NeuroSym-BO: Bayesian Optimization Closed Loop
Figure 1 : Overview of NeuroSym-BO . A Bayesian Optimizer (1) selects instruction strategies that are assembled into prompts (2) with historical context. The LLM generates candidate equations for evaluation (3), and feedback updates both the history and the optimizer (4), forming a closed-loop system.
Paper context
Paper title: Dynamic Bayesian Optimization Framework for Instruction Tuning in Partial Differential Equation Discovery Abstract: Large Language Models (LLMs) show promise for equation discovery, yet their outputs are highly sensitive to prompt phrasing, a phenomenon we term instruction brittleness. Static prompts cannot adapt to the evolving state of a multi-step generation process, causing models to plateau at suboptimal solutions. To address this, we propose NeuroSymBO, which reframes prompt engineering as a sequential decision problem. Our method maintains a discrete library of reasoning strategies and uses Bayesian Optimization to select the optimal instruction at each step based on numerical feedback. Experiments on PDE discovery benchmarks show that adaptive instruction selection significantly outperforms fixed prompts, achieving higher recovery rates with more parsimonious solutions. Passages referencing this figure: 2 Background Figure 1 : Overview of NeuroSym-BO . 3 Methodology NeuroSym-BO addresses the challenge of PDE discovery through a three-agent closed-loop architecture (Figure 1 ).
