  In simulation-based models of the galaxy-halo connection, theoretical
predictions for galaxy clustering and lensing are typically made based on Monte
Carlo realizations of a mock universe. In this paper, we use Subhalo Abundance
Matching (SHAM) as a toy model to introduce an alternative to stochastic
predictions based on mock population, demonstrating how to make
simulation-based predictions for clustering and lensing that are both exact and
differentiable with respect to the parameters of the model. Conventional
implementations of SHAM are based on iterative algorithms such as
Richardson-Lucy deconvolution; here we use the JAX library for automatic
differentiation to train SHAMNet, a neural network that accurately approximates
the stellar-to-halo mass relation (SMHM) defined by abundance matching. In our
approach to making differentiable predictions for large scale structure, we map
parameterized PDFs onto each simulated halo, and calculate gradients of summary
statistics of the galaxy distribution by using autodiff to propagate the
gradients of the SMHM through the statistical estimators used to measure one-
and two-point functions. Our techniques are quite general, and we conclude with
an overview of how they can be applied in tandem with more complex,
higher-dimensional models, creating the capability to make differentiable
predictions for the multi-wavelength universe of galaxies.
