In machine learning, pattern classification assigns high-dimensional vectors (observations) to classes based on generalization from examples. Artificial neural networks currently achieve state-of-the-art results in this task. Although such networks are typically used as black-boxes, they are also widely believed to learn (high-dimensional) higher-level representations of the original observations. In this paper, we propose using dimensionality reduction for two tasks: visualizing the relationships between learned representations of observations, and visualizing the relationships between artificial neurons. Through experiments conducted in three traditional image classification benchmark datasets, we show how visualization can provide highly valuable feedback for network designers. For instance, our discoveries in one of these datasets (SVHN) include the presence of interpretable clusters of learned representations, and the partitioning of artificial neurons into groups with apparently related discriminative roles.