Soliton-Inspired Machine Learning Architectures
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2026
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| _version_ | 1866901558993616896 |
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| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <div> <h4>Abstract</h4> <p>We develop two complementary applications of topological soliton physics to machine learning. First, we extend topological data analysis (TDA) beyond standard persistent homology by introducing <b>Hopf persistence</b> — a filtration based on the Hopf invariant $\pi_3(S^2) = \mathbb{Z}$ that captures linking structure invisible to ordinary homology. Second, we propose <b>soliton interaction layers</b> for neural networks, in which feature vectors collide like topological solitons: maintaining their identity through interactions, exchanging only phase information, and carrying integer-valued topological charges that are immune to continuous perturbation. We prove that the resulting learned representations inherit topological protection — adversarial perturbations below a computable energy gap cannot change the representation's topological class. The framework unifies ideas from the Faddeev-Niemi soliton model, persistent homology, and geometric deep learning into a coherent architecture with provable robustness guarantees. <b>This paper is a theoretical proposal:</b> we develop the mathematical framework, prove the core theorems, and analyze computational feasibility, but defer full-scale numerical experiments to future work. We provide detailed benchmark specifications, complexity estimates, and feasibility analysis (Section 10) to guide implementation.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>machine learning</span> <span>topology</span> <span>soliton</span> <span>TDA</span> <span>neural networks</span> <span>applied</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-25</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163353">10.5281/zenodo.19163353</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19228137 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Soliton-Inspired Machine Learning Architectures Novickis, Alexander physics machine-learning topology soliton TDA neural-networks applied <div> <h4>Abstract</h4> <p>We develop two complementary applications of topological soliton physics to machine learning. First, we extend topological data analysis (TDA) beyond standard persistent homology by introducing <b>Hopf persistence</b> — a filtration based on the Hopf invariant $\pi_3(S^2) = \mathbb{Z}$ that captures linking structure invisible to ordinary homology. Second, we propose <b>soliton interaction layers</b> for neural networks, in which feature vectors collide like topological solitons: maintaining their identity through interactions, exchanging only phase information, and carrying integer-valued topological charges that are immune to continuous perturbation. We prove that the resulting learned representations inherit topological protection — adversarial perturbations below a computable energy gap cannot change the representation's topological class. The framework unifies ideas from the Faddeev-Niemi soliton model, persistent homology, and geometric deep learning into a coherent architecture with provable robustness guarantees. <b>This paper is a theoretical proposal:</b> we develop the mathematical framework, prove the core theorems, and analyze computational feasibility, but defer full-scale numerical experiments to future work. We provide detailed benchmark specifications, complexity estimates, and feasibility analysis (Section 10) to guide implementation.</p> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>machine learning</span> <span>topology</span> <span>soliton</span> <span>TDA</span> <span>neural networks</span> <span>applied</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-25</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163353">10.5281/zenodo.19163353</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| title | Soliton-Inspired Machine Learning Architectures |
| topic | physics machine-learning topology soliton TDA neural-networks applied |
| url | https://doi.org/10.5281/zenodo.19228137 |