It's a form of compression the dense network acts as compressed representation of the colour mapping to each vertex position, a dense network is good for this because they simply divide points of data with hyperplanes and in 3D mesh vertex positions with associated colors can be divided into color groups by 3-dimensional planes.

pip install tensorflow numpy pandas trimesh "pyglet<2"
python3 run.py

A set of reconstructed PLY files from low to high quality are available here: reconstructed.7z.