The increasing event complexity and data rates foreseen for future LHC coinditions motivate a transition from selecting proton-proton ($pp$) collision events by reconstructing predefined signal candidates to constructing a reduced data stream by interpreting the relevant event features in a signal-agnostic way. We explore the capabilities of deep-learning-based architectures on heavy-flavour physics using LHCb as a case study. Graph-based full-event interpretation techniques address the problem by representing visible products of $pp$ collisions as nodes of a graph, and reconstructing heavy-hadron decay chains hierarchically. A new neutral-particle-aware architecture extends the input data from charged tracks to calorimeter clusters, and uses metric learning to clusterize particles from the same decay chain in a common latent space. Tests on inclusive simulated $pp\to b\bar b$ events show that this approach retains its ability to reconstruct decay chains across a broad range of topologies and multiplicities. We discuss the resulting physics opportunities, with a focus on inclusive $b\to s\ell\ell$ measurements and on searches for exotic hadrons.