The field of large language models (LLMs) is moving towards more efficient and optimized models, with a focus on quantization, pruning, and knowledge distillation techniques. Researchers are exploring various methods to reduce the computational cost and memory footprint of LLMs, while maintaining their performance. One notable direction is the development of quantization-aware training approaches, which can significantly improve the accuracy of quantized models. Another area of research is the investigation of mixed-precision quantization methods, which can achieve ultra-low bit widths while minimizing performance degradation. Furthermore, the application of lattice algorithms to LLM quantization is providing new insights and theoretical foundations for the development of more efficient quantization methods. Noteworthy papers in this area include: SiLQ, which demonstrates a simple and effective quantization-aware training approach; Squeeze10-LLM, which proposes a staged mixed-precision post-training quantization framework; and The Geometry of LLM Quantization, which provides a geometric interpretation of the GPTQ algorithm and its connection to lattice algorithms.