Abstract
Most behaviors involve neural dynamics in high-dimensional activity spaces. A common approach is to extract dimensions that capture task-related variability, such as those separating stimuli or choices, yielding low-dimensional, task-aligned neural activity subspaces ("coding dimensions"). However, whether these dimensions actively drive decisions or merely reflect underlying computations remains unclear. Moreover, neural activity outside these coding subspaces ("residual dimensions") is often ignored, though it could also causally shape neural dynamics driving behavior. We developed a recurrent neural network model that fits population activity and uncovers the dynamic interactions between coding and residual subspaces on single trials. Applied to electrophysiological recordings from the anterior lateral motor cortex (ALM) and motor thalamus in mice performing a delayed response task, our model demonstrates that perturbations of residual dimensions reliably alter behavioral choices, whereas perturbations of the choice dimension, which strongly encodes the animal's upcoming decision, are largely ineffective. These perturbation effects arise because residual dimensions drive transient amplification across an intermediate number of coding and residual dimensions (~10), before the dynamics collapse into discrete attractor states corresponding to the animal's choice. By dissecting the low-dimensional variability underlying error trials, we find that it primarily shifts trajectories along residual dimensions, biasing single decisions. Residual activity in thalamus shapes cortical decision dynamics, implicating weakly selective thalamic populations in the emergence of cortical selectivity. Our findings challenge the conventional focus on low-dimensional coding subspaces as sufficient framework for understanding neural computations, demonstrating that dimensions previously considered task-irrelevant and accounting for little variance can have a critical role in driving behavior.