Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network

[2608.14636] Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2608.14636 (cs) [Submitted on 28 Jul 2026] Title: Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network Authors: Sebastian Raubitzek , Georg Goldenits , Sebastian Schrittwieser , Philip König , Kevin Mallinger View a PDF of the paper titled Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network, by Sebastian Raubitzek and 4 other authors View PDF HTML (experimental) Abstract: Fractional optimization methods and fractal activation functions are two independent directions for improving neural network training. Fractional optimizers extend first-order optimization through fractional derivatives and memory effects, whereas fractal activations introduce multi-scale nonlinear representations based on self-similar Weierstrass- and Blancmange-type functions. Here, we investigate their interaction within a unified experimental framework. We evaluate fractional optimizer families on Ackley and Himmelblau benchmark surfaces, in standard form and with additive Weierstrass-type perturbations, and then in feed-forward neural networks with conventional and fractal activations on ten classification datasets. The comparison includes standard methods, regularization-style optimizers, explicit and adaptive memory-based fractional optimizers, and other representative literature methods. Overall, fractional optimization and fractal activations show useful but selective pairings. Regularization-style fractional scaling performs well with selected fractal activations in network training, while Grünwald--Letnikov memory is most relevant on perturbed surfaces. Adaptive memory improves plain memory substitution in several cases, supporting controlled fractional memory as a promising direction rather than a universal replacement. Comments: Quite extensive paper, more than 100 pages Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2608.14636 [cs.LG] (or arXiv:2608.14636v1 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2608.14636 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Sebastian Raubitzek Dr. techn. MSc. BSc. [ view email ] [v1] Tue, 28 Jul 2026 08:31:24 UTC (24,213 KB) Full-text links: Access Paper: View a PDF of the paper titled Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network, by Sebastian Raubitzek and 4 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2026-08 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Artificial neural networks: a practical review of applications involving fractional calculus#19797
• Mixed-Precision Ab Initio Tensor Network State Methods Adapted for NVIDIA Blackwell Technology via Emulated FP64 Arithmetic.#375469
• Neural Network Operator-Based Fractal Approximation: Smoothness Preservation and Convergence Analysis#1082943
• QUADS: Stabilizing NVFP4 Reinforcement Learning for MoE via QUantization-error Alignment across Dual Sides#381767
• Multimodal FRACTAL-MSI and Image Fusion Improves Detection and Resolution of Biomolecule Imaging.#613369