  At high redshift, observational limitations reduce the effectiveness of
visual morphological classifications. Quantitative measures of galaxy structure
provide an alternative, with model-independent approaches being preferred, due
to the variety of galaxy morphologies in the early universe. Non-parametric
measurements, such as the CAS system, have therefore become an important
tool.Recently, convolutional neural networks (CNNs) have been shown to be adept
at image analysis, and are beginning to supersede traditional measurements of
visual morphology and model-based structural parameters. In this work, we take
a further step by extending CNNs to measure well known non-parametric
structural quantities: concentration ($C$) and asymmetry ($A$). We train CNNs
to predict $C$ and $A$ from individual images of $\sim 150,000$ galaxies at $0
< z < 7$ in the CANDELS fields, using Bayesian hyperparameter optimisation to
select suitable network architectures. Our resulting networks accurately
reproduce measurements compared with standard algorithms. Furthermore, using
simulated images, we show that our networks are more stable than the standard
algorithms at low signal-to-noise. While both approaches suffer from similar
systematic biases with redshift, these remain small out to $z \sim 7$. Once
trained, measurements with our networks are $> 10^3$ times faster than previous
methods. Our approach is thus not only able to reproduce standard measurements
of non-parametric quantities, but gives superior results in substantially less
time. This will be vital for making best use of the large and complex datasets
provided by upcoming galaxy surveys, such as Euclid and Rubin-LSST.
