Topology-Aware Activation Functions in Neural Networks

Fuente: arXiv
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Autori principali: Snopov, Pavel, Musin, Oleg R.
Natura: Preprint
Pubblicazione: 2025
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author Snopov, Pavel
Musin, Oleg R.
author_facet Snopov, Pavel
Musin, Oleg R.
contents 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 $\mathrm{ReLU}$, we propose $\mathrm{SmoothSplit}$ and $\mathrm{ParametricSplit}$, 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 $\mathrm{ParametricSplit}$ 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.
format Preprint
id arxiv_https___arxiv_org_abs_2507_12874
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Topology-Aware Activation Functions in Neural Networks
Snopov, Pavel
Musin, Oleg R.
Machine Learning
Neural and Evolutionary Computing
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 $\mathrm{ReLU}$, we propose $\mathrm{SmoothSplit}$ and $\mathrm{ParametricSplit}$, 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 $\mathrm{ParametricSplit}$ 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.
title Topology-Aware Activation Functions in Neural Networks
topic Machine Learning
Neural and Evolutionary Computing
url https://arxiv.org/abs/2507.12874