The electroencephalography (EEG), which is one of the easiest modes of recording brain activations in a non-invasive manner, is often distorted due to recording artifacts which adversely impacts the stimulus-response analysis. The most prominent techniques thus far attempt to improve the stimulus-response correlations using linear methods. In this paper, we propose a neural network based correlation analysis framework that significantly improves over the linear methods for auditory stimuli. A deep model is proposed for intra-subject audio-EEG analysis based on directly optimizing the correlation loss. Further, a neural network model with a shared encoder architecture is proposed for improving the inter-subject stimulus response correlations. These models attempt to suppress the EEG artifacts while preserving the components related to the stimulus. Several experiments are performed using EEG recordings from subjects listening to speech and music stimuli. In these experiments, we show that the deep models improve the Pearson correlation significantly over the linear methods (average absolute improvements of 7.4% in speech tasks and 29.3% in music tasks). We also analyze the impact of several model parameters on the stimulus-response correlation.