Large language models (LLMs) have been widely adopted in mathematical optimization in scientific scenarios for their extensive knowledge and advanced reasoning capabilities. Existing methods mainly focus on utilizing LLMs to solve optimization problems in a prompt-based manner, which takes observational feedback as additional textual descriptions. However, due to LLM's \textbf{high sensitivity to the prompts} and \textbf{tendency to get lost in lengthy prompts}, these methods struggle to effectively utilize the {observational} feedback from each optimization step, which severely hinders the applications for real-world scenarios. To address these challenges, we propose a conceptually simple and general {bi-level} optimization method, namely \textbf{G}eneral \textbf{S}cientific \textbf{O}ptimizers (GSO). Specifically, GSO first utilizes inner-level simulators as experimental platforms to evaluate the current solution and provide observational feedback. Then, LLMs serve as knowledgeable and versatile scientists, generating new solutions by refining potential errors from the feedback as the outer-level optimization. Finally, simulations together with the expert knowledge in LLMs are jointly updated with bi-level interactions via model editing. Extensive experiments show that GSO consistently outperforms existing state-of-the-art methods using \textit{six} different LLM backbones on \textit{seven} different tasks, demonstrating the effectiveness and a wide range of applications.

Generative language models often struggle with specialized or less-discussed knowledge. A potential solution is found in Retrieval-Augmented Generation (RAG) models which act like retrieving information before generating responses. In this study, we explore how the \textsc{Atlas} approach, a RAG model, decides between what it already knows (parametric) and what it retrieves (non-parametric). We use causal mediation analysis and controlled experiments to examine how internal representations influence information processing. Our findings disentangle the effects of parametric knowledge and the retrieved context. They indicate that in cases where the model can choose between both types of information (parametric and non-parametric), it relies more on the context than the parametric knowledge. Furthermore, the analysis investigates the computations involved in \emph{how} the model uses the information from the context. We find that multiple mechanisms are active within the model and can be detected with mediation analysis: first, the decision of \emph{whether the context is relevant}, and second, how the encoder computes output representations to support copying when relevant.