Forthcoming imaging surveys will potentially increase the number of
known galaxy-scale strong lenses by several orders of magnitude. For
this to happen, images of tens of millions of galaxies will have to be
inspected to identify potential candidates. In this context, deep
learning techniques are particularly suitable for the finding patterns
in large data sets, and convolutional neural networks (CNNs) in
particular can efficiently process large volumes of images. We assess
and compare the performance of three network architectures in the
classification of strong lensing systems on the basis of their
morphological characteristics. We train and test our models on different
subsamples of a data set of forty thousand mock images, having
characteristics similar to those expected in the wide survey planned
with the ESA mission \Euclid, gradually including larger fractions of
faint lenses. We also evaluate the importance of adding information
about the colour difference between the lens and source galaxies by
repeating the same training on single-band and multi-band images. Our
models find samples of clear lenses with $\gtrsim 90\%$ precision and
completeness, without significant differences in the performance of the
three architectures. Nevertheless, when including lenses with fainter
arcs in the training set, the three models' performance deteriorates
with accuracy values of $\sim 0.87$ to $\sim 0.75$ depending on the
model. Our analysis confirms the potential of the application of CNNs to
the identification of galaxy-scale strong lenses. We suggest that
specific training with separate classes of lenses might be needed for
detecting the faint lenses since the addition of the colour information
does not yield a significant improvement in the current analysis, with
the accuracy ranging from $\sim 0.89$ to $\sim 0.78$ for the different
models.