Topological Effects in Neural Network Field Theory
This work provides a theoretical extension for researchers in mathematical physics and machine learning, though it appears incremental as it builds on existing neural network field theory frameworks.
The authors tackled the problem of extending neural network field theory to topological settings by incorporating discrete parameters labeling topological quantum numbers, successfully recovering the Berezinskii-Kosterlitz-Thouless transition and verifying T-duality in bosonic string theory with specific transformations and enhancements.
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.