This paper points out that the geometric similarity model used in deep learning lacks psychological validity and proposes a differentiable parameterization for applying Tversky's feature-set-based similarity model to deep learning. Through this, we develop novel neural network components, such as the Tversky projection layer, and demonstrate performance improvements over conventional linear projection layers through various experiments, including image recognition and language modeling. Furthermore, we interpret the two types of projection layers as computing the similarity between input stimuli and learned prototypes, and propose a novel visualization technique that highlights the interpretability of the Tversky projection layer.