Derives Schwinger-Dyson equations and Ward identities in NN-FT to study anomalies in QFTs via a conserved parameter-space current, yielding a new perspective on symmetries.
Topological Effects in Neural Network Field Theory
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abstract
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.
fields
hep-th 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
α=0 architecture in NNFT minimizes finite-width variance, removes IR corrections, and sets a fundamental SNR bound for correlation functions in scalar field theory.
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Anomalies in Neural Network Field Theory
Derives Schwinger-Dyson equations and Ward identities in NN-FT to study anomalies in QFTs via a conserved parameter-space current, yielding a new perspective on symmetries.
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Optimal Architecture and Fundamental Bounds in Neural Network Field Theory
α=0 architecture in NNFT minimizes finite-width variance, removes IR corrections, and sets a fundamental SNR bound for correlation functions in scalar field theory.