Knowledge distillation trains a small student model to reproduce the outputs of a large teacher model, and its progress is typically monitored through the teacher--student discrepancy. The quantity of ultimate interest, however, is the student's error with respect to the true task. We study the relation between these two objectives in a minimal three-party model, a true teacher (generative model), a teacher, and a student, all soft committee machines, in which the true teacher contains a shared latent factor that the teacher cannot represent, with mismatch strength controlled by a single scalar $\dmiss$. Within an order-parameter description of online distillation, and exploiting closed-form (arcsine-type) expressions for all errors under error-function activations, we prove that the learning dynamics and the distillation error $\Ets$ are exactly invariant to $\dmiss$, whereas the true error $\Etzs$ and the gap $Δ=\Etzs-\Ets$ are strictly increasing in $\dmiss$, with a rate that is amplified linearly by the complexity $M_0$ of the true teacher. Numerical phase diagrams over the plane spanned by true-teacher complexity and student capacity confirm the predicted deformation: the contours of $\Ets$ do not move while the landscape of $\Etzs$ rises systematically, and a teacher-miss regime, where mimicry succeeds but the task fails, expands with $\dmiss$. The results give a quantitative warning against evaluating distillation solely through teacher-mimicry metrics and identify the gap $Δ$ as a minimal diagnostic for distinguishing teacher-miss from capacity-limited failure.
Hongyang He, Jiuming Liu, Victor Sanchezcs.CV cs.ET
Vision-Language-Action (VLA) models enable robots to predict actions directly from visual observations and language instructions, but adapting them to new environments still depends on costly action-labeled demonstrations. To reduce this dependence, we study semi-supervised VLA adaptation under limited supervision signals, where only a small portion of trajectories contain robot actions and the remaining trajectories provide action-unlabeled vision-language observations. Unlike standard semi-supervised learning, the missing supervision is an embodied action signal that must be visually grounded, language-consistent, physically feasible, and temporally stable. To address this problem, we propose SemiVLA, a self-distilled teacher-student framework that learns from reliable pseudo-actions on unlabeled trajectories. SemiVLA introduces a VLA-specific reliability controller to assess vision-language alignment, action feasibility, and temporal transition consistency, and further updates the teacher through a Bottleneck-Projected Alignment Update to avoid noisy feedback contamination. With OpenVLA as the backbone, SemiVLA consistently improves multiple PEFT strategies across LIBERO and CALVIN. Under 10\% labeled trajectories, SemiVLA with Selective LoRA achieves 89.0\% average success on LIBERO, outperforming supervised LoRA by 8.0 points without extra inference cost.