When the Answer Lies at the End of a Branch: The Complete Architecture of Inference-Time Search Methods for LLM Reasoning
The emergence of reasoning models like DeepSeek-R1, OpenAI’s o3, and Google’s Gemini thinking mode has fundamentally shifted how we think about LLM inference. These models don’t just generate—they search. The question is no longer “what should the model output?” but “how should the model search for the answer?” This shift from generation to search has spawned an entire taxonomy of inference-time algorithms, each with distinct trade-offs between computational cost and output quality. Understanding these methods—their mathematical foundations, implementation details, and practical performance—is essential for anyone deploying reasoning models in production. ...