Brain–machine interfaces (BMIs) for reaching have enjoyed continued performance improvements, yet there remains significant need for BMIs that control other movement classes. Recent scientific findings suggest that the intrinsic covariance structure of neural activity depends strongly on movement class, potentially necessitating different decode algorithms across classes. To address this possibility, we developed a self-motion BMI based on cortical activity as monkeys cycled a hand-held pedal to progress along a virtual track. Unlike during reaching, we found no high-variance dimensions that directly correlated with to-be-decoded variables. This was due to no neurons having consistent correlations between their responses and kinematic variables. Yet we could decode a single variable—self-motion—by nonlinearly leveraging structure that spanned multiple high-variance neural dimensions. Resulting online BMI-control success rates approached those during manual control. These findings make two broad points rega...