Subcellular RNA localization is a critical mechanism for the spatial control of gene expression. Its mechanism and precise functional role is not yet very well understood. Single Molecule Fluorescence in Situ Hybridization (smFISH) images allow for the detection of individual RNA molecules with subcellular accuracy. In return, smFISH requires robust methods to quantify and classify RNA spatial distribution. Here, we present PointFISH, a novel computational approach for the recognition of RNA localization patterns. PointFISH is an attention-based network for computing continuous vector representations of RNA point clouds. Trained on simulations only, it can directly process extracted coordinates from experimental smFISH images. The resulting embedding allows scalable and flexible spatial transcriptomics analysis and matches performance of hand-crafted pipelines.