  Understanding and anticipating intraoperative events and actions is critical
for intraoperative assistance and decision-making during minimally invasive
surgery. Automated prediction of events, actions, and the following
consequences is addressed through various computational approaches with the
objective of augmenting surgeons' perception and decision-making capabilities.
We propose a predictive neural network that is capable of understanding and
predicting critical interactive aspects of surgical workflow from
intra-abdominal video, while flexibly leveraging surgical knowledge graphs. The
approach incorporates a hypergraph-transformer (HGT) structure that encodes
expert knowledge into the network design and predicts the hidden embedding of
the graph. We verify our approach on established surgical datasets and
applications, including the detection and prediction of action triplets, and
the achievement of the Critical View of Safety (CVS). Moreover, we address
specific, safety-related tasks, such as predicting the clipping of cystic duct
or artery without prior achievement of the CVS. Our results demonstrate the
superiority of our approach compared to unstructured alternatives.
