The field of natural language processing is witnessing significant developments in uncertainty quantification for large language models (LLMs). Researchers are exploring innovative methods to quantify and manage uncertainty in LLMs, which is essential for their reliable deployment in high-stakes applications. A key direction in this area is the development of probabilistic frameworks that can effectively capture the uncertainty inherent in LLMs. These frameworks are being designed to provide more accurate and informative uncertainty estimates, which can help improve the overall performance and trustworthiness of LLM-based systems. Notable papers in this area include Conformal Prediction with Query Oracle, which introduces a novel framework for uncertainty quantification in LLMs, and Inv-Entropy, which proposes a fully probabilistic framework for uncertainty quantification based on an inverse model. Additionally, researchers are investigating the application of Bayesian inference methods, such as Markov Chain Monte Carlo (MCMC) and Variational Inference (VI), to approximate the posterior distribution in probabilistic matrix factorization. Other works, like Textual Bayes and A quantum semantic framework for natural language processing, are exploring the use of Bayesian methods and quantum-inspired approaches to improve uncertainty quantification and linguistic interpretation in LLMs. Overall, these advancements are paving the way for more reliable and calibrated LLM-based systems, which can have significant impacts on a wide range of applications.