A2DB: Affordance as a Distillation Bottleneck for Compressing Vision-Language-Action Models

Vision-language-action (VLA) models offer broad manipulation capabilities but remain costly to train and deploy. Standard knowledge distillation requires compact students to reproduce dense teacher representations that contain control-irrelevant information. We introduce A2DB, an affordance-bottleneck VLA distillation framework that transfers only the interaction affordance information needed to determine where and how to act. Automatic affordance labels supervise the frozen ${\pi }_0$ teacher probe, whose scaled leading first-layer singular directions define a compact affordance subspace. A2DB follows a two-stage distillation strategy. Phase I distills an external-view student VLM through selective feature matching, affordance supervision, and language alignment. Phase II freezes this student VLM and trains an affordance-conditioned action expert with behavior cloning, sliced Wasserstein action distillation, and cycle consistency; deployment retains only the student VLM and action expert. Across four LIBERO suites, A2DB reaches 76.7% average success with 0.29 B parameters and 38.6 ms latency, outperforming standard knowledge distillation by 11.6 percentage points while using about 91% fewer parameters and 51% lower latency than the ${\pi }_0$ teacher. Phase I controls show that leading probe-weight directions and singular-value scaling outperform rank-matched and alternative extraction rules, with performance approaching a plateau at $d_A=128$. Phase II controls identify a near-saturated sampling regime and show that action-distribution guidance and aligned cycle supervision are both important. Affordance predictions, attention maps, label-corruption tests, and failure analysis connect the gains to object, contact, and motion cues, while identifying contact and motion precision as the dominant residual errors and motivating evaluation across seeds, perceptual shifts, embodiments, and real robots. Code will be released after the paper is accepted.