  The difficult problem of relating the static structure of glassy liquids and
their dynamics is a good target for Machine Learning, an approach which excels
at finding complex patterns hidden in data. Indeed, this approach is currently
a hot topic in the glassy liquids community, where the state of the art
consists in Graph Neural Networks (GNNs), which have great expressive power but
are heavy models and lack interpretability. Inspired by recent advances in the
field of Machine Learning group-equivariant representations, we build a GNN
that learns a robust representation of the glass' static structure by
constraining it to preserve the roto-translation (SE(3)) equivariance. We show
that this constraint significantly improves the predictive power at comparable
or reduced number of parameters but most importantly, improves the ability to
generalize to unseen temperatures. While remaining a Deep network, our model
has improved interpretability compared to other GNNs, as the action of our
basic convolution layer relates directly to well-known rotation-invariant
expert features. Through transfer-learning experiments displaying unprecedented
performance, we demonstrate that our network learns a robust representation,
which allows us to push forward the idea of a learned structural order
parameter for glasses.
