Recently conducted research demonstrated the potential use of mouse dynamics as a behavioral biometric for user authentication systems. However, the state-of-the-art methods in this field rely on classical machine learning methods that necessitate the design of hand crafted mouse features for feature extraction. To simplify the feature extraction process, we leverage various deep learning architectures for mouse movement sequences classification, including convolutional networks, recurrent networks, and a hybrid model which combines convolutional and recurrent layers. It is known that the training of these networks with random initialization of weights on small datasets will produce models that perform poorly. Therefore, we consider a two-dimensional convolutional neural network that allows transfer learning, which is a domain adaptation technique effective for learning on small datasets. Although employing such architecture may seem counterintuitive, since the temporal information is discarded from the input data, the architecture has outperformed all the other deep architectures investigated, as well as a classical machine learning method. In order to understand the features learned, we adopt the layer-wise relevance propagation (LRP) algorithm to compute relevance scores for each part of the mouse curves. In addition, the models are measured for their usability and effectiveness in realistic scenarios.