Beyond In-Distribution Preservation: Recovering Generalization in Quantized VLAs via Vulnerability-Oriented Tuning

Shen Ruan; Wenchang Gao; Jin Wang; Siao Liu; Zhoxizhuoma; Dongchun Ren; Xin Zheng

cs.LGOct 5, 2026

Beyond In-Distribution Preservation: Recovering Generalization in Quantized VLAs via Vulnerability-Oriented Tuning

Authors: Shen Ruan, Wenchang Gao, Jin Wang, Siao Liu, Zhoxizhuoma, Dongchun Ren, Xin Zheng

Organizations: Soochow University · Independent Researcher · Shanghai Jiao Tong University · Yootta · RMIT University

Abstract

Post-training quantization has been shown to preserve VLA performance under standard evaluation conditions, but whether it preserves the full-precision model's robustness and generalization remains underexplored. In this study, we systematically study the robustness and generalization of post-quantized VLA policies under environmental disturbances. Empirical results show that quantized policies can become fragile to subtle environmental variations despite retaining comparable in-distribution performance. We further observe that action discrepancies are concentrated in a small subset of rollout states, while teacher guidance has opposite effects depending on discrepancy: it improves generalization at high-discrepancy states but can degrade it at low-discrepancy states. These findings reveal that effective post-quantization recovery requires selectively intervening on vulnerable states rather than globally distilling the student. We therefore propose Policy-Induced Vulnerability-Oriented Tuning (PIVOT-Q), a vulnerability-aware On-Policy Distillation (OPD) framework that selectively corrects vulnerable states encountered during quantized-student rollouts using the frozen full-precision policy as a teacher. PIVOT-Q identifies vulnerable states using discounted accumulated discrepancies over a short horizon, applies phase-balanced sparse supervision, and uses a Behavioral Anchor to prevent unnecessary changes. Experiments under seven LIBERO-Plus environmental variations demonstrate consistent recovery across multiple VLA backbones and quantization methods. Notably, PIVOT-Q consistently outperforms full-state distillation across all settings while using only 7.4% of its state-level distillation budget. Our code is available at https://github.com/ruanruan-andy/PIVOT-Q.

Figures & tables

Figure 1: Generalization degradation after quantization and action discrepancy. (a) Average success over 560 LIBERO-Plus episodes for each original and quantized policy. (b) Distributions of action discrepancy between each quantized policy and its original counterpart. The horizontal action discrepancy axis is in log-scale.

Method	Cam.	Init.	Lang.	Light	Back.	Noise	Layout	Mean
Original	85.0	42.5	78.8	95.0	96.2	85.0	88.8	81.6
QuantVLA	61.2	30.0	60.0	92.5	75.0	61.2	85.0	66.4
Ran. Int.	66.3 ↑5.1	33.8 ↑3.8	61.3 ↑1.3	93.8 ↑1.3	75.0 0.0	60.0 ↓1.2	87.5 ↑2.5	68.2 ↑1.8
HD Int.	67.5 ↑6.3	30.0 0.0	76.2 ↑16.2	96.2 ↑3.7	76.2 ↑1.2	87.5 ↑26.3	82.5 ↓2.5	73.8 ↑7.4
LD Int.	62.5 ↑1.3	32.5 ↑2.5	58.8 ↓1.2	86.2 ↓6.3	78.8 ↑3.8	58.8 ↓2.4	86.2 ↑1.2	66.2 ↓0.2

Table 1: Effect of intervention at different action-discrepancy levels Task success rate (%) in the GR00T-N1.5 QuantVLA setting. “Ran. Int.”, “HD Int.”, and “LD Int.” denote interventions at random, high-discrepancy, and low-discrepancy states, respectively. Superscripts indicate absolute changes relative to QuantVLA. Best and second-best results among intervention strategies are shown in bold and underline , respectively. The full-precision original policy is shaded as a reference.

Figure 2: Overview of PIVOT-Q . PIVOT-Q identifies vulnerable states from student-controlled rollouts using discounted accumulated discrepancy within a short future segment, performs phase-balanced sparse distillation, and uses a Behavioral Anchor to preserve retained behavior.

Model	Method	Cam.	Init.	Lang.	Light	Back.	Noise	Layout	Avg. $\uparrow$	#States	$\Delta\uparrow$
HoloQ-VLA (W4A4)
GR00T-N1.5	Original	$86.3\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.5}$	$35.0\,{\color[rgb]{0.5,0.5,0.5}\pm\,3.3}$	$77.9\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.4}$	$97.5\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.0}$	$97.9\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.7}$	$87.5\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.0}$	$91.7\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.9}$	$82.0\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.2}$	–	–
	Quantized	$67.5\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.2}$	$27.1\,{\color[rgb]{0.5,0.5,0.5}\pm\,3.1}$	$65.0\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.2}$	$95.0\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.2}$	$81.7\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.6}$	$59.2\,{\color[rgb]{0.5,0.5,0.5}\pm\,3.1}$	$82.1\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.6}$	$68.2\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.5}$	–	$-13.8$
	FSD	$79.2\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.9}$	$32.1\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.6}$	$\mathbf{75.4}\,{\color[rgb]{0.5,0.5,0.5}\pm\,3.8}$	$\mathbf{96.2}\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.5}$	$\mathbf{98.8}\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.2}$	$74.2\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.9}$	$90.0\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.2}$	$78.0\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.4}$	199.4	$-4.0$
	PIVOT-Q	$\mathbf{85.0}\,{\color[rgb]{0.5,0.5,0.5}\pm\,2.2}$	$\mathbf{36.2}\,{\color[rgb]{0.5,0.5,0.5}\pm\,4.3}$	$71.2\,{\color[rgb]{0.5,0.5,0.5}\pm\,5.7}$	$92.5\,{\color[rgb]{0.5,0.5,0.5}\pm\,3.3}$	$96.7\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.7}$	$\mathbf{75.4}\,{\color[rgb]{0.5,0.5,0.5}\pm\,4.0}$	$\mathbf{91.2}\,{\color[rgb]{0.5,0.5,0.5}\pm\,0.0}$	$\mathbf{78.3}\,{\color[rgb]{0.5,0.5,0.5}\pm\,1.6}$	16.0	$-3.7$
QuantVLA (W4A8)

Table 2: Performance recovery across models and quantization methods. We report task success rates (%) for seven LIBERO-Plus distribution shifts. FSD denotes Full State Distillation , which distills the student on all recorded rollout states. “#States” denotes the average number of distilled states per episode. Results are reported as mean

\pm

standard deviation across three independent runs with different seeds, with standard deviations shown in gray. Boldface marks the larger value between FSD and PIVOT-Q for each reported shift and the overall average.

Method	Selection	Anchor	Cam.	Init.	Lang.	Light	Back.	Noise	Layout	Avg. $\uparrow$
Original	–	–	$84.6\,{\color[rgb]{0.5,0.5,0.5}\pm 0.7}$	$34.6\,{\color[rgb]{0.5,0.5,0.5}\pm 2.6}$	$78.3\,{\color[rgb]{0.5,0.5,0.5}\pm 0.7}$	$96.7\,{\color[rgb]{0.5,0.5,0.5}\pm 1.9}$	$97.9\,{\color[rgb]{0.5,0.5,0.5}\pm 0.7}$	$87.9\,{\color[rgb]{0.5,0.5,0.5}\pm 2.6}$	$90.0\,{\color[rgb]{0.5,0.5,0.5}\pm 2.2}$	$81.4\,{\color[rgb]{0.5,0.5,0.5}\pm 0.8}$
Quantized	–	–	$60.4\,{\color[rgb]{0.5,0.5,0.5}\pm 2.6}$	$31.7\,{\color[rgb]{0.5,0.5,0.5}\pm 3.1}$	$61.3\,{\color[rgb]{0.5,0.5,0.5}\pm 2.2}$	$86.7\,{\color[rgb]{0.5,0.5,0.5}\pm 3.6}$	$76.7\,{\color[rgb]{0.5,0.5,0.5}\pm 1.4}$	$66.3\,{\color[rgb]{0.5,0.5,0.5}\pm 1.3}$	$83.3\,{\color[rgb]{0.5,0.5,0.5}\pm 0.7}$	$66.6\,{\color[rgb]{0.5,0.5,0.5}\pm 0.9}$
Per-Phase Random	Random	✓	$70.4\,{\color[rgb]{0.5,0.5,0.5}\pm 3.1}$	$37.1\,{\color[rgb]{0.5,0.5,0.5}\pm 1.4}$	$75.4\,{\color[rgb]{0.5,0.5,0.5}\pm 3.1}$	$99.6\,{\color[rgb]{0.5,0.5,0.5}\pm 0.7}$	$100.0\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$75.8\,{\color[rgb]{0.5,0.5,0.5}\pm 1.9}$	$90.8\,{\color[rgb]{0.5,0.5,0.5}\pm 1.9}$	$78.5\,{\color[rgb]{0.5,0.5,0.5}\pm 0.8}$
Per-Phase Uniform	Uniform	✓	$82.9\,{\color[rgb]{0.5,0.5,0.5}\pm 4.4}$	$35.0\,{\color[rgb]{0.5,0.5,0.5}\pm 3.3}$	$66.2\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$100.0\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$100.0\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$82.1\,{\color[rgb]{0.5,0.5,0.5}\pm 3.8}$	$89.6\,{\color[rgb]{0.5,0.5,0.5}\pm 3.1}$	$79.4\,{\color[rgb]{0.5,0.5,0.5}\pm 1.0}$
Globally Greedy	Greedy	✓	$74.2\,{\color[rgb]{0.5,0.5,0.5}\pm 3.1}$	$33.3\,{\color[rgb]{0.5,0.5,0.5}\pm 2.1}$	$72.5\,{\color[rgb]{0.5,0.5,0.5}\pm 1.8}$	$98.3\,{\color[rgb]{0.5,0.5,0.5}\pm 1.2}$	$99.6\,{\color[rgb]{0.5,0.5,0.5}\pm 0.6}$	$80.8\,{\color[rgb]{0.5,0.5,0.5}\pm 0.6}$	$92.5\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$78.8\,{\color[rgb]{0.5,0.5,0.5}\pm 0.7}$
w/o Future Discrepancy	$C$ only	✓	$76.7\,{\color[rgb]{0.5,0.5,0.5}\pm 5.6}$	$31.7\,{\color[rgb]{0.5,0.5,0.5}\pm 4.4}$	$78.8\,{\color[rgb]{0.5,0.5,0.5}\pm 1.2}$	$100.0\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$100.0\,{\color[rgb]{0.5,0.5,0.5}\pm 0.0}$	$82.9\,{\color[rgb]{0.5,0.5,0.5}\pm 1.4}$	$87.5\,{\color[rgb]{0.5,0.5,0.5}\pm 1.2}$	$79.6\,{\color[rgb]{0.5,0.5,0.5}\pm 1.2}$

Table 3: Component ablations and sparse selection baselines. Task success rate (SR, %) on 560 LIBERO-Plus episodes with GR00T-N1.5 and W4A8 QuantVLA. All recovery methods use the same 16-state supervision budget.

Figure 3: Global and phase-wise vulnerability selection. A representative rollout from LIBERO-Spatial under the Camera Viewpoints variation.

Figure 4: Phase-wise vulnerability-oriented state selection. Distribution of candidate and selected states across the four temporal phases for GR00T-N1.5 with W4A8 QuantVLA. Gray hexagonal bins denote candidate-state density, and colored points denote sampled PIVOT-Q selections.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	$N_{e}/N_{s}$	$\hat{\mu}$	$\hat{\sigma}$	KS $\downarrow$
GR00T-N1.5 / QuantVLA	560/125,569	$-5.630$	2.079	0.0732/0.1033
$\pi_{0.5}$ / QuantVLA	560/128,739	$-3.817$	1.366	0.0163/0.0733
GR00T-N1.5 / HoloQ-VLA	560/115,135	$-6.126$	1.924	0.0720/0.0914
OpenVLA-OFT / QVLA †	140/14,942	$-5.675$	0.961	0.0243/0.0738

Appendix

Table 4: Log-normal discrepancy fits.

N_{e}/N_{s}

: episodes/positive states. KS: pooled/median episode distance. † Spatial only.

Setting	Log-normal	Gamma	Weibull
GR00T-N1.5 / QuantVLA	0.0732/0.1033	0.2078/0.2924	0.1176/0.1953
$\pi_{0.5}$ / QuantVLA	0.0163/0.0733	0.1285/0.1312	0.0785/0.1104
GR00T-N1.5 / HoloQ-VLA	0.0720/0.0914	0.2450/0.2895	0.1330/0.1935
OpenVLA-OFT / QVLA †	0.0243/0.0738	0.1146/0.1017	0.0993/0.1006

Appendix

Table 5: Alternative distribution fits. Entries report pooled/median episode KS; lower is better. † Spatial only.

Setting	Top 1%	Top 5%	Top 10%	Top 20%
GR00T-N1.5 / QuantVLA	24.6	72.3	84.4	93.2
$\pi_{0.5}$ / QuantVLA	16.0	43.8	58.5	73.5
GR00T-N1.5 / HoloQ-VLA	26.3	78.5	88.6	94.5
OpenVLA-OFT / QVLA †	18.3	34.6	45.4	60.1

Appendix

Table 6: Discrepancy concentration. Share of total discrepancy (%) contributed by the largest fraction of state discrepancies. † Spatial only.

Setting	$N$	Phase 1	Phase 2	Phase 3	Phase 4
GR00T-N1.5 / QuantVLA	560	$0.534$ [0.509, 0.551]	$0.477$ [0.449, 0.498]	$0.516$ [0.498, 0.546]	$0.563$ [0.542, 0.589]
$\pi_{0.5}$ / QuantVLA	560	$0.486$ [0.455, 0.510]	$0.468$ [0.447, 0.488]	$0.534$ [0.511, 0.559]	$0.467$ [0.432, 0.504]
GR00T-N1.5 / HoloQ-VLA	560	$0.409$ [0.381, 0.426]	$0.422$ [0.407, 0.440]	$0.401$ [0.378, 0.424]	$0.449$ [0.428, 0.468]
OpenVLA-OFT / QVLA	558	$0.537$ [0.515, 0.553]	$0.576$ [0.554, 0.593]	$0.621$ [0.598, 0.644]	$0.632$ [0.605, 0.662]

Appendix

Table 7: Current–future discrepancy association. Median Spearman correlation with a 95% bootstrap interval underneath.

N

is the trajectory count per phase.

Figure 5: Temporal coverage of sparse selection. Six LIBERO-Plus rollouts span camera-viewpoint and background-texture variations across Spatial, Object, Goal, and Long. Red diamonds denote global vulnerability selection; blue circles denote PIVOT-Q. Both select 16 states. Global selection occupies one or two phases in these examples, while PIVOT-Q selects four states per phase.

Setting	$N$	KL (nats)	JS (bits)
GR00T-N1.5 / QuantVLA	560	$0.0997$ [0.0818, 0.1333]	$0.0287$ [0.0238, 0.0357]
$\pi_{0.5}$ / QuantVLA	560	$0.0042$ [0.0035, 0.0085]	$0.0015$ [0.0012, 0.0030]
GR00T-N1.5 / HoloQ-VLA	560	$0.0567$ [0.0468, 0.0712]	$0.0187$ [0.0155, 0.0229]
OpenVLA-OFT / QVLA †	140	$0.0571$ [0.0468, 0.0789]	$0.0208$ [0.0174, 0.0280]

Appendix

Table 8: Recorded discrepancy distribution changes. KL/JS divergence with 95% bootstrap intervals.

N

is episodes per method. † Final-policy Spatial evaluations; other rows use archived or recovery-time cohorts.

Figure 6: Selection diagnostics and paired recovery outcomes. The four panels correspond to GR00T-N1.5 / QuantVLA, $\pi_{0.5}$ / QuantVLA, GR00T-N1.5 / HoloQ-VLA, and OpenVLA-OFT / QVLA. Points show mean selected-state discrepancy on a logarithmic axis; color represents mean vulnerability score using a shared continuous scale from 0.5 to 1.0, and black ticks mark group medians. Counts and percentages use all 560 final-evaluation pairs per setting. OpenVLA-OFT has 558 plotted selection records.

GR00T-N1.5 / QuantVLA (W4A8)
$(\alpha,\beta)$	Cam.	Init.	Lang.	Light	Back.	Noise	Layout	Avg. $\uparrow$
$(0.3,0.7)$	73.8	40.0	81.2	98.8	100.0	82.5	88.8	80.7
$(0.4,0.6)$	78.8	27.5	76.2	100.0	100.0	86.2	85.0	79.1
$(0.5,0.5)$	80.0	37.5	77.5	98.8	100.0	88.8	90.0	81.8
$(0.7,0.3)$	76.2	30.0	80.0	100.0	97.5	82.5	85.0	78.8

Appendix

Table 9: Sensitivity to vulnerability-score weighting. Single-seed task success rate (%) on 560 LIBERO-Plus episodes. All variants use 16 supervision states. Bold and underline denote the highest and second-highest distinct values in each column, including ties.

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