{"ID":2893395,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.12874","arxiv_id":"2507.12874","title":"Topology-Aware Activation Functions in Neural Networks","abstract":"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.","short_abstract":"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 \"cuttin...","url_abs":"https://arxiv.org/abs/2507.12874","url_pdf":"https://arxiv.org/pdf/2507.12874v1","authors":"[\"Pavel Snopov\",\"Oleg R. Musin\"]","published":"2025-07-17T07:48:36Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.NE\"]","methods":"[]","has_code":false,"code_links":[{"ID":612051,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2893395,"paper_url":"https://arxiv.org/abs/2507.12874","paper_title":"Topology-Aware Activation Functions in Neural Networks","repo_url":"https://github.com/Snopoff/Topology-Aware-Activations","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}