Title: Post-Training Weighted Quantization of Neural Networks for Language Models. Abstract: As a practical model compression technique, parameter quantization is effective especially for language models associated with a large memory footprint. Neural network quantization is usually performed to reduce quantization loss assuming that quantization error of each parameter equally contributes to the overall training loss. The importance of each parameter, however, may highly differ such that for the same number of quantization bits, certain parameters lead to higher training loss than the others after quantization. In this paper, we consider a non-uniform quantization scheme, specifically binary-coding-based quantization, for high compression ratio and efficient computations while avoiding large accuracy degradation by uniform quantization (e.g., INT8). Then, we derive quantization optimization methods to take into account the importance of each parameter. We demonstrate that for post-training quantization, weight magnitude can represent importance and improve model accuracy significantly compared to the previous schemes lacking importance considerations. For various language models including BERT, DistilBERT, AWD-LSTM, and Transformer, we achieve 2-4 bits per weight by our proposed post-training quantization with reasonable accuracy degradation.