# Filter Response Normalization Layer: Eliminating Batch Dependence in the Training of Deep Neural Networks

arXiv: https://arxiv.org/abs/1911.09737 · HTML: https://mlsanity.com/paper/1911.09737/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2019.

## Built on by (most cited first, 30 of 45)

- [What Are Bayesian Neural Network Posteriors Really Like?](https://mlsanity.com/paper/2104.14421/) (2021)
- [Rethinking "Batch" in BatchNorm](https://mlsanity.com/paper/2105.07576/) (2021)
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- [Beyond BatchNorm: Towards a Unified Understanding of Normalization in Deep Learning](https://mlsanity.com/paper/2106.05956/) (2021)
- [Beyond Deep Ensembles: A Large-Scale Evaluation of Bayesian Deep Learning under Distribution Shift](https://mlsanity.com/paper/2306.12306/) (2023)
- [On the Pitfalls of Batch Normalization for End-to-End Video Learning: A Study on Surgical Workflow Analysis](https://mlsanity.com/paper/2203.07976/) (2022)
- [The Memory Perturbation Equation: Understanding Model's Sensitivity to Data](https://mlsanity.com/paper/2310.19273/) (2023)
- [Metadata Normalization](https://mlsanity.com/paper/2104.09052/) (2021)
- [M"obius Convolutions for Spherical CNNs](https://mlsanity.com/paper/2201.12212/) (2022)
- [Stronger Normalization-Free Transformers](https://mlsanity.com/paper/2512.10938/) (2025)
- [Proxy-Normalizing Activations to Match Batch Normalization while Removing Batch Dependence](https://mlsanity.com/paper/2106.03743/) (2021)
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- [Single Mesh Diffusion Models with Field Latents for Texture Generation](https://mlsanity.com/paper/2312.09250/) (2023)
- [A Survey of Robust 3D Object Detection Methods in Point Clouds](https://mlsanity.com/paper/2204.00106/) (2022)
- [Sandwich Batch Normalization: A Drop-In Replacement for Feature Distribution Heterogeneity](https://mlsanity.com/paper/2102.11382/) (2021)
- [TS-Net: OCR Trained to Switch Between Text Transcription Styles](https://mlsanity.com/paper/2103.05489/) (2021)
- [Multi-Horizon Representations with Hierarchical Forward Models for Reinforcement Learning](https://mlsanity.com/paper/2206.11396/) (2022)
- [Can Microcanonical Langevin Dynamics Leverage Mini-Batch Gradient Noise?](https://mlsanity.com/paper/2602.06500/) (2026)
- [Making EfficientNet More Efficient: Exploring Batch-Independent Normalization, Group Convolutions and Reduced Resolution Training](https://mlsanity.com/paper/2106.03640/) (2021)
- [Entropy-MCMC: Sampling from Flat Basins with Ease](https://mlsanity.com/paper/2310.05401/) (2023)
- [SDGMNet: Statistic-based Dynamic Gradient Modulation for Local Descriptor Learning](https://mlsanity.com/paper/2106.04434/) (2021)
- [Robustness to corruption in pre-trained Bayesian neural networks](https://mlsanity.com/paper/2206.12361/) (2022)
- [Enhancing Transfer Learning with Flexible Nonparametric Posterior Sampling](https://mlsanity.com/paper/2403.07282/) (2024)
- [Learning to Explore for Stochastic Gradient MCMC](https://mlsanity.com/paper/2408.09140/) (2024)
- [Unconditional stability of a recurrent neural circuit implementing divisive normalization](https://mlsanity.com/paper/2409.18946/) (2024)
- [Exploiting Invariance in Training Deep Neural Networks](https://mlsanity.com/paper/2103.16634/) (2021)
- [Distribution Mismatch Correction for Improved Robustness in Deep Neural Networks](https://mlsanity.com/paper/2110.01955/) (2021)
- [DGFont++: Robust Deformable Generative Networks for Unsupervised Font Generation](https://mlsanity.com/paper/2212.14742/) (2022)
- [Traversing Between Modes in Function Space for Fast Ensembling](https://mlsanity.com/paper/2306.11304/) (2023)
- [Fast Ensembling with Diffusion Schr"odinger Bridge](https://mlsanity.com/paper/2404.15814/) (2024)

## Abstract (arXiv)

Batch Normalization (BN) uses mini-batch statistics to normalize the activations during training, introducing dependence between mini-batch elements. This dependency can hurt the performance if the mini-batch size is too small, or if the elements are correlated. Several alternatives, such as Batch Renormalization and Group Normalization (GN), have been proposed to address this issue. However, they either do not match the performance of BN for large batches, or still exhibit degradation in performance for smaller batches, or introduce artificial constraints on the model architecture. In this paper we propose the Filter Response Normalization (FRN) layer, a novel combination of a normalization and an activation function, that can be used as a replacement for other normalizations and activations. Our method operates on each activation channel of each batch element independently, eliminating the dependency on other batch elements. Our method outperforms BN and other alternatives in a variety of settings for all batch sizes. FRN layer performs ≈ 0.7-1.0% better than BN on top-1 validation accuracy with large mini-batch sizes for Imagenet classification using InceptionV3 and ResnetV2-50 architectures. Further, it performs >1% better than GN on the same problem in the small mini-batch size regime. For object detection problem on COCO dataset, FRN layer outperforms all other methods by at least 0.3-0.5% in all batch size regimes.