  We propose an approach to symbolic regression based on a novel variational
autoencoder for generating hierarchical structures, HVAE. It combines simple
atomic units with shared weights to recursively encode and decode the
individual nodes in the hierarchy. Encoding is performed bottom-up and decoding
top-down. We empirically show that HVAE can be trained efficiently with small
corpora of mathematical expressions and can accurately encode expressions into
a smooth low-dimensional latent space. The latter can be efficiently explored
with various optimization methods to address the task of symbolic regression.
Indeed, random search through the latent space of HVAE performs better than
random search through expressions generated by manually crafted probabilistic
grammars for mathematical expressions. Finally, EDHiE system for symbolic
regression, which applies an evolutionary algorithm to the latent space of
HVAE, reconstructs equations from a standard symbolic regression benchmark
better than a state-of-the-art system based on a similar combination of deep
learning and evolutionary algorithms.\v{z}
