Parallel processing of orthogonal manifolds enables zero-shot composition in recurrent networks

Animals flexibly combine learned behaviors into novel actions without practicing their combinations, yet the computational mechanisms that enable independently acquired computations to be expressed in parallel remain unclear. Here we show that feedback geometry during learning determines whether recurrent dynamics can be recombined through zero-shot parallel composition. Using recurrent networks trained by a local predictive plasticity rule, we found that distinct feedback vectors embed independently learned computations in separable dynamical subspaces, allowing novel input combinations to co-activate these components and generate composite outputs without joint training. In contrast, aligned feedback vectors, as well as networks trained by backpropagation through time, exhibited accurate single-task performance but failed to support parallel composition, demonstrating that task acquisition and future reusability are dissociable properties of learning. A combined input evoked a single composite population trajectory, whose projections onto feedback-shaped task subspaces recovered the independently learned component dynamics. The same principle reproduced additive reach-posture geometry observed in motor cortex and generalized to higher-dimensional movement primitives. These results identify feedback geometry as a computational principle by which learning systems structure recurrent dynamics for future compositional reuse.