Overcoming Semantic Misalignment in Latent Reasoning Auto-Design

We envision large language models (LLMs) not only as reasoners, but also as designers of reasoning algorithms. A key step toward this goal is to make reasoning algorithms explicit objects of auto-design. We study this step in training-free latent reasoning, where hand-crafted algorithms can improve reasoning by reorganizing inference-time computation without updating model weights. The central challenge is semantic misalignment between program representations and the the algorithmic semantics of latent reasoning: implementation details obscure algorithm design, also making accumulated experience difficult to translate into targeted revisions. Our key idea is to construct a semantically aligned design space for LLM-driven algorithm evolution. To this end, we introduce LRDSL, a domain-specific language that represents algorithm logic using composable components for observation, stateful control, latent-input construction, and inference-budget management. These components serve as shared semantic units for algorithm design, behavioral measurement, and experience accumulation.Within this space, a proposer LLM designs reasoning algorithms for a target LLM and iteratively refines them using experience distilled from execution feedback. Across three design systems and two backbones, LRDSL improves the macro-average accuracy of the discovered algorithms on five reasoning benchmarks in all six configurations, by up to 5.65 percentage points. The best discovered policies exceed the strongest human-designed baseline by 1.53.