# NoiseGrad: Enhancing Explanations by Introducing Stochasticity to Model Weights

arXiv: https://arxiv.org/abs/2106.10185 · HTML: https://mlsanity.com/paper/2106.10185/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 86 references that are in the map.
- First posted on arXiv 18 Jun 2021.

## Builds on (most cited first, 30 of 41)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Axiomatic Attribution for Deep Networks](https://mlsanity.com/paper/1703.01365/) (2017)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Learning Important Features Through Propagating Activation Differences](https://mlsanity.com/paper/1704.02685/) (2017)
- [Sanity Checks for Saliency Maps](https://mlsanity.com/paper/1810.03292/) (2018)
- [SmoothGrad: removing noise by adding noise](https://mlsanity.com/paper/1706.03825/) (2017)
- [A Survey Of Methods For Explaining Black Box Models](https://mlsanity.com/paper/1802.01933/) (2018)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Towards Robust Interpretability with Self-Explaining Neural Networks](https://mlsanity.com/paper/1806.07538/) (2018)
- [Variational Dropout and the Local Reparameterization Trick](https://mlsanity.com/paper/1506.02557/) (2015)
- [A Benchmark for Interpretability Methods in Deep Neural Networks](https://mlsanity.com/paper/1806.10758/) (2018)
- [Evaluating the visualization of what a Deep Neural Network has learned](https://mlsanity.com/paper/1509.06321/) (2015)
- [Methods for Interpreting and Understanding Deep Neural Networks](https://mlsanity.com/paper/1706.07979/) (2017)
- [The (Un)reliability of saliency methods](https://mlsanity.com/paper/1711.00867/) (2017)
- [Top-down Neural Attention by Excitation Backprop](https://mlsanity.com/paper/1608.00507/) (2016)
- [On the (In)fidelity and Sensitivity for Explanations](https://mlsanity.com/paper/1901.09392/) (2019)
- [Variational Dropout Sparsifies Deep Neural Networks](https://mlsanity.com/paper/1701.05369/) (2017)
- [Explanations can be manipulated and geometry is to blame](https://mlsanity.com/paper/1906.07983/) (2019)
- [Evaluating and Aggregating Feature-based Model Explanations](https://mlsanity.com/paper/2005.00631/) (2020)
- [Synthesizing the preferred inputs for neurons in neural networks via deep generator networks](https://mlsanity.com/paper/1605.09304/) (2016)
- [Practical Deep Learning with Bayesian Principles](https://mlsanity.com/paper/1906.02506/) (2019)
- [Benchmarking Attribution Methods with Relative Feature Importance](https://mlsanity.com/paper/1907.09701/) (2019)
- [On quantitative aspects of model interpretability](https://mlsanity.com/paper/2007.07584/) (2020)

## Built on by (most cited first, 28 of 28)

- [Quantus: An Explainable AI Toolkit for Responsible Evaluation of Neural Network Explanations and Beyond](https://mlsanity.com/paper/2202.06861/) (2022)
- [The Meta-Evaluation Problem in Explainable AI: Identifying Reliable Estimators with MetaQuantus](https://mlsanity.com/paper/2302.07265/) (2023)
- [Finding the right XAI method -- A Guide for the Evaluation and Ranking of Explainable AI Methods in Climate Science](https://mlsanity.com/paper/2303.00652/) (2023)
- [What Makes a Good Explanation?: A Harmonized View of Properties of Explanations](https://mlsanity.com/paper/2211.05667/) (2022)
- [Explaining Bayesian Neural Networks](https://mlsanity.com/paper/2108.10346/) (2021)
- [DORA: Exploring Outlier Representations in Deep Neural Networks](https://mlsanity.com/paper/2206.04530/) (2022)
- [SInGE: Sparsity via Integrated Gradients Estimation of Neuron Relevance](https://mlsanity.com/paper/2207.04089/) (2022)
- [Sanity Checks Revisited: An Exploration to Repair the Model Parameter Randomisation Test](https://mlsanity.com/paper/2401.06465/) (2024)
- [A Fresh Look at Sanity Checks for Saliency Maps](https://mlsanity.com/paper/2405.02383/) (2024)
- [SoK: Modeling Explainability in Security Analytics for Interpretability, Trustworthiness, and Usability](https://mlsanity.com/paper/2210.17376/) (2022)
- [Provably Better Explanations with Optimized Aggregation of Feature Attributions](https://mlsanity.com/paper/2406.05090/) (2024)
- [Visualizing the Diversity of Representations Learned by Bayesian Neural Networks](https://mlsanity.com/paper/2201.10859/) (2022)
- [From Flexibility to Manipulation: The Slippery Slope of XAI Evaluation](https://mlsanity.com/paper/2412.05592/) (2024)
- [PASA: Attack Agnostic Unsupervised Adversarial Detection using Prediction & Attribution Sensitivity Analysis](https://mlsanity.com/paper/2404.10789/) (2024)
- [GARNN: An Interpretable Graph Attentive Recurrent Neural Network for Predicting Blood Glucose Levels via Multivariate Time Series](https://mlsanity.com/paper/2402.16230/) (2024)
- [AdaptGrad: Adaptive Sampling to Reduce Noise](https://mlsanity.com/paper/2410.07711/) (2024)
- [On the Complexity-Faithfulness Trade-off of Gradient-Based Explanations](https://mlsanity.com/paper/2508.10490/) (2025)
- [On Spectral Properties of Gradient-based Explanation Methods](https://mlsanity.com/paper/2508.10595/) (2025)
- [Multi-Label Classification of Thoracic Diseases using Dense Convolutional Network on Chest Radiographs](https://mlsanity.com/paper/2202.03583/) (2022)
- [The Paradox of Noise: An Empirical Study of Noise-Infusion Mechanisms to Improve Generalization, Stability, and Privacy in Federated Learning](https://mlsanity.com/paper/2311.05790/) (2023)
- [CNN-based explanation ensembling for dataset, representation and explanations evaluation](https://mlsanity.com/paper/2404.10387/) (2024)
- [Beyond the Black Box: Do More Complex Deep Learning Models Provide Superior XAI Explanations?](https://mlsanity.com/paper/2405.08658/) (2024)
- [Axiomatization of Gradient Smoothing in Neural Networks](https://mlsanity.com/paper/2407.00371/) (2024)
- [Pulling Back the Curtain on Deep Networks](https://mlsanity.com/paper/2507.22832/) (2025)
- [Smaller is Better: Enhancing Transparency in Vehicle AI Systems via Pruning](https://mlsanity.com/paper/2509.20148/) (2025)
- [Training for Trustworthy Saliency Maps: Adversarial Training Meets Feature-Map Smoothing](https://mlsanity.com/paper/2603.07302/) (2026)
- [Explanation of Dynamic Physical Field Predictions using WassersteinGrad: Application to Autoregressive Weather Forecasting](https://mlsanity.com/paper/2604.22580/) (2026)
- [Scaling Vision Models Does Not Consistently Improve Localisation-Based Explanation Quality](https://mlsanity.com/paper/2605.10142/) (2026)

## Abstract (arXiv)

Many efforts have been made for revealing the decision-making process of black-box learning machines such as deep neural networks, resulting in useful local and global explanation methods. For local explanation, stochasticity is known to help: a simple method, called SmoothGrad, has improved the visual quality of gradient-based attribution by adding noise to the input space and averaging the explanations of the noisy inputs. In this paper, we extend this idea and propose NoiseGrad that enhances both local and global explanation methods. Specifically, NoiseGrad introduces stochasticity in the weight parameter space, such that the decision boundary is perturbed. NoiseGrad is expected to enhance the local explanation, similarly to SmoothGrad, due to the dual relationship between the input perturbation and the decision boundary perturbation. We evaluate NoiseGrad and its fusion with SmoothGrad -- FusionGrad -- qualitatively and quantitatively with several evaluation criteria, and show that our novel approach significantly outperforms the baseline methods. Both NoiseGrad and FusionGrad are method-agnostic and as handy as SmoothGrad using a simple heuristic for the choice of the hyperparameter setting without the need of finetuning.