Large Language Models (LLMs) often exhibit extreme sensitivity to surface-level prompt variations, where minor lexical perturbations trigger disproportionate performance fluctuations. Moving beyond black-box optimization or coarse-grained templates, we conduct the first analysis of n-gram token-level mechanisms, leveraging a large-scale dataset of 132,000 prompt variants. Our investigation uncovers the Scaling Law of Prompt Performance Stability: higher average performance is inherently associated with lower variance and greater stability. We identify that this robustness is driven by two linguistic pillars: Domain-Specific Terminology, which anchors semantic boundaries, and Explicit Action Directives, which formalize reasoning trajectories. By narrowing the model’s interpretative space, these patterns effectively “lock” the generation process. We operationalize these findings into an automated Prompt-Refining Agent that autonomously restructures queries via domain anchoring and operational constraints. Empirical results show a 40.7% reduction in performance variance for code generation, offering a statistically grounded framework for robust prompt engineering.

LLM-based forecasting systems have improved on real-world tasks like financial markets and sports outcomes, largely by strengthening search, but the final prediction step remains crude: systems typically ask an LLM to read all collected evidence and emit one answer. We call this approach Monolithic Prediction, which fits forecasting poorly: probabilities over competing outcomes carry information valuable for downstream decisions, but a holistic answer collapses the supporting evidence, discarding this information. To address the above issue, we propose LEAP Likelihood Elicitation and Aggregation for Probabilistic forecasting) to keep the LLM out of the final prediction. LEAP treats evidence items as local signals, uses likelihood parameters to estimate how each supports candidate outcomes, and aggregates them through a deterministic probabilistic model into a posterior over candidate outcomes, thereby preserving per-item contributions, yielding comprehensive forecasts, and simplifying audits. We build a benchmark covering real-world prediction, information-seeking, and browsing tasks, evaluating LEAP on our custom agent loop and practical agent CLI frameworks. Given the same evidence, LEAP outperforms Monolithic Prediction in most settings and metrics across models.