Mathematics and Machine Learning

Neural network field theory (NN-FT) provides a first principles framework for quantum field theory by replacing the traditional spacetime path integral with a statistical ensemble defined by a network architecture and a density over its parameter space. In this talk, I will explore how the parameter space approach captures Ward identities and encodes anomalies. I also illustrate how NN-FT is modified to include topological sectors. The Berezinskii--Kosterlitz--Thouless transition and T-duality of the bosonic string are illustrative examples.