Multiple sclerosis (MS) is a neurological disease with an early course that is characterized by attacks of clinical worsening, separated by variable periods of remission. The ability to predict the risk of attacks in a given time frame can be used to identify patients who are likely to benefit from more proactive treatment. In this paper, we aim to determine whether deep learning can extract, from segmented lesion masks, latent features that can predict short-term disease activity in patients with early MS symptoms more accurately than lesion volume, which is a very commonly used MS imaging biomarker. More specifically, we use convolutional neural networks to extract latent MS lesion patterns that are associated with early disease activity using lesion masks computed from baseline MR images. The main challenges are that lesion masks are generally sparse and the number of training samples is small relative to the dimensionality of the images. To cope with sparse voxel data, we propose utilizing the Euclidean distance transform (EDT) for increasing information density by populating each voxel with a distance value. To reduce the risk of overfitting resulting from high image dimensionality, we use a synergistic combination of downsampling, unsupervised pretraining, and regularization during training. A detailed analysis of the impact of EDT and unsupervised pretraining is presented. Using the MRIs from 140 subjects in a 7-fold cross-validation procedure, we demonstrate that our prediction model can achieve an accuracy rate of 72.9 % (SD = 10.3 %) over 2 years using baseline MR images only, which is significantly higher than the 65.0 % (SD = 14.6 %) that is attained with the traditional MRI biomarker of lesion load.