Abstract: Transformer-based deep NLP models are trained using hundreds of millions of parameters, limiting their applicability in computationally constrained environments. In this paper, we study the cause of these limitations by defining a notion of Redundancy, which we categorize into two classes: General Redundancy and Task-specific Redundancy. We dissect two popular pretrained models, BERT and XLNet, studying how much redundancy they exhibit at a representation-level and at a more fine-grained neuron-level. Our analysis reveals interesting insights, such as i) 85% of the neurons across the network are redundant and ii) at least 92% of them can be removed when optimizing towards a downstream task. Based on our analysis, we present an efficient feature-based transfer learning procedure, which maintains 97% performance while using at-most 10% of the original neurons.