Title: FlexRound: Learnable Rounding by Element-wise Division for Post-Training Quantization. Abstract: Post-training Quantization (PTQ) has been gaining popularity for the deployment of deep neural networks on resource-limited devices since unlike quantization-aware training, neither a full training dataset nor end-to-end training is required at all. As PTQ schemes based on reconstructing each layer or block output turn out to be effective to enhance quantized model performance, recent works have developed algorithms to devise and learn a new weight-rounding scheme so as to better reconstruct each layer or block output. We notice that, however, such new rounding schemes are established on element-wise addition. In this work, we propose a simple yet effective new rounding mechanism for PTQ, coined FlexRound, via element-wise division to learn not only a common quantization grid size but also a different scale for each pre-trained weight. Thanks to the reciprocal rule of derivatives induced by element-wise division, FlexRound is inherently able to exploit the importance of a pre-trained weight when updating its corresponding scale, and thus, flexibly quantize a pre-trained weight depending on its own importance. We empirically validate the efficacy of FlexRound on a wide range of models and tasks. To the best of our knowledge, our work is the first to carry out comprehensive experiments on image classification, natural language understanding, and natural language generation in the per-tensor uniform PTQ setting. Our code will be open-sourced soon.