Patterns are fundamental to human cognition, enabling the recognition of structure and regularity across diverse domains. In this work, we focus on structural repeats, patterns that arise from the repetition of hierarchical relations within sequential data, and develop a candidate computational model of how humans detect and understand such structural repeats. Based on a weighted deduction system, our model infers the minimal generative process of a given sequence in the form of a Template program, a formalism that enriches the context-free grammar with repetition combinators. Such representation efficiently encodes the repetition of sub-computations in a recursive manner. As a proof of concept, we demonstrate the expressiveness of our model on short sequences from music and action planning. The proposed model offers broader insights into the mental representations and cognitive mechanisms underlying human pattern recognition.

People grasp flexible visual concepts from a few examples. We explore a neurosymbolic system that learns how to infer programs that capture visual concepts in a domain-general fashion. We introduce Template Programs: programmatic expressions from a domain-specific language that specify structural and parametric patterns common to an input concept. Our framework supports multiple concept-related tasks, including few-shot generation and co-segmentation through parsing. We develop a learning paradigm that allows us to train networks that infer Template Programs directly from visual datasets that contain concept groupings. We run experiments across multiple visual domains: 2D layouts, Omniglot characters, and 3D shapes. We find that our method outperforms task-specific alternatives, and performs competitively against domain-specific approaches for the limited domains where they exist.