The field of large language models (LLMs) is moving towards more efficient deployment through innovative quantization techniques. Recent developments have focused on addressing the limitations of existing methods, which struggle with low-precision quantization and fail to account for inter-layer interactions. New approaches have been proposed to optimize the structure of the representation, reducing biases and improving generalization. Additionally, novel quantization methods have been introduced to enable more accurate compression and faster inference. These advancements have pushed the boundaries of ultra-low precision post-training quantization, achieving state-of-the-art performance and efficiency. Notable papers include: IMPQ, which proposes a cooperative game-based approach to mixed-precision quantization, and MEC-Quant, which introduces a maximum entropy coding objective to optimize the representation structure. SBVR is also noteworthy for its novel bitvector representation, enabling Gaussian-like code representation and fast inference. Bi-VLM and Q-Palette have also made significant contributions to the field, with Bi-VLM proposing a saliency-aware hybrid quantization algorithm and Q-Palette introducing fractional-bit quantizers for optimal bit allocation.