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This work introduces novel approaches, based on geometrical deep learning, for predicting protein–protein interactions. A dataset containing both interacting and non-interacting proteins is selected from the Negatome Database. Interactions are predicted from a graph representing the proteins’ three-dimensional macromolecular surfaces. The nodes are described with heat and wave kernel signatures. Twenty-one neural network architectures are proposed and compared; these are based on graph convolutional neural networks, spectral convolutional neural networks, and a novel spatio–spectral spatialized-gated convolutional neural network. The experimental results demonstrate the accuracy and the efficiency of the proposed architectures.