Explore the computational advantages and constraints of Transformers and state-space models in this 51-minute lecture by Eran Malach from the Kempner Institute at Harvard University. Delve into the mechanisms enabling retrieval, copying, and length generalization in language models, and examine how network architecture choices impact model performance on fundamental tasks. Discover theoretical and empirical evidence highlighting Transformers' superiority in copying and retrieval tasks compared to LSTM and state-space models like Mamba. Learn how Transformers' ability to copy long sequences can be harnessed for length generalization across various algorithmic and arithmetic tasks, providing valuable insights into the capabilities and limitations of different sequence modeling architectures.