Neural dynamics represent the hard-to-interpret substrate of circuit computations. However, not all changes in population activity may have equal meaning, i.e., a small change in the evolution of activity along a particular dimension may have a bigger effect on a given computation than a large change in another. We term such conditions dimension-specific computation. If the brain operates under such conditions, our chances to learn what computations a circuit is performing from observing its activity will be greatly improved. We used neural recordings and simultaneous optogenetic perturbations to probe cortical dynamics during motor preparatory activity. We found remarkably robust dynamics along certain dimensions of the population activity, which can be shown to carry nearly all of the decodable behavioral information. The circuit thus appears set up to make informative dimensions stiff, i.e., resistive to perturbations, while leaving uninformative dimensions sloppy, i.e., sensitive to perturbations. This robustness can be achieved by a modular circuit organization, whereby modules with normally independent dynamics correct each other, a common feature in robust systems engineering.