Descriptif

In recent years, AI Reasoning has emerged as one of the most exciting paradigms in modern AI, driven by the impressive success of Large Reasoning Models (LRMs). Unlike the classical paradigm of scaling parameters to improve performance, LRMs leverage test-time compute to "think" through a problem before answering, resulting in markedly stronger problem-solving abilities, as evidenced by gold-medal-winning performances at IMO 2025. Despite these advances, however, we still lack a fundamental understanding of reasoning models and their inner workings, owing to their black-box nature and the heuristic training pipelines used to build them.

This course takes a principled look at AI reasoning and introduces the key ideas underpinning it. Starting with a brief historical perspective on the emergence of LRMs, we will study the gains they offer over traditional LLMs, both mathematically and empirically. We will then examine the core ingredients behind modern reasoning models, including Chain-of-Thought, supervised fine-tuning, reinforcement learning from human feedback (RLHF), reinforcement learning from verifiable rewards (RLVR), test-time scaling strategies, and alternative paradigms such as latent reasoning. We will also discuss the limitations and pitfalls of current approaches—including overthinking—and explore recent ideas aimed at addressing these shortcomings. Finally, we will examine some of the most exciting open problems and emerging directions in AI reasoning.