Classically perfect fixed-point lattice actions preserve continuum classical properties while reducing lattice artifacts at the quantum level. They allow the extraction of continuum physics from coarser lattices and hence provide an effective way to overcome the challenges of critical slowing down and topological freezing. In this talk I describe how such FP actions can be parametrized through machine learning a gauge covariant convolutional neural network for $SU(3)$ gauge theories in $4d$. I show how they can be used to define classically perfect gradient-flow observables which are free of tree-level lattice artifacts to all orders.