Topological Effects in Neural Network Field Theory
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908934291324928 |
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| author | Ferko, Christian Halverson, James Jejjala, Vishnu Robinson, Brandon |
| author_facet | Ferko, Christian Halverson, James Jejjala, Vishnu Robinson, Brandon |
| contents | Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on $S^1$, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement of the current algebra at self-dual radius, and non-geometric T-fold transition functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_02313 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological Effects in Neural Network Field Theory Ferko, Christian Halverson, James Jejjala, Vishnu Robinson, Brandon High Energy Physics - Theory Disordered Systems and Neural Networks Machine Learning Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete parameters that label the topological quantum number. We recover the Berezinskii--Kosterlitz--Thouless transition, including the spin-wave critical line and the proliferation of vortices at high temperatures. We also verify the T-duality of the bosonic string, showing invariance under the exchange of momentum and winding on $S^1$, the transformation of the sigma model couplings according to the Buscher rules on constant toroidal backgrounds, the enhancement of the current algebra at self-dual radius, and non-geometric T-fold transition functions. |
| title | Topological Effects in Neural Network Field Theory |
| topic | High Energy Physics - Theory Disordered Systems and Neural Networks Machine Learning |
| url | https://arxiv.org/abs/2604.02313 |