Beyond Prompt or Skill? Attribution-Guided Optimization of Modular LLM Programs

Large language models can solve increasingly diverse reasoning tasks, yet their performance remains highly sensitive to task prompts, intermediate instructions, and the way reusable problem-solving knowledge is incorporated. Existing optimization methods usually focus on only one part of this design space: they either optimize a monolithic prompt, or separately induce and refine skills from model traces. As a result, they lack a principled mechanism for deciding which component should be updated when failures occur, and they rarely optimize prompts, skills, and skill-use policies in a unified framework. We propose SPARO (Skill, Prompt, And Routing Optimization), a framework that jointly optimizes task instructions, reusable skill blocks, and routing rules. It performs controlled counterfactual evaluations, converts examples' effects into a probabilistic responsibility distribution over prompt, skill, and routing components, samples one component from that distribution, and applies the corresponding targeted mutation. This design moves language-program optimization beyond global prompt rewriting toward structured, reusable, and selectively activated task knowledge. Across five benchmarks and five worker models, SPARO consistently outperforms both prompt-centered and skill-centered optimization baselines. These results suggest that effective language-program optimization depends not only on discovering useful task knowledge, but also on deciding where that knowledge should be stored and when it should be activated.