In this talk I will review essentials of quantum field theory (QFT) and demonstrate how the function-space distribution of many neural networks (NNs) shares similar properties. This allows, for instance, computation of correlators of neural network outputs in terms of Feynman diagrams and a direct analogy between non-Gaussian corrections in NN distributions and particle interactions. Some cases yield divergences in perturbation theory, requiring the introduction of regularization and renormalization. Potential advantages of this perspective will be discussed, including a duality between function-space and parameter-space descriptions of neural networks.