Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of conceptual knowledge through low-dimensional interpretable similarity spaces. These similarity spaces are often based on psychological dissimilarity ratings for a small set of stimuli, which are then transformed into a spatial representation by a technique called multidimensional scaling. Unfortunately, this approach is incapable of generalizing to novel stimuli. In this paper, we use convolutional neural networks to learn a generalizable mapping between perceptual inputs (pixels of grayscale line drawings) and a recently proposed psychological similarity space for the shape domain. We investigate different network architectures (classification network vs. autoencoder) and different training regimes (transfer learning vs. multi-task learning). Our results indicate that a classification-based multi-task learning scenario yields the best results, but that its performance is relatively sensitive to the dimensionality of the similarity space.
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