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This paper extends neural network field theory to topological settings by incorporating discrete parameters representing topological quantum numbers. They recover the Berezinskii--Kosterlitz--Thouless transition, validating the approach against known physics. Furthermore, they verify the T-duality of the bosonic string, demonstrating the framework's ability to capture advanced theoretical physics concepts.
Neural networks can now model topological quantum phenomena and string theory dualities, suggesting a new bridge between deep learning and fundamental physics.
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.