Recent studies posit that Reinforcement Learning with Verifiable Rewards (RLVR) primarily amplifies behaviors inherent to the pre-training distribution rather than inducing new capabilities, but these insights are predominantly limited to language-only domains, leaving the dynamics of visual-centric spatial reasoning under-explored. To examine the impact of RLVR on the capability boundaries of Vision-Language Models (VLMs), we introduce \textbf{Ariadne}, a controlled framework based on synthetic maze navigation where the reasoning difficulty is precisely regulated by path length and the number of turns. We demonstrate that applying RLVR extends the spatial reasoning boundary, achieving success on problems where the base policy VLM consistently attains $0\%$ accuracy despite increasing pass@k sampling budgets, indicating that the optimized policy successfully navigates search spaces that were effectively unreachable by the base distribution. Furthermore, despite being trained exclusively on synthetic mazes, we evaluate the model on two real-world navigation benchmarks (MapBench and ReasonMap) in a zero-shot setting. The observed improvements in these out-of-domain tasks suggest genuine spatial reasoning capability expansion rather than mere sampling efficiency.

Current approaches for training Process Reward Models (PRMs) often involve deconposing responses into multiple reasoning steps using rule-based techniques, such as using predefined placeholder tokens or setting the reasoning step’s length to a fixed size. These approaches overlook the fact that certain words don’t usually indicate true decision points. To address this, we propose AdaptiveStep, a method that divides reasoning steps based on the model’s confidence in predicting the next word, offering more information on decision-making at each step, improving downstream tasks like reward model training. Moreover, our method requires no manual annotation. Experiments with AdaptiveStep-trained PRMs in mathematical reasoning and code generation show that the outcome PRM achieves state-of-the-art Best-of-N performance, surpassing greedy search strategy with token-level value-guided decoding, while also reducing construction costs by over 30% compared to existing open-source PRMs. We also provide a thorough analysis and case study on its performance, transferability, and generalization capabilities. We provide our code on https://github.com/Lux0926/ASPRM.