1. Dynamic Superposition in Modular Subspaces
The primate motor cortex (M1/PMd) avoids catastrophic cross-talk when executing compound movements by constraining individual motor sub-routines (e.g., target tracking vs rhythmic stirring) to mutually orthogonal low-dimensional latent subspaces.
where ⟨U_reach, U_osc⟩ ≈ 0 (Null-Space Orthogonality)
2. Biomechanical Null-Space Projection
For redundant multi-joint effectors, intrinsic joint velocity vectors $\mathbf{\dot{q}}$ decompose into end-effector task kinematics and null-space postural self-motion via the Moore-Penrose pseudo-inverse Jacobian $J^\dagger$:
3. Subspace Interference & Out-Of-Distribution Robustness
When tasks are blended, the total cross-primitive interference index $\xi$ quantifies the projection of primitive dynamical flows into competing task spaces. High orthogonality ($\theta \to 90^\circ$) preserves modular compositionality.