# Balanced Group Convolution: An Improved Group Convolution Based on Approximability Estimates

arXiv: https://arxiv.org/abs/2310.12461 · HTML: https://mlsanity.com/paper/2310.12461/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 46 references that are in the map.
- First posted on arXiv 19 Oct 2023.

## Builds on (most cited first, 30 of 31)

- [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)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices](https://mlsanity.com/paper/1707.01083/) (2017)
- [EfficientNetV2: Smaller Models and Faster Training](https://mlsanity.com/paper/2104.00298/) (2021)
- [MnasNet: Platform-Aware Neural Architecture Search for Mobile](https://mlsanity.com/paper/1807.11626/) (2018)
- [GhostNet: More Features from Cheap Operations](https://mlsanity.com/paper/1911.11907/) (2019)
- [Deeply-Supervised Nets](https://mlsanity.com/paper/1409.5185/) (2014)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [CondenseNet: An Efficient DenseNet using Learned Group Convolutions](https://mlsanity.com/paper/1711.09224/) (2017)
- [Accelerating Very Deep Convolutional Networks for Classification and Detection](https://mlsanity.com/paper/1505.06798/) (2015)
- [Neural Machine Translation: A Review and Survey](https://mlsanity.com/paper/1912.02047/) (2019)
- [Efficient and Accurate Approximations of Nonlinear Convolutional Networks](https://mlsanity.com/paper/1411.4229/) (2014)
- [Pruning Algorithms to Accelerate Convolutional Neural Networks for Edge Applications: A Survey](https://mlsanity.com/paper/2005.04275/) (2020)
- [Fully Learnable Group Convolution for Acceleration of Deep Neural Networks](https://mlsanity.com/paper/1904.00346/) (2019)
- [Approximation Properties of Deep ReLU CNNs](https://mlsanity.com/paper/2109.00190/) (2021)
- [Self-grouping Convolutional Neural Networks](https://mlsanity.com/paper/2009.13803/) (2020)

## Abstract (arXiv)

The performance of neural networks has been significantly improved by increasing the number of channels in convolutional layers. However, this increase in performance comes with a higher computational cost, resulting in numerous studies focused on reducing it. One promising approach to address this issue is group convolution, which effectively reduces the computational cost by grouping channels. However, to the best of our knowledge, there has been no theoretical analysis on how well the group convolution approximates the standard convolution. In this paper, we mathematically analyze the approximation of the group convolution to the standard convolution with respect to the number of groups. Furthermore, we propose a novel variant of the group convolution called balanced group convolution, which shows a higher approximation with a small additional computational cost. We provide experimental results that validate our theoretical findings and demonstrate the superior performance of the balanced group convolution over other variants of group convolution.