# Drift is a Sampling Error: SNR-Aware Power Distributions for Long-Horizon Robotic Planning arXiv: https://arxiv.org/abs/2605.09537 · HTML: https://mlsanity.com/paper/2605.09537/ ## Key facts - Cited by 3 papers in the map (data through 14 Oct 2026). - Placed in Reinforcement learning and post-training, one of 13 directions in Vision-language-action models. - Builds on 32 of its 40 references that are in the map. - First posted on arXiv 10 May 2026. ## Placed in - Vision-language-action models / [Reinforcement learning and post-training](https://mlsanity.com/vla/reinforcement-learning-and-post-training/) ## Builds on (most cited first, 30 of 32) - [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022) - [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022) - [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023) - [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023) - [RT-2: Vision-Language-Action Models Transfer Web Knowledge to Robotic Control](https://mlsanity.com/paper/2307.15818/) (2023) - [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024) - [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024) - [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022) - [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025) - [Octo: An Open-Source Generalist Robot Policy](https://mlsanity.com/paper/2405.12213/) (2024) - [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023) - [Open X-Embodiment: Robotic Learning Datasets and RT-X Models](https://mlsanity.com/paper/2310.08864/) (2023) - [RDT-1B: a Diffusion Foundation Model for Bimanual Manipulation](https://mlsanity.com/paper/2410.07864/) (2024) - [BLINK: Multimodal Large Language Models Can See but Not Perceive](https://mlsanity.com/paper/2404.12390/) (2024) - [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025) - [Evaluating Real-World Robot Manipulation Policies in Simulation](https://mlsanity.com/paper/2405.05941/) (2024) - [CoT-VLA: Visual Chain-of-Thought Reasoning for Vision-Language-Action Models](https://mlsanity.com/paper/2503.22020/) (2025) - [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024) - [VLABench: A Large-Scale Benchmark for Language-Conditioned Robotics Manipulation with Long-Horizon Reasoning Tasks](https://mlsanity.com/paper/2412.18194/) (2024) - [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025) - [Reasoning with Sampling: Your Base Model is Smarter Than You Think](https://mlsanity.com/paper/2510.14901/) (2025) - [The Ingredients for Robotic Diffusion Transformers](https://mlsanity.com/paper/2410.10088/) (2024) - [M2Diffuser: Diffusion-based Trajectory Optimization for Mobile Manipulation in 3D Scenes](https://mlsanity.com/paper/2410.11402/) (2024) - [The Pitfalls of Imitation Learning when Actions are Continuous](https://mlsanity.com/paper/2503.09722/) (2025) - [Long-horizon Locomotion and Manipulation on a Quadrupedal Robot with Large Language Models](https://mlsanity.com/paper/2404.05291/) (2024) - [Steering Vision-Language-Action Models as Anti-Exploration: A Test-Time Scaling Approach](https://mlsanity.com/paper/2512.02834/) (2025) - [A Survey of Slow Thinking-based Reasoning LLMs using Reinforced Learning and Inference-time Scaling Law](https://mlsanity.com/paper/2505.02665/) (2025) - [QUEST: Quality-Aware Metropolis-Hastings Sampling for Machine Translation](https://mlsanity.com/paper/2406.00049/) (2024) - [REALM: A Real-to-Sim Validated Benchmark for Generalization in Robotic Manipulation](https://mlsanity.com/paper/2512.19562/) (2025) - [Enhancing Multi-Robot Semantic Navigation Through Multimodal Chain-of-Thought Score Collaboration](https://mlsanity.com/paper/2412.18292/) (2024) ## Built on by (most cited first, 3 of 3) - [CANVAS: Consistency-Aware Navigation via Visual Adaptive Sampling for Long-Context Text-to-SVG Generation](https://mlsanity.com/paper/2608.30689/) (2026) - [ReSync: Re-Aligning the Two Clocks of Asynchronous World-Action Models](https://mlsanity.com/paper/2609.33944/) (2026) - [ReSight-SMC: Two-Stage Power Sampling via Island SMC with Visual Scouts](https://mlsanity.com/paper/2609.34905/) (2026) ## Abstract (arXiv) Despite rapid progress in Vision-Language-Action (VLA) models for robotic control, instruction drift remains a persistent failure mode in long-horizon tasks. This paper reconceptualizes this phenomenon, positing that instruction drift is fundamentally a systematic sampling error: local greedy sampling is prone to collapsing into "Negative Pivotal Windows"--irreversible local optima with high local probability that sever global success pathways. To address this, we propose Context-Aware Power Sampling (CAPS), a training-free inference-time computation framework. CAPS leverages power distributions to sharpen global trajectory probabilities, enabling lookahead search over the model's conditional generative trajectory distribution. Furthermore, we introduce a metacognitive control mechanism based on Signal-to-Noise Ratio (SNR). This mechanism triggers adaptive MCMC search solely when drift risk is detected, enabling a dynamic transition from "intuitive fast thinking" to "rational slow search." Experiments on RoboTwin, Simpler-WindowX, and Libero-long benchmarks show that CAPS achieves substantial improvements over strong baselines, including OpenVLA and TACO, without parameter updates. These results support the effectiveness of adaptive inference-time computation for improving long-horizon robustness in embodied control.