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High-resolution spectroscopic surveys of the Milky Way have entered the BigData regime and have opened avenues for solving outstanding questions inGalactic archaeology. However, exploiting their full potential is limited bycomplex systematics, whose characterization has not received much attention inmodern spectroscopic analyses. In this work, we present a novel method todisentangle the component of spectral data space intrinsic to the stars fromthat due to systematics. Using functional principal component analysis on asample of $18,933$ giant spectra from APOGEE, we find that the intrinsicstructure above the level of observational uncertainties requires ${\approx}$10functional principal components (FPCs). Our FPCs can reduce the dimensionalityof spectra, remove systematics, and impute masked wavelengths, thereby enablingaccurate studies of stellar populations. To demonstrate the applicability ofour FPCs, we use them to infer stellar parameters and abundances of 28 giantsin the open cluster M67. We employ Sequential Neural Likelihood, asimulation-based Bayesian inference method that learns likelihood functionsusing neural density estimators, to incorporate non-Gaussian effects inspectral likelihoods. By hierarchically combining the inferred abundances, welimit the spread of the following elements in M67: $\mathrm{Fe} \lesssim 0.02$dex; $\mathrm{C} \lesssim 0.03$ dex; $\mathrm{O}, \mathrm{Mg}, \mathrm{Si},\mathrm{Ni} \lesssim 0.04$ dex; $\mathrm{Ca} \lesssim 0.05$ dex; $\mathrm{N},\mathrm{Al} \lesssim 0.07$ dex (at 68% confidence). Our constraints suggest alack of self-pollution by core-collapse supernovae in M67, which has promisingimplications for the future of chemical tagging to understand the starformation history and dynamical evolution of the Milky Way.

Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67