AbstractComputational intelligence, particularly deep learning, offers powerful tools for discriminating and generating samples such as images. Deep learning methods have been used in different artistic contexts for neural style transfer, artistic style recognition, and musical genre recognition. Using a constrained manifold analysis protocol, we discuss to what extent spaces induced by deep-learning convolutional neural networks can capture historical/stylistic progressions in music and visual art. We use a path-finding algorithm, called principal path, to move from one point to another. We apply it to the vector space induced by convolutional neural networks. We perform experiments with visual artworks and songs, considering a subset of classes. Within this simplified scenario, we recover a reasonable historical/stylistic progression in several cases. We use the principal path algorithm to conduct an evolutionary analysis of vector spaces induced by convolutional neural networks. We perform several experiments in the visual art and music spaces. The principal path algorithm finds reasonable connections between visual artworks and songs from different styles/genres with respect to the historical evolution when a subset of classes is considered. This approach could be used in many areas to extract evolutionary information from an arbitrary high-dimensional space and deliver interesting cognitive insights.