Blurs Behave Like Ensembles: Spatial Smoothings to Improve Accuracy, Uncertainty, and Robustness
Not on the map. Why?
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.
Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 46 of its 60 references that are in the map. First posted on arXiv 26 May 2021.
Builds on
46 of 60 references.
References · 46
- 2017Attention Is All You Needcited by 59,932
- 2015Deep Residual Learning for Image Recognitioncited by 51,809
- 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
- 2015U-Net: Convolutional Networks for Biomedical Image Segmentationcited by 19,604
- 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
- 2020End-to-End Object Detection with Transformerscited by 7,384
- 2014Explaining and Harnessing Adversarial Examplescited by 7,287
- 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
- 2017On Calibration of Modern Neural Networkscited by 4,860
- 2018MobileNetV2: Inverted Residuals and Linear Bottleneckscited by 4,773
- 2020Training data-efficient image transformers & distillation through attentioncited by 4,560
- 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
34 more
- 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
- 2016Wide Residual Networkscited by 3,057
- 2019Benchmarking Neural Network Robustness to Common Corruptions and Perturbationscited by 2,857
- 2016Aggregated Residual Transformations for Deep Neural Networkscited by 2,540
- 2015Learning Deep Features for Discriminative Localizationcited by 2,430
- 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
- 2017Non-local Neural Networkscited by 2,290
- 2016Identity Mappings in Deep Residual Networkscited by 1,960
- 2017Accurate, Large Minibatch SGD: Training ImageNet in 1 Hourcited by 1,479
- 2020Sharpness-Aware Minimization for Efficiently Improving Generalizationcited by 1,404
- 2016On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minimacited by 1,337
- 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,274
- 2017Visualizing the Loss Landscape of Neural Netscited by 1,126
- 2018Predictive Uncertainty Estimation via Prior Networkscited by 555
- 2020Bayesian Deep Learning and a Probabilistic Perspective of Generalizationcited by 480
- 2019Deep Ensembles: A Loss Landscape Perspectivecited by 438
- 2019Making Convolutional Networks Shift-Invariant Againcited by 390
- 2020BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learningcited by 368
- 2018How Does Batch Normalization Help Optimization?cited by 355
- 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
- 2019PyHessian: Neural Networks Through the Lens of the Hessiancited by 291
- 2019An Investigation into Neural Net Optimization via Hessian Eigenvalue Densitycited by 289
- 2015Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understandingcited by 218
- 2018Why do deep convolutional networks generalize so poorly to small image transformations?cited by 198
- 2018Bayesian Model-Agnostic Meta-Learningcited by 194
- 2020Efficient and Scalable Bayesian Neural Nets with Rank-1 Factorscited by 171
- 2019A General Framework for Uncertainty Estimation in Deep Learningcited by 119
- 2020Training BatchNorm and Only BatchNorm: On the Expressive Power of Random Features in CNNscited by 103
- 2019Sampling-free Epistemic Uncertainty Estimation Using Approximated Variance Propagationcited by 74
- 2020Delving Deeper into Anti-aliasing in ConvNetscited by 60
- 2020Depth Uncertainty in Neural Networkscited by 56
- 2016Natural-Parameter Networks: A Class of Probabilistic Neural Networkscited by 33
- 2020An Effective Anti-Aliasing Approach for Residual Networkscited by 23
- 2019Vector Quantized Bayesian Neural Network Inference for Data Streamscited by 5
Built on by
Citing papers per year: 2022: 4; 2023: 5; 2024: 2; 2025: 2; 2026: 1.
14 papers.
Sort:
By area:
- 2022How Do Vision Transformers Work?cited by 305
- 2023What Do Self-Supervised Vision Transformers Learn?cited by 90
- 2022Architecture-Agnostic Masked Image Modeling -- From ViT back to CNNcited by 31
- 2023A Survey on the Robustness of Computer Vision Models against Common Corruptionscited by 20
- 2023Limited Data, Unlimited Potential: A Study on ViTs Augmented by Masked Autoencoderscited by 17
- 2023Achelous: A Fast Unified Water-surface Panoptic Perception Framework based on Fusion of Monocular Camera and 4D mmWave Radarcited by 16
- 2025A Step Toward World Models: A Survey on Robotic Manipulationcited by 15
- 2022On Divergence Measures for Bayesian Pseudocoresetscited by 10
- 2022Towards Flexible Inductive Bias via Progressive Reparameterization Schedulingcited by 4
- 2024UniTT-Stereo: Unified Training of Transformer for Enhanced Stereo Matchingcited by 3
- 2024Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKAcited by 2
- 2023Enhancing Face Recognition with Latent Space Data Augmentation and Facial Posture Reconstructioncited by 0
2 more
- 2026UECP: Uncertainty-Enhanced Collaborative Perception22 Jun 2026
- 2025A Step Toward World Models: A Survey on Robotic Manipulation31 Oct 2025
- 2025Understanding Differential Transformer Unchains Pretrained Self-Attentions22 May 2025
- 2024Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKA31 Oct 2024
- 2024UniTT-Stereo: Unified Training of Transformer for Enhanced Stereo Matching4 Sep 2024
- 2023Limited Data, Unlimited Potential: A Study on ViTs Augmented by Masked Autoencoders31 Oct 2023
- 2023Achelous: A Fast Unified Water-surface Panoptic Perception Framework based on Fusion of Monocular Camera and 4D mmWave Radar14 Jul 2023
- 2023A Survey on the Robustness of Computer Vision Models against Common Corruptions10 May 2023
- 2023What Do Self-Supervised Vision Transformers Learn?1 May 2023
- 2023Enhancing Face Recognition with Latent Space Data Augmentation and Facial Posture Reconstruction27 Jan 2023
- 2022On Divergence Measures for Bayesian Pseudocoresets12 Oct 2022
- 2022Towards Flexible Inductive Bias via Progressive Reparameterization Scheduling4 Oct 2022
2 more
- 2022Architecture-Agnostic Masked Image Modeling -- From ViT back to CNN27 May 2022
- 2022How Do Vision Transformers Work?14 Feb 2022
- 2025A Step Toward World Models: A Survey on Robotic Manipulationcited by 15
- 2025A Step Toward World Models: A Survey on Robotic Manipulation31 Oct 2025
- 2022How Do Vision Transformers Work?cited by 305
- 2023What Do Self-Supervised Vision Transformers Learn?cited by 90
- 2022Architecture-Agnostic Masked Image Modeling -- From ViT back to CNNcited by 31
- 2023A Survey on the Robustness of Computer Vision Models against Common Corruptionscited by 20
- 2023Limited Data, Unlimited Potential: A Study on ViTs Augmented by Masked Autoencoderscited by 17
- 2023Achelous: A Fast Unified Water-surface Panoptic Perception Framework based on Fusion of Monocular Camera and 4D mmWave Radarcited by 16
- 2022On Divergence Measures for Bayesian Pseudocoresetscited by 10
- 2022Towards Flexible Inductive Bias via Progressive Reparameterization Schedulingcited by 4
- 2024UniTT-Stereo: Unified Training of Transformer for Enhanced Stereo Matchingcited by 3
- 2024Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKAcited by 2
- 2023Enhancing Face Recognition with Latent Space Data Augmentation and Facial Posture Reconstructioncited by 0
- 2025Understanding Differential Transformer Unchains Pretrained Self-Attentionscited by 0
12 most cited of 13 All 13 (JSON)
- 2026UECP: Uncertainty-Enhanced Collaborative Perception22 Jun 2026
- 2025Understanding Differential Transformer Unchains Pretrained Self-Attentions22 May 2025
- 2024Enhancing Diversity in Bayesian Deep Learning via Hyperspherical Energy Minimization of CKA31 Oct 2024
- 2024UniTT-Stereo: Unified Training of Transformer for Enhanced Stereo Matching4 Sep 2024
- 2023Limited Data, Unlimited Potential: A Study on ViTs Augmented by Masked Autoencoders31 Oct 2023
- 2023Achelous: A Fast Unified Water-surface Panoptic Perception Framework based on Fusion of Monocular Camera and 4D mmWave Radar14 Jul 2023
- 2023A Survey on the Robustness of Computer Vision Models against Common Corruptions10 May 2023
- 2023What Do Self-Supervised Vision Transformers Learn?1 May 2023
- 2023Enhancing Face Recognition with Latent Space Data Augmentation and Facial Posture Reconstruction27 Jan 2023
- 2022On Divergence Measures for Bayesian Pseudocoresets12 Oct 2022
- 2022Towards Flexible Inductive Bias via Progressive Reparameterization Scheduling4 Oct 2022
- 2022Architecture-Agnostic Masked Image Modeling -- From ViT back to CNN27 May 2022
12 newest of 13 All 13 (JSON)