Recent research in AI theory is increasingly focused on understanding the fundamental principles that govern intelligence and agency, particularly in complex systems. A notable trend is the exploration of how AI can effectively manage uncertainty, with distinctions made between epistemic and subjective uncertainty, which could enhance decision-making processes in uncertain environments. Additionally, investigations into the expressive power of transformer architectures are revealing their capabilities in approximating complex functions, which has implications for optimizing model performance across various applications. Theoretical advancements are also being made in Bayesian network learning, with new parameterization strategies that could simplify the learning process. Furthermore, the analysis of reasoning mechanisms in large language models is shedding light on the computational costs associated with chain-of-thought reasoning, providing insights into optimizing inference time. Collectively, these developments are paving the way for more resilient, adaptive AI systems that can better navigate real-world complexities and uncertainties.