Recent research highlights fundamental limitations in the reasoning capabilities of large language models (LLMs), particularly in compositional tasks. Studies by Nouha Dziri at the Allen Institute for AI and Binghui Peng at Stanford University reveal that transformer-based architectures, which underpin most LLMs, struggle with complex reasoning tasks such as multi-step logic puzzles and mathematical operations. Dziri's team found that models like GPT-4 often fail to generalize beyond their training data, achieving low accuracy in tasks such as multiplying large numbers or solving Einstein's riddle. Peng's research mathematically proved that even advanced transformer models have inherent computational limits for compositional reasoning. While techniques like chain-of-thought prompting and embedding enhancements have shown promise in improving performance, these approaches do not eliminate the fundamental constraints of transformer architectures. Additionally, new methods such as MMOA-RAG optimization from Renmin University and Microsoft, the Matryoshka Re-Ranker architecture, and the ARM retrieval method have been developed to address specific challenges in LLM reasoning and retrieval. The findings suggest that alternative architectures or significant modifications may be necessary to overcome these limitations.