Automatic Symmetry Discovery with Lie Algebra Convolutional Network

Existing equivariant neural networks for continuous groups require discretization or group representations. All these approaches require detailed knowledge of the group parametrization and cannot learn entirely new symmetries. We propose to work with the Lie algebra (infinitesimal generators) instead of the Lie group.Our model, the Lie algebra convolutional network (L-conv) can learn potential symmetries and does not require discretization of the group. We show that L-conv can serve as a building block to construct any group equivariant architecture. We discuss how CNNs and Graph Convolutional Networks are related to and can be expressed as L-conv with appropriate groups. We also derive the MSE loss for a single L-conv layer and find a deep relation with Lagrangians used in physics, with some of the physics aiding in defining generalization and symmetries in the loss landscape. Conversely, L-conv could be used to propose more general equivariant ansatze for scientific machine learning.

Understanding the onset of hot streaks across artistic, cultural, and scientific careers

Hot streaks dominate the main impact of creative careers. Despite their ubiquitous nature across a wide range of creative domains, it remains unclear if there is any regularity underlying the beginning of hot streaks. Here, we develop computational methods using deep learning and network science and apply them to novel, large-scale datasets tracing the career outputs of artists, film directors, and scientists, allowing us to build high-dimensional representations of the artworks, films, and scientific publications they produce. By examining individuals career trajectories within the underlying creative space, we find that across all three domains, individuals tend to explore diverse styles or topics before their hot streak, but become notably more focused in what they work on after the hot streak begins. Crucially, we find that hot streaks are associated with neither exploration nor exploitation behavior in isolation, but a particular sequence of exploration followed by exploitation, where the transition from exploration to exploitation closely traces the onset of a hot streak. Overall, these results unveil among the first identifiable regularity underlying the onset of hot streaks, which appears universal across diverse creative domains, suggesting that a sequential view of creative strategies that balances experimentation and implementation may be particularly powerful for producing long-lasting contributions, which may have broad implications for identifying and nurturing creative talents.

Finding Patient Zero: Learning Contagion Source with Graph Neural Networks

Locating the source of an epidemic, or patient zero (P0), can provide critical insights into the infections transmission course and allow efficient resource allocation. Existing methods use graph-theoretic centrality measures and expensive message-passing algorithms, requiring knowledge of the underlying dynamics and its parameters. In this paper, we revisit this problem using graph neural networks (GNNs) to learn P0. We establish a theoretical limit for the identification of P0 in a class of epidemic models. We evaluate our method against different epidemic models on both synthetic and a real-world contact network considering a disease with history and characteristics of COVID-19. % We observe that GNNs can identify P0 close to the theoretical bound on accuracy, without explicit input of dynamics or its parameters. In addition, GNN is over 100 times faster than classic methods for inference on arbitrary graph topologies. Our theoretical bound also shows that the epidemic is like a ticking clock, emphasizing the importance of early contact-tracing. We find a maximum time after which accurate recovery of the source becomes impossible, regardless of the algorithm used.