arXiv:2604.14484v1 Announce Type: cross
Abstract: Behavior cloning (BC) policies on position-controlled robots inherit the closed-loop response of the underlying PD controller, yet the effect of controller gains on BC failure lacks a nonasymptotic theory. We show that independent sub-Gaussian action errors propagate through the gain-dependent closed-loop dynamics to yield sub-Gaussian position errors whose proxy matrix $X_infty(K)$ governs the failure tail. The probability of horizon-$T$ task failure factorizes into a gain-dependent amplification index $Gamma_T(K)$ and the validation loss plus a generalization slack, so training loss alone cannot predict closed-loop performance. Under shape-preserving upper-bound structural assumptions the proxy admits the scalar bound $X_infty(K)preceqPsi(K)bar X$ with $Psi(K)$ decomposed into label difficulty, injection strength, and contraction, ranking the four canonical regimes with compliant-overdamped (CO) tightest, stiff-underdamped (SU) loosest, and the stiff-overdamped versus compliant-underdamped ordering system-dependent. For the canonical scalar second-order PD system the closed-form continuous-time stationary variance $X_infty^mathrmc(alpha,beta)=sigma^2alpha/(2beta)$ is strictly monotone in stiffness and damping over the entire stable orthant, covering both underdamped and overdamped regimes, and the exact zero-order-hold (ZOH) discretization inherits this monotonicity. The analysis provides the first nonasymptotic explanation of the empirical finding that compliant, overdamped controllers improve BC success rates.
Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control
arXiv:2604.19018v1 Announce Type: cross Abstract: Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods,