This lecture covers two new insights into beam search, focusing on decoding sequence models in natural language processing. It explores the challenges of decoding neural language generators and the concept of beam search as an iterative subset optimization. The instructor discusses the importance of considering task-specific output spaces and the exponential complexity of exact decoding. Additionally, the lecture delves into the best-first beam search algorithm, which prioritizes hypotheses based on model scores. The presentation concludes with a discussion on the cognitive motivation behind beam search and the concept of uniform information density regularization in generated text.