the formal charge, (4) the hybridization state, (5) the chiral tag as defined by RDKit, (6) whether the atom is in a ring, and (7) the number of hydrogens covalently bound to the atom. MRS2 expands on this concept and implements a neural network architecture with two parallel set representation layers, where the first takes the same input as the single layer in MSR1. In contrast, the second takes a set of vectors encoding bond invariants as an input. We include the following bond invariants: (1) the bond type, (2) whether the bond is aromatic, (3) whether the bond is conjugated, (4) the degree of the two atoms forming the bond, and (5) the atomic numbers of the two atoms forming the bond. Therefore, with MSR2, we introduce more information about molecular topology while avoiding explicit definitions of topology beyond bonded atom pairs. In addition to the purely set-representation architectures, we introduce SR-GINE, a graph invariant network with edge attributes (GINE) and a set RepSet representation pooling layer instead of global mean pooling in the vanilla GINE implementation. In all our architectures, the output of the set representation layer is read by an MLP with a single hidden layer for regression or classification. In the case of dual-set architectures, such as MSR2, the two sets' outputs are first concatenated. Finally, we chose the combination of RepSet and GINE based on their respective reported performances and the inert interpretability of RepSet . Further reasoning and data substantiating our choice can be found in Section 4.3. To benchmark our proposed architectures, we rely on well-known and recently published data sets to compare our method to widely used graph-based methods as a baseline. Initially, we focused on evaluating our methods on data sets commonly known as the MoleculeNet benchmark. We selected the relatively small data set BBBP (n = 2039), with Molecular Set Representation Learning the task of classifying small molecules on whether they penetrate the blood-brain barrier, to tune the hyperparameters, namely the number of hidden sets, the number of elements in the hidden sets, the number of epochs, as well as the number of hidden channels in the MLPs of all our models. Unless otherwise indicated, the established hyperparameters were used for all the benchmarks discussed in this study. We then compared our model to the performance achieved by MGCN (multiscale graph convolutional network), SchNet (quantum chemical deep tensor neural network), GCN (graph convolutional network), GIN (graph isomorphism network), and D-MPNN (directed message-passing neural network), as reported by Wang et al. [20]. In addition, we compare our approach to the current state of the art outside graph neural network-based approaches, namely MolFormer, a chemical large language model trained on approximately 100 million molecules extracted from the ZINC and PubChem databases . As a control, we benchmark an implementation of GINE with the standard global mean-pooling layer and the same one-hot encoded vectors as atom and bond attributes that were used for MSR1 and MSR2 . For all data sets, Murcko scaffold splits in accordance with Yang et al. [17] and