# Blurs Behave Like Ensembles: Spatial Smoothings to Improve Accuracy, Uncertainty, and Robustness

arXiv: https://arxiv.org/abs/2105.12639 · HTML: https://mlsanity.com/paper/2105.12639/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 60 references that are in the map.
- First posted on arXiv 26 May 2021.

## Builds on (most cited first, 30 of 46)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Training data-efficient image transformers & distillation through attention](https://mlsanity.com/paper/2012.12877/) (2020)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Benchmarking Neural Network Robustness to Common Corruptions and Perturbations](https://mlsanity.com/paper/1903.12261/) (2019)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Learning Deep Features for Discriminative Localization](https://mlsanity.com/paper/1512.04150/) (2015)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [Making Convolutional Networks Shift-Invariant Again](https://mlsanity.com/paper/1904.11486/) (2019)
- [BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning](https://mlsanity.com/paper/2002.06715/) (2020)

## Built on by (most cited first, 14 of 14)

- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [What Do Self-Supervised Vision Transformers Learn?](https://mlsanity.com/paper/2305.00729/) (2023)
- [Architecture-Agnostic Masked Image Modeling -- From ViT back to CNN](https://mlsanity.com/paper/2205.13943/) (2022)
- [A Survey on the Robustness of Computer Vision Models against Common Corruptions](https://mlsanity.com/paper/2305.06024/) (2023)
- [Limited Data, Unlimited Potential: A Study on ViTs Augmented by Masked Autoencoders](https://mlsanity.com/paper/2310.20704/) (2023)
- [Achelous: A Fast Unified Water-surface Panoptic Perception Framework based on Fusion of Monocular Camera and 4D mmWave Radar](https://mlsanity.com/paper/2307.07102/) (2023)
- [A Step Toward World Models: A Survey on Robotic Manipulation](https://mlsanity.com/paper/2511.02097/) (2025)
- [On Divergence Measures for Bayesian Pseudocoresets](https://mlsanity.com/paper/2210.06205/) (2022)
- [Towards Flexible Inductive Bias via Progressive Reparameterization Scheduling](https://mlsanity.com/paper/2210.01370/) (2022)
- [UniTT-Stereo: Unified Training of Transformer for Enhanced Stereo Matching](https://mlsanity.com/paper/2409.02545/) (2024)
- [Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKA](https://mlsanity.com/paper/2411.00259/) (2024)
- [Enhancing Face Recognition with Latent Space Data Augmentation and Facial Posture Reconstruction](https://mlsanity.com/paper/2301.11986/) (2023)
- [Understanding Differential Transformer Unchains Pretrained Self-Attentions](https://mlsanity.com/paper/2505.16333/) (2025)
- [UECP: Uncertainty-Enhanced Collaborative Perception](https://mlsanity.com/paper/2606.23046/) (2026)

## Abstract (arXiv)

Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of predictions to produce reliable results, leading to a significant increase in computational cost. To alleviate this issue, we propose spatial smoothing, a method that spatially ensembles neighboring feature map points of convolutional neural networks. By simply adding a few blur layers to the models, we empirically show that spatial smoothing improves accuracy, uncertainty estimation, and robustness of BNNs across a whole range of ensemble sizes. In particular, BNNs incorporating spatial smoothing achieve high predictive performance merely with a handful of ensembles. Moreover, this method also can be applied to canonical deterministic neural networks to improve the performances. A number of evidences suggest that the improvements can be attributed to the stabilized feature maps and the smoothing of the loss landscape. In addition, we provide a fundamental explanation for prior works - namely, global average pooling, pre-activation, and ReLU6 - by addressing them as special cases of spatial smoothing. These not only enhance accuracy, but also improve uncertainty estimation and robustness by making the loss landscape smoother in the same manner as spatial smoothing. The code is available at https://github.com/xxxnell/spatial-smoothing.