  Modern astronomical surveys are observing spectral data for millions of
stars. These spectra contain chemical information that can be used to trace the
Galaxy's formation and chemical enrichment history. However, extracting the
information from spectra, and making precise and accurate chemical abundance
measurements are challenging. Here, we present a data-driven method for
isolating the chemical factors of variation in stellar spectra from those of
other parameters (i.e. \teff, \logg, \feh). This enables us to build a spectral
projection for each star with these parameters removed. We do this with no ab
initio knowledge of elemental abundances themselves, and hence bypass the
uncertainties and systematics associated with modeling that rely on synthetic
stellar spectra. To remove known non-chemical factors of variation, we develop
and implement a neural network architecture that learns a disentangled spectral
representation. We simulate our recovery of chemically identical stars using
the disentangled spectra in a synthetic APOGEE-like dataset. We show that this
recovery declines as a function of the signal to noise ratio, but that our
neural network architecture outperforms simpler modeling choices. Our work
demonstrates the feasibility of data-driven abundance-free chemical tagging.
