The application of physics formulas is a fundamental human capability in numerical reasoning. While existing datasets often rely on implicit mathematical knowledge, they rarely explicitate the underlying formulas. To address this, we introduce FormulaReasoning, a new benchmark for formula-based numerical reasoning comprising 5,324 questions requiring calculations grounded in external physics principles. We provide high-quality, fine-grained annotations in English and Chinese—including formula structures, parameter names, symbols, values, and units—curated through manual effort and LLM-assisted validation. Additionally, we provide a consolidated formula database as an external knowledge source. To further challenge model performance, we develop an extended version of the dataset by coupling multiple questions. We evaluate various architectural and methodological frameworks, including retrieval-augmented methods, modular reasoning (formula generation, parameter extraction, and calculation), and preference-based optimization. Our analysis identifies critical challenges in formula-based reasoning, highlighting significant opportunities for future methodological advancement.

As Large Language Models (LLMs) and Retrieval Augmentation Generation (RAG) techniques have evolved, query rewriting has been widely incorporated into the RAG system for downstream tasks like open-domain QA to enhance document retrieval by reformulating queries. Many works have attempted to improve query rewriting in smaller models to avoid rewriting with costly LLMs, and the most common method is to employ reinforcement learning for feedback training. However, current methods require annotations (labeled relevant documents or downstream answers) or predesigned rewards for feedback, lack generalization, and fail to utilize signals tailored for query rewriting. In this paper, we propose RaFe, a framework for training query rewriting models. By leveraging reranker, RaFe provides ranking feedback aligned well with the rewriting objectives without needing signals from annotations and supports both online and offline training models. Experimental results demonstrate that with a general and publicly available reranker, RaFe can effectively steer the training for rewrite models.