Reduced-Order Linear Optimal Control Steering (LA-LQR)

Projects high-dimensional activations onto a low-rank subspace built from contrastive-prompt-pair SVD, fits a local linear (Jacobian) dynamics model within that subspace, and solves a latent linear-quadratic-regulator (LQR) problem to compute timestep- and layer-specific closed-loop feedback corrections that track a target coordinate along the contrastive direction — rather than adding a single fixed-scale vector.