Explore the limitations of the attention mechanism in Transformer models through a 48-minute lecture by Bingbin Liu from Carnegie Mellon University. Delve into the study of Transformer's reasoning capabilities using sequential reasoning tasks formulated with finite-state automata. Discover how o(T)-layer Transformers can simulate T steps of sequential reasoning, utilizing tools from Krohn-Rhodes theory and circuit complexity. Examine empirical findings that reveal practical challenges in optimization and representation richness, preventing models from discovering optimal constructions. Investigate Transformers' struggles with out-of-distribution generalization on simple tasks easily solved by RNNs, highlighting two inherent limitations of the Transformer architecture. Gain insights into the implications of these limitations for generalization and optimization in Transformer models.