Representational geometry is a framework that enables us to relate brain, computation, and cognition.
Representations in brains and models can be characterized by representational distance matrices.
Distance matrices can be readily compared to test computational models.
We review recent insights into perception, cognition, memory, and action and discuss current challenges.
The cognitive concept of representation plays a key role in theories of brain information processing. However, linking neuronal activity to representational content and cognitive theory remains challenging. Recent studies have characterized the representational geometry of neural population codes by means of representational distance matrices, enabling researchers to compare representations across stages of processing and to test cognitive and computational theories. Representational geometry provides a useful intermediate level of description, capturing both the information represented in a neuronal population code and the format in which it is represented. We review recent insights gained with this approach in perception, memory, cognition, and action. Analyses of representational geometry can compare representations between models and the brain, and promise to explain brain computation as transformation of representational similarity structure.