Computational representation of molecules can take many forms, including graphs, string encodings of graphs, binary vectors or learned embeddings in the form of real-valued vectors. These representations are then used in downstream classification and regression tasks using a wide range of machine learning models. However, existing models come with limitations, such as the requirement for clearly defined chemical bonds, which often do not represent the true underlying nature of a molecule. Here we propose a framework for molecular machine learning tasks based on set representation learning. We show that learning on sets of atom invariants alone reaches the performance of state-of-the-art graph-based models on the most-used chemical benchmark datasets and that introducing a set representation layer into graph neural networks can surpass the performance of established methods in the domains of chemistry, biology and material science. We introduce specialized set representation-based neural network architectures for reaction-yield and protein-ligand binding-affinity prediction. Overall, we show that the technique we denote molecular set representation learning is both an alternative and an extension to graph neural network architectures for machine learning tasks on molecules, molecule complexes and chemical reactions.