Learn probability fundamentals and practical implementation techniques for large language model inference through this comprehensive lecture from CMU's Advanced NLP course. Explore essential probability concepts that underpin modern language models, then dive into hands-on transformer implementation details. Master various text generation strategies and evaluation methodologies used to assess model performance. Discover meta-generation techniques that enable models to reason about their own generation processes. Gain practical coding experience through detailed examples that demonstrate how theoretical concepts translate into working implementations, providing you with both the mathematical foundation and programming skills necessary for advanced natural language processing applications.