The 'neat' and 'messy' in task-dependent neural geometry and computation

To solve diverse real-world tasks, the brain must flexibly switch between task rules and adjust computations. Recent advances in analyzing neural data and modeling neural networks have revealed their 'neat' features: neuronal population activity encodes distinct task states and forms structured, interpretable representations of task variables, enabling efficient task switching. However, 'messy' features are also observed: task-irrelevant variables shape neuronal responses, representations become entangled, and behaviors exhibit apparent suboptimalities such as switch costs. We review these dual facets of experimental observations of task-dependent computation in the brain, particularly in primates. Recognizing this duality points to two future directions: refining theories to better capture brain-specific constraints and leveraging network models fitted directly to behavioral and neural data.