We explore the application of deep learning techniques to accelerate gravitational wave surrogate modeling. We focus on two recent approaches, using artificial neural networks (ANNs) with residual error modeling and autoencoder-driven spiral representation learning. For the ANN method, we demonstrate that adding a second network to learn residual errors significantly improves surrogate model accuracy. The autoencoder approach reveals an inherent spiral structure in the latent space representation of empirical interpolation coefficients. We take advantage of this insight to develop a neural spiral module that can be integrated into network architectures to accelerate training and improve performance. Comprehensive evaluations show that these methods achieve state-of-the-art accuracy while enabling faster waveform generation. The techniques presented have the potential to substantially accelerate gravitational wave data analysis as detector sensitivity improves and event rates increase.