The task of hyper-parameter optimization (HPO) is burdened with heavy computational costs due to the intractability of optimizing both a model's weights and its hyper-parameters simultaneously. In this work, we introduce a new class of HPO method and explore how the low-rank factorization of the convolutional weights of intermediate layers of a convolutional neural network can be used to define an analytical response surface for optimizing hyper-parameters, using only training data. We quantify how this surface behaves as a surrogate to model performance and can be solved using a trust-region search algorithm, which we call autoHyper. The algorithm outperforms state-of-the-art such as Bayesian Optimization and generalizes across model, optimizer, and dataset selection. Our code can be found at \url{https://github.com/MathieuTuli/autoHyper}.
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