One of the most concealed parts of the known Universe is the far side of our own Galaxy. Occupying only a few percent of the sky and disguised by interstellar dust, stellar tracers in these distant regions have been elusive until now. The exploration of these vast uncharted areas of the Milky Way by deep photometric surveys has just begun. We conducted a census of distant classical and type II Cepheids along the southern Galactic mid-plane using near-infrared photometry from the VVV (VISTA Variables in the Vía Láctea) Survey. After the complete revision of the survey's calibration, we leveraged the photometry to its full potential. A machine-learned classification of the Cepheids based on infrared light curves was performed for the first time, using a convolutional neural network. We have discovered 640 classical and over 500 type II Cepheids in the IV-th Galactic quadrant and behind the bulge, with up to 40 magnitudes of visual extinction. We also employ neural networks to estimate the Cepheids' reddening from sparse photometric data, revealing a space-varying extinction curve toward low Galactic latitude regions. The type II Cepheids were used to probe the 3-dimensional structure of the ancient stellar population in the inner bulge. Likewise, we used the classical Cepheids to trace large-scale spatial structures of the Galactic disk.