Given the vast amounts of data generated by modern particle detectors, computational efficiency is essential for many data-analysis jobs in high-energy physics. We develop a new class of physically interpretable boost invariant polynomial (BIP) features for jet tagging that achieves such efficiency. We show that, for both supervised and unsupervised tasks, integrating BIPs with conventional classification techniques leads to models achieving high accuracy on jet tagging benchmarks while being orders of magnitudes faster to train and evaluate than contemporary deep learning systems.