Ok.. the naive approach works great for the toy models, though there is an overfit threshold of the number of points. Simply, the increment of randomness by putting more points causes this overfit.

This can give some implications when we pool down the features, extracted from these point clouds.

A simple MLP with naive coordinate values can give a 90% accuracy for classifying these two kinds of point clouds.

So... this is the limitation of the featureless MLP approach. To break this 90% barrier, we need to explore various feature extractions with new more complex NN baselines.

My guess is to combine CNN-ish Networks with Healpix-ish Convolution Kernels.