A collection of new
approaches to building and training neural
networks, collectively referred to as deep learning, are attracting
attention in theoretical chemistry. Several groups aim to replace
computationally expensive <i>ab initio</i> quantum mechanics
calculations with learned estimators. This raises questions about
the representability of complex quantum chemical systems with neural
networks. Can local-variable models efficiently approximate nonlocal
quantum chemical features? Here, we find that convolutional architectures,
those that only aggregate information locally, cannot efficiently
represent aromaticity and conjugation in large systems. They cannot
represent long-range nonlocality known to be important in quantum
chemistry. This study uses aromatic and conjugated systems computed
from molecule graphs, though reproducing quantum simulations is the
ultimate goal. This task, by definition, is both computable and known
to be important to chemistry. The failure of convolutional architectures
on this focused task calls into question their use in modeling quantum
mechanics. To remedy this heretofore unrecognized deficiency, we introduce
a new architecture that propagates information back and forth in waves
of nonlinear computation. This architecture is still a local-variable
model, and it is both computationally and representationally efficient,
processing molecules in sublinear time with far fewer parameters than
convolutional networks. Wave-like propagation models aromatic and
conjugated systems with high accuracy, and even models the impact
of small structural changes on large molecules. This new architecture
demonstrates that some nonlocal features of quantum chemistry can
be efficiently represented in local variable models