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Characterizing the physical properties of cool supergiants allows us to probethe final stages of a massive star's evolution before it undergoes corecollapse. Despite their importance, the fundamental properties for these stars-- $T_{\rm eff}$ and $\log L/L_\odot$ -- are only known for a limited number ofobjects. The third data release of the Gaia mission contains precise photometryand low-resolution spectroscopy of hundreds of cool supergiants in the LMC withwell-constrained properties. Using these data, we train a simple andeasily-interpretable machine learning model to regress effective temperaturesand luminosities with high accuracy and precision comparable to the trainingdata. We then apply our model to 5000 cool supergiants, many of which have nopreviously-published $T_{\rm eff}$ or $L$ estimates. The resultingHertzprung-Russell diagram is well-populated, allowing us to study thedistribution of cool supergiants in great detail. Examining the luminosityfunctions of our sample, we find a notable flattening in the luminosityfunction of yellow supergiants above $\log L/L_\odot=5$, and a correspondingsteepening of the red supergiant luminosity function. We place this finding incontext with previous results, and present its implications for the infamousred supergiant problem.

Physical Properties of 5,000 Cool LMC Supergiants with Gaia XP Spectra:  A Detailed Portrait of the Upper HR Diagram Hints at Missing Supernova  Progenitors