Abstract: This short paper presents the main findings of our work titled Informed Down-Sampled Lexicase Selection: Identifying Productive Training Cases for Efficient Problem Solving, which was recently published in the Evolutionary Computation Journal. In this work, we introduce informed down-sampled lexicase selection to dynamically build diverse subsets of training cases during evolution using population statistics. We evaluate our method on a set of program synthesis problems in two genetic programming systems and find that informed down-sampling improves performance in both systems compared to random down-sampling when using lexicase selection. Additionally, we investigate the constructed down-samples and find that informed down-sampling can identify important training cases and does so across different evolutionary runs and systems.