SGEvolve: Semantic Gradient Guidance for LLM-Driven Evolutionary Search

Large language model (LLM)-driven evolutionary frameworks have emerged as a promising paradigm for iterative search in complex optimization and structured generation tasks. However, existing methods typically rely on heuristic variation operators and lack an explicit mechanism to extract directional information from observed performance feedback, limiting both efficiency and reliability. To address this, we propose SGEvolve, a semantic gradient-guided evolutionary framework for LLM-driven optimization. The key idea is to treat the performance differences between parent and offspring as zeroth-order evidence of an underlying ascent direction. Based on this view, we formulate semantic gradient extraction as a Maximum A Posteriori (MAP) estimation problem, where the LLM infers the most probable direction of improvement conditioned on observed evolutionary steps. The inferred gradients are then used to guide mutation and crossover, biasing generation toward more promising regions of the search space. We evaluate SGEvolve on a diverse set of tasks, including mathematical optimization, algorithm design, and real-world industrial problems. Experimental results demonstrate that SGEvolve consistently outperforms existing open-source baselines, achieving superior performance in both solution quality and search efficiency.