Beyond Scalar Recovery: Residual Geometry in Quantized Vision-Language-Action Models

Post-quantization recovery in vision-language-action (VLA) models is typically summarized by scalar error or task-level metrics, which measure how much error remains but not how that error is organized across a multi-step action chunk. We characterize this missing structure through teacher-relative residual geometry in a controlled OpenVLA-OFT setting. Across 13 heterogeneous ternary quantization configurations, mean pairwise Spearman similarity increases from 0.037 before adaptation to 0.557 afterward, with a demonstration-bootstrap median gain of +0.520 (95% CI [0.472, 0.568]). This geometric reorganization is not explained by uniform error shrinkage, and scalar recovery magnitude can diverge substantially from final residual alignment. The shared-alignment trend persists across additional optimization seeds, matched ground-truth-only adaptation, and a distinct 3-bit quantizer. Matched full-precision controls further demonstrate that shared alignment does not require an initial quantization perturbation. Finally, a leave-one-out template formed directly from other configurations’ adapted residuals strongly predicts the final residual geometry of a held-out configuration, reaching mean Spearman correlation 0.678 and substantially outperforming both raw geometry and a leave-one-out recovery-field predictor. Shared chunk-position and action-dimension effects explain much of this predictability, while the complete template retains additional predictive structure in reconstruction error.