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Humans have the ability to reason about geometric patterns in images and scenes from a young age. However, developing large multimodal models (LMMs) capable of similar reasoning remains a challenge, highlighting the need for robust evaluation methods to assess these capabilities. We introduce TurtleBench, a benchmark designed to evaluate LMMs’ capacity to interpret geometric patterns—given visual examples, textual instructions, or both—and generate precise code outputs. Inspired by turtle geometry, a notion used to teach children foundational coding and geometric concepts, TurtleBench features tasks with patterned shapes that have underlying algorithmic logic. Our evaluation reveals that leading LMMs struggle significantly with these tasks, with GPT-4V achieving only 19% accuracy on the simplest tasks and few-shot prompting only marginally improves their performance (<2%). TurtleBench highlights the gap between human and AI performance in intuitive and visual geometrical understanding, setting the stage for future research in this area and stands as one of the few benchmarks to evaluate the integration of visual understanding and code generation capabilities in LMMs, setting the stage for future research. 

Abstract An important part of research is situating one’s work in a body of existing literature, thereby connecting to existing ideas. Despite this, the various kinds of relationships that might exist among academic literature do not appear to have been formally studied. Here I present a graphical representation of academic work in terms of entities and relations, drawing on structure-mapping theory (used in the study of analogies). I then use this representation to present a typology of operations that could relate two pieces of academic work. I illustrate the various types of relationships with examples from medicine, physics, psychology, history and philosophy of science, machine learning, education, and neuroscience. The resulting typology not only gives insights into the relationships that might exist between static publications, but also the rich process whereby an ongoing research project evolves through interactions with the research literature.