Wei Chen

Wei Chen, Jiacheng Li, Shigui Li et al.

Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal, ground-truth objective by a crucial, overlooked term: the path variance of the score function. We propose the MVP (**M**imum **V**ariance **P**ath) Principle to minimize this path variance. Our key contribution is deriving a closed-form expression for the variance, making optimization tractable. By parameterizing the path with a flexible Kumaraswamy Mixture Model, our method learns data-adaptive, low-variance paths without heuristic manual selection. This principled optimization of the complete objective yields more accurate and stable estimators, establishing new state-of-the-art results on challenging benchmarks and providing a general framework for optimizing score-based interpolation. Our code can be found in https://github.com/Hoemr/OpenDRE.git.

Wei Chen, Yanbin Fang, Shuran Fu et al.

Large Language Models (LLMs) are increasingly embedded in enterprise workflows, yet their performance remains highly sensitive to prompt design. Automatic Prompt Optimization (APO) seeks to mitigate this instability, but existing approaches face two persistent challenges. First, commonly used prompt strategies rely on static instructions that perform well on average but fail to adapt to heterogeneous queries. Second, more dynamic approaches depend on offline reward models that are fundamentally correlational, confounding prompt effectiveness with query characteristics. We propose Causal Prompt Optimization (CPO), a framework that reframes prompt design as a problem of causal estimation. CPO operates in two stages. First, it learns an offline causal reward model by applying Double Machine Learning (DML) to semantic embeddings of prompts and queries, isolating the causal effect of prompt variations from confounding query attributes. Second, it utilizes this unbiased reward signal to guide a resource-efficient search for query-specific prompts without relying on costly online evaluation. We evaluate CPO across benchmarks in mathematical reasoning, visualization, and data analytics. CPO consistently outperforms human-engineered prompts and state-of-the-art automated optimizers. The gains are driven primarily by improved robustness on hard queries, where existing methods tend to deteriorate. Beyond performance, CPO fundamentally reshapes the economics of prompt optimization: by shifting evaluation from real-time model execution to an offline causal model, it enables high-precision, per-query customization at a fraction of the inference cost required by online methods. Together, these results establish causal inference as a scalable foundation for reliable and cost-efficient prompt optimization in enterprise LLM deployments.