# Topology-Aware Activation Functions in Neural Networks

arXiv: https://arxiv.org/abs/2507.12874 · HTML: https://mlsanity.com/paper/2507.12874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 6 references that are in the map.
- First posted on arXiv 17 Jul 2025.

## Builds on (most cited first, 3 of 3)

- [Topology of deep neural networks](https://mlsanity.com/paper/2004.06093/) (2020)
- [Activation Landscapes as a Topological Summary of Neural Network Performance](https://mlsanity.com/paper/2110.10136/) (2021)
- [Graph-Adaptive Activation Functions for Graph Neural Networks](https://mlsanity.com/paper/2009.06723/) (2020)

## Abstract (arXiv)

This study explores novel activation functions that enhance the ability of neural networks to manipulate data topology during training. Building on the limitations of traditional activation functions like ReLU, we propose SmoothSplit and ParametricSplit, which introduce topology "cutting" capabilities. These functions enable networks to transform complex data manifolds effectively, improving performance in scenarios with low-dimensional layers. Through experiments on synthetic and real-world datasets, we demonstrate that ParametricSplit outperforms traditional activations in low-dimensional settings while maintaining competitive performance in higher-dimensional ones. Our findings highlight the potential of topology-aware activation functions in advancing neural network architectures. The code is available via https://github.com/Snopoff/Topology-Aware-Activations.