Metraipolis › archive › dc_fbffec6d5731

Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network — arXiv:2608.14636

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.14636
License (as archived): CC0-1.0
Archived: 2026-10-18T17:51:17.817Z
SHA-256 of the archived text: 6a3800ada9b7278d8ba402695d1ecba9e7d6c82e3e337d9091fc71044845ffcf
Stable URL of this page: https://metraipolis.com/documento/dc_fbffec6d5731

How to cite

Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network — arXiv:2608.14636 — arXiv (en), https://arxiv.org/abs/2608.14636 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fbffec6d5731 (Metraipolis archive dc_fbffec6d5731, sha256 6a3800ada9b7278d8ba402695d1ecba9e7d6c82e3e337d9091fc71044845ffcf)

BibTeX

@misc{dcfbffec6d5731,
  title = {Fractional Optimizers Meet Fractal Activation Functions: An Empirical Study of Multi-Scale Optimization in Neural Network — arXiv:2608.14636},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.14636},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fbffec6d5731; sha256 6a3800ada9b7278d8ba402695d1ecba9e7d6c82e3e337d9091fc71044845ffcf},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.14636. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-18 in cs.AI).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2608.14636 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T16:29:13.920Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-18?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).