# Shifting Mean Activation Towards Zero with Bipolar Activation Functions

arXiv: https://arxiv.org/abs/1709.04054 · HTML: https://mlsanity.com/paper/1709.04054/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2017.

## Built on by (most cited first, 5 of 5)

- [Constrained Monotonic Neural Networks](https://mlsanity.com/paper/2205.11775/) (2022)
- [Smooth Min-Max Monotonic Networks](https://mlsanity.com/paper/2306.01147/) (2023)
- [Fully Non-Homogeneous Atmospheric Scattering Modeling with Convolutional Neural Networks for Single Image Dehazing](https://mlsanity.com/paper/2108.11292/) (2021)
- [Enhancing Monotonic Modeling with Spatio-Temporal Adaptive Awareness in Diverse Marketing](https://mlsanity.com/paper/2406.14132/) (2024)
- [Rethinking Activation Functions: Reducing Bias Can Improve Learning](https://mlsanity.com/paper/2610.14500/) (2026)

## Abstract (arXiv)

We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with up to 144 layers, and show that bipolar activation functions help learning in this setting. On the Penn Treebank and Text8 language modeling tasks we obtain competitive results, improving on the best reported results for non-gated networks. In experiments with convolutional neural networks without batch normalization, we find that bipolar activations produce a faster drop in training error, and results in a lower test error on the CIFAR-10 classification task.