Primitive Subspaces Mediate Few-Shot Transfer in VLAs

Deploying vision-language-action (VLA) policies in industrial environments requires the ability to teach new tasks at low cost, a property current VLAs lack, since each new task requires fine-tuning. We investigate whether primitive-aware training produces a transferable artifact: a learned library of sub-skills that can be composed at inference time, conditioned on a small number of demonstrations, to perform tasks the policy was never trained on. We train two VLA architectures with different inductive biases, OpenVLA and $π_{0.5}$, on the REASSEMBLE contact-rich assembly dataset under matched LoRA fine-tuning recipes and locked hyperparameters, varying training between flat trajectories and primitive-segmented episodes with primitive-specific language prompts. We hold out 6 object-task combinations from training and evaluate few-shot transfer: models receive $m \in \{0, 1, 3, 5, 10\}$ demonstrations of a held-out task and attempt execution without weight updates. We replicate across three training seeds and validate on a second dataset (LIBERO-Long). Primitive-trained models reach 78% of fine-tuned upper-bound performance with only m=3 demonstrations, while flat-trained models require m=10 demonstrations to reach the same level -- a $3\times$ sample efficiency gap that replicates across seeds, architectures, and datasets. To establish causation, we ablate the primitive-decodable subspace of hidden states and show few-shot transfer degrades by 32 percentage points while ablating a random subspace of equal dimensionality has no effect, indicating primitive representations are causally necessary rather than incidentally correlated with transfer. We identify and correct a methodological pitfall in evaluating chunked policies: family-wise inflation of single-step action-range gates produces order-of-magnitude higher false-failure rates against ground-truth human demonstrations.