# Generalization as diffusion: human function learning on graphs

- Charley Wu, Center for Adaptive Rationality, Max Planck Institute for Human Development, Berlin, Germany
- Eric Schulz, Psychology, Harvard, Boston, Massachusetts, United States
- Samuel Gershman, Harvard University, Cambridge, Massachusetts, United States

**Abstract**From social networks to public transportation, graph structures are a ubiquitous feature of life. How do humans learn functions on graphs, where relationships are defined by the connectivity structure? We adapt a Bayesian framework for function learning to graph structures, and propose that people perform generalization by assuming that the observed function values diffuse across the graph. We evaluate this model by asking participants to make predictions about passenger volume in a virtual subway network. The model captures both generalization and confidence judgments, and provides a quantitatively superior account relative to several heuristic models. Our work suggests that people exploit graph structure to make generalizations about functions in complex discrete spaces.