  In recent years large visual-language (V+L) models have achieved great
success in various downstream tasks. However, it is not well studied whether
these models have a conceptual grasp of the visual content. In this work we
focus on conceptual understanding of these large V+L models. To facilitate this
study, we propose novel benchmarking datasets for probing three different
aspects of content understanding, 1) \textit{relations}, 2)
\textit{composition}, and 3) \textit{context}. Our probes are grounded in
cognitive science and help determine if a V+L model can, for example, determine
if snow garnished with a man is implausible, or if it can identify beach
furniture by knowing it is located on a beach. We experimented with many recent
state-of-the-art V+L models and observe that these models mostly \textit{fail
to demonstrate} a conceptual understanding. This study reveals several
interesting insights such as that \textit{cross-attention} helps learning
conceptual understanding, and that CNNs are better with \textit{texture and
patterns}, while Transformers are better at \textit{color and shape}. We
further utilize some of these insights and investigate a \textit{simple
finetuning technique} that rewards the three conceptual understanding measures
with promising initial results. The proposed benchmarks will drive the
community to delve deeper into conceptual understanding and foster advancements
in the capabilities of large V+L models. The code and dataset is available at:
\url{https://tinyurl.com/vlm-robustness}
