  Community detection is an essential tool for unsupervised data exploration
and revealing the organisational structure of networked systems. With a long
history in network science, community detection typically relies on objective
functions, optimised with custom-tailored search algorithms, but often without
leveraging recent advances in deep learning. Recently, first works have started
incorporating such objectives into loss functions for neural graph clustering
and pooling. We consider the map equation, a popular information-theoretic
objective function for unsupervised community detection, and express it in
differentiable tensor form for optimisation through gradient descent. Our
formulation turns the map equation compatible with any neural network
architecture, enables end-to-end learning, incorporates node features, and
chooses the optimal number of clusters automatically, all without requiring
explicit regularisation. Applied to unsupervised graph clustering tasks, we
achieve competitive performance against state-of-the-art neural graph
clustering baselines in synthetic and real-world datasets.
