy, which extends from the information entropy and measures the complexity of the task. After introducing the task entropy, the noise can be classified into two kinds, Positive-incentive noise (Pi-noise or π-noise) and pure noise, according to whether the noise can reduce the complexity of the task. Interestingly, as shown theoretically and empirically, even the simple random noise can be the π-noise that simplifies the task. π-noise offers new explanations for some models and provides a new principle for some fields, such as multi-task learning, adversarial training, etc. Moreover, it reminds us to rethink the investigation of noises.