At the heart of both lossy compression and clustering is a trade-off between the fidelity and size of the learned representation. Our goal is to map out and study the Pareto frontier that quantifies this trade-off. We focus on the optimization of the Deterministic Information Bottleneck (DIB) objective over the space of hard clusterings. https://www.roneverhart.com/5-15P-ANGLE-PLUG-B-W-HUBBELL-HBL5266CA/