LoopQuant: Loop-Aware Post-Training Quantization for Vision-Language-Action Models

Vision-language-action (VLA) models achieve strong manipulation performance, yet their substantial memory footprint and latency hinder real-time execution on robot accelerators. In practice, a VLA operates across two nested loops: an inner loop over denoising steps and an outer control loop that initiates each re-planning request from a new observation. Under W4A8 post-training quantization (PTQ), static four-bit weights cause reconstruction errors to recur at every denoising step and compound across consecutive requests through executed actions. Meanwhile, dynamic activations shift across denoising steps, and we find that their channel peaks drift across observations, requiring offline calibration thresholds to cover both loops. We propose **LoopQuant**, a training-free W4A8 PTQ framework tailored to these nested loops. **Request-aware multi-observation activation extremal calibration** (RMAEC) records per-channel token percentiles at every denoising step, aggregates their maxima within each request and across diverse observations, and freezes the resulting scales. An extreme-value model predicts that these scales grow sub-linearly with the number of observations. To reduce weight error, **exact non-uniform codebook construction** aggregates repeated weight values to make dynamic programming tractable at layer scale, yielding globally optimal levels for fixed row scales. At runtime, **fused packed execution** decodes four-bit weights in a Triton kernel for half-precision matrix multiplication and executes the expert core with a single launch per denoising step. Averaged across four LIBERO suites, LoopQuant achieves $97.3\%$ closed-loop success on $\pi$0.5 and $84.3\%$ on GR00T-N1.5, outperforming the strongest quantized baseline by $2.5$ and $4.0$ percentage points, respectively. The packed $\pi$0.5 runtime serves requests $1.88\times$ faster than the unquantized BF16 model, requiring only $0.59\times$ of its resident GPU memory.