# VeLU: Variance-enhanced Learning Unit for Deep Neural Networks

arXiv: https://arxiv.org/abs/2504.15051 · HTML: https://mlsanity.com/paper/2504.15051/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 43 of its 73 references that are in the map.
- First posted on arXiv 21 Apr 2025.

## Builds on (most cited first, 30 of 43)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [EfficientNet: Rethinking Model Scaling for Convolutional Neural Networks](https://mlsanity.com/paper/1905.11946/) (2019)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications](https://mlsanity.com/paper/1704.04861/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Searching for MobileNetV3](https://mlsanity.com/paper/1905.02244/) (2019)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [How transferable are features in deep neural networks?](https://mlsanity.com/paper/1411.1792/) (2014)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs)](https://mlsanity.com/paper/1511.07289/) (2015)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [AutoAugment: Learning Augmentation Policies from Data](https://mlsanity.com/paper/1805.09501/) (2018)
- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [MedMNIST v2 -- A large-scale lightweight benchmark for 2D and 3D biomedical image classification](https://mlsanity.com/paper/2110.14795/) (2021)
- [Network In Network](https://mlsanity.com/paper/1312.4400/) (2013)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)

## Built on by (most cited first, 1 of 1)

- [Stress-Aware Resilient Neural Training](https://mlsanity.com/paper/2508.00098/) (2025)

## Abstract (arXiv)

Activation functions play a critical role in deep neural networks by shaping gradient flow, optimization stability, and generalization. While ReLU remains widely used due to its simplicity, it suffers from gradient sparsity and dead-neuron issues and offers no adaptivity to input statistics. Smooth alternatives such as Swish and GELU improve gradient propagation but still apply a fixed transformation regardless of the activation distribution. In this paper, we propose VeLU, a Variance-enhanced Learning Unit that introduces variance-aware and distributionally aligned nonlinearity through a principled combination of ArcTan-ArcSin transformations, adaptive scaling, and Wasserstein-2 regularization (Optimal Transport). This design enables VeLU to modulate its response based on local activation variance, mitigate internal covariate shift at the activation level, and improve training stability without adding learnable parameters or architectural overhead. Extensive experiments across six deep neural networks show that VeLU outperforms ReLU, ReLU6, Swish, and GELU on 12 vision benchmarks. The implementation of VeLU is publicly available in GitHub.