The performance of machine learning (ML) models fundamentally hinges on their ability to discriminate between relevant and irrelevant features in data. We introduce a first-of-its-kind Wilsonian RG framework to analyze the predictions of overparameterized neural networks (NN), these are models characterized by an excess of parameters relative to the complexity of the task. These networks, trained via supervised learning, are known to produce noisy outputs. In our formulation, irrelevant features within the data are systematically coarse-grained through momentum shell RG, inducing an RG flow that governs the evolution of noise in the predictions. When the irrelevant features follow a Gaussian distribution, this RG flow exhibits universality across different NN architectures. In contrast, non-Gaussian features give rise to more intricate, data-dependent RG flows. This approach reveals novel behaviors in NNs that have eluded conventional ML methods. By advancing beyond philosophical analogies between RG and ML, our framework offers a field theory-based methodology for understanding feature learning.