The field of large language models (LLMs) is moving towards developing more trustworthy and safe AI systems. Recent research has focused on addressing critical failures such as spurious reasoning, deceptive alignment, and instruction disobedience. A key direction is the development of theoretical frameworks for analyzing the stability of reward-policy maps, which provides a unified explanation for various failures and offers insights for designing safer AI systems. Another area of research is the development of novel optimization methods, such as geometric-mean policy optimization, which improves stability and performance in multi-reward reinforcement learning settings. Additionally, there is a growing interest in corrigibility, with frameworks being developed to ensure that AI systems are aligned with human values and can be trusted to behave correctly even in complex, partially observed environments. Noteworthy papers in this area include: The Policy Cliff, which presents a rigorous mathematical framework for analyzing policy stability. Core Safety Values for Provably Corrigible Agents, which introduces a framework for corrigibility with provable guarantees in multi-step environments. Geometric-Mean Policy Optimization, which proposes a stabilized variant of Group Relative Policy Optimization. From Sufficiency to Reflection, which analyzes existing retrieval-augmented generation methods and proposes a novel framework for improving reasoning quality. Trustworthy Reasoning, which evaluates and enhances factual accuracy in LLM intermediate thought processes.