LLM Reasoning and Test-Time Compute Scaling Cheat Sheet

Modern reasoning-optimized LLMs allocate additional inference compute to deliberate on complex problems before generating answers, a paradigm known as test-time compute scaling. These models—pioneered by OpenAI's o1/o3 series and DeepSeek-R1—generate extended internal thinking traces during inference, enabling them to solve graduate-level math (AIME), scientific reasoning (GPQA Diamond), and code generation (Codeforces) tasks that stump standard LLMs. Unlike traditional pretraining scaling (more parameters, more data), test-time scaling improves accuracy by investing compute at inference time, turning reasoning into a search problem over possible solution paths. The key insight: spending more time thinking often outperforms adding more training data, opening a new axis of performance improvement orthogonal to model size.