Reinforcement learning with verifiable rewards (RLVR) improves language-model reasoning, but how these gains relate to inference-time decoding and search remains unclear. Does RL produce reasoning behavior the base model does not have, or does it shift the rollout distribution toward trajectories the base model can already reach but rarely samples? We study this behaviorally with a Unified Decoding Framework (UDF), which expresses token-level sampling, beam-like search, tree search and sequence-level resampling as executable policies over a shared budgeted operating space. Operating points are scored after generation with pass@k, self-consistency, best-of-N and first-finish success, so the generation policy stays separate from the evaluation metric.

Using paired Base/RL checkpoints from SimpleRL-Zoo, we ask whether an RL default-policy curve can be approximated by a structured path of Base operating points (𝜋, N_Base) rather than by post-hoc per-budget matching. On Math500, AIME, GPQA and IFEval, the pass@k recovery path follows a Budgeted Operating-Point Transition Rule (BOPTR), N_Base ≈ 𝛼 N_RL^𝛽, with benchmark-conditioned exponents. On Qwen2.5-7B, BOPTR gives the lowest transfer error among the non-oracle rules we test, 3.41 pp. Across models the rule family remains informative, but its parameters and selected policies are model-specific: Qwen models trained on the same difficulty split share operating-point structure, while cross-family models and different training distributions mark the limits of direct transfer.

These results support a qualified internalized-search reading: under the recipe we test, much of the measured RL gain corresponds to a change in sampling efficiency, toward operating points the base model can already reach under search. We treat the benchmark-wise scaling patterns as descriptive of this recipe and cohort, report the cases in which they break down, and use UDF and BOPTR as behavioral diagnostics rather than as evidence of parameter-level equivalence or as general predictors of post-RL performance.

Since the emergence of large language models, prompt learning has become a popular method for optimizing and customizing these models. Special prompts, such as Chain-of-Thought, have even revealed previously unknown reasoning capabilities within these models. However, the progress of discovering effective prompts has been slow, driving a desire for general prompt optimization methods. Unfortunately, few existing prompt learning methods satisfy the criteria of being truly “general”, i.e., automatic, discrete, black-box, gradient-free, and interpretable all at once. In this paper, we introduce metaheuristics, a branch of discrete non-convex optimization methods with over 100 options, as a promising approach to prompt learning. Within our paradigm, we test six typical methods: hill climbing, simulated annealing, genetic algorithms with/without crossover, tabu search, and harmony search, demonstrating their effectiveness in white-box and black-box prompt learning. Furthermore, we show that these methods can be used to discover more human-understandable prompts that were previously unknown in both reasoning and image generation tasks, opening the door to a cornucopia of possibilities in prompt optimization.