  We present a new method to interpret the $\gamma$-ray data of our inner
Galaxy as measured by the Fermi Large Area Telescope (Fermi LAT). We train and
test convolutional neural networks with simulated Fermi-LAT images based on
models tuned to real data. We use this method to investigate the origin of an
excess emission of GeV $\gamma$-rays seen in previous studies. Interpretations
of this excess include $\gamma$ rays created by the annihilation of dark matter
particles and $\gamma$ rays originating from a collection of unresolved point
sources, such as millisecond pulsars. Our new method allows precise
measurements of the contribution and properties of an unresolved population of
$\gamma$-ray point sources in the interstellar diffuse emission model.
