  Around a glass transition, the dynamics of a supercooled liquid dramatically
slow down, exhibited by caging of particles, while the structural changes
remain subtle. In alternative to recent machine learning studies searching for
structural predictors of glassy dynamics, here we propose to learn directly
particle caging features defined purely according to dynamics. We focus on
three transitions in a simulated hard sphere glass model, the melting of
ultra-stable glasses, the Gardner transition and the liquid to ordinary glass
transition. Implementing the machine learning algorithm based on a two-level
nested neural network, we attain not only proper caging order parameters for
all three transitions, but also a phase classification for input samples. A
finite-size scaling analysis of the phase classification results identifies the
order of melting (first) and Gardner (second) transitions. A false positive is
avoided, as the liquid to glass transition is indicated as a crossover, rather
than a phase transition with a well-defined transition point. This study paves
the way to a generic approach for learning dynamical features in glassy
systems, with a minimum requirement of system-specific knowledge.
