# Improving Normalization with the James-Stein Estimator

arXiv: https://arxiv.org/abs/2312.00313 · HTML: https://mlsanity.com/paper/2312.00313/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 65 references that are in the map.
- First posted on arXiv 1 Dec 2023.

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

- [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)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Group Normalization](https://mlsanity.com/paper/1803.08494/) (2018)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation](https://mlsanity.com/paper/1909.11065/) (2019)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [How Does Batch Normalization Help Optimization?](https://mlsanity.com/paper/1805.11604/) (2018)
- [OverFeat: Integrated Recognition, Localization and Detection using Convolutional Networks](https://mlsanity.com/paper/1312.6229/) (2013)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Understanding Batch Normalization](https://mlsanity.com/paper/1806.02375/) (2018)

## Built on by (most cited first, 6 of 6)

- [On the Effect of Image Resolution on Semantic Segmentation](https://mlsanity.com/paper/2402.05398/) (2024)
- [FedStein: Enhancing Multi-Domain Federated Learning Through James-Stein Estimator](https://mlsanity.com/paper/2410.03499/) (2024)
- [PrivacyCD: Hierarchical Unlearning for Protecting Student Privacy in Cognitive Diagnosis](https://mlsanity.com/paper/2511.03966/) (2025)
- [Multi-Scale Semantic Segmentation with Modified MBConv Blocks](https://mlsanity.com/paper/2402.04618/) (2024)
- [Early Fusion of Features for Semantic Segmentation](https://mlsanity.com/paper/2402.06091/) (2024)
- [Admissibility of Stein Shrinkage for Batch Normalization in the Presence of Adversarial Attacks](https://mlsanity.com/paper/2507.08261/) (2025)

## Abstract (arXiv)

Stein's paradox holds considerable sway in high-dimensional statistics, highlighting that the sample mean, traditionally considered the de facto estimator, might not be the most efficacious in higher dimensions. To address this, the James-Stein estimator proposes an enhancement by steering the sample means toward a more centralized mean vector. In this paper, first, we establish that normalization layers in deep learning use inadmissible estimators for mean and variance. Next, we introduce a novel method to employ the James-Stein estimator to improve the estimation of mean and variance within normalization layers. We evaluate our method on different computer vision tasks: image classification, semantic segmentation, and 3D object classification. Through these evaluations, it is evident that our improved normalization layers consistently yield superior accuracy across all tasks without extra computational burden. Moreover, recognizing that a plethora of shrinkage estimators surpass the traditional estimator in performance, we study two other prominent shrinkage estimators: Ridge and LASSO. Additionally, we provide visual representations to intuitively demonstrate the impact of shrinkage on the estimated layer statistics. Finally, we study the effect of regularization and batch size on our modified batch normalization. The studies show that our method is less sensitive to batch size and regularization, improving accuracy under various setups.