The backbones of modern-day Deep Learning, Neural Networks (NN), define field theories on Euclidean background through their architectures, where field interaction strengths depend on the choice of NN architecture width and stochastic parameters. Infinite width limit of NN architectures, combined with independently distributed stochastic parameters, lead to generalized free field theories by the Central Limit Theorem (CLT). Small and large deviations from the CLT, due to finite architecture width and/or correlated stochastic parameters, respectively give rise to weakly coupled field theories and non-perturbative non-Lagrangian field theories in Neural Networks. I will present a systematic exploration of Neural Network field theories via a dual framework of NN parameters: non-Gaussianity, locality by cluster decomposition, and symmetries are studied without necessitating the knowledge of an action. Such a dual description to statistical or quantum field theories in Neural Networks can have potential implications for physics.