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This paradigm breaks down in novel domains and for sophisticated queries that cannot be answered from prior knowledge alone. Knowing the laws of physics, for instance, does not by itself enable LLMs to answer queries or complete long-horizon tasks in a complex physical system. To address this, we introduce Hierarchical Experimentalist Agents (HExA), an in-context self-improvement framework to learn from active experimentation. HExA iteratively designs and refines query-relevant experiments, learns a reusable library of composable skills from experience, and integrates experimental evidence to answer queries or take actions. 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