Title: DNN Quantization with Attention. Abstract: Low-bit quantization of network weights and activations can drastically reduce the memory footprint, complexity, energy consumption and latency of Deep Neural Networks (DNNs). Many different quantization methods like min-max quantization, Statistics-Aware Weight Binning (SAWB) or Binary Weight Network (BWN) have been proposed in the past. However, they still cause a considerable accuracy drop, in particular when applied to complex learning tasks or lightweight DNN architectures. In this paper, we propose a novel training procedure that can be used to improve the performance of existing quantization methods. We call this procedure \textit{DNN Quantization with Attention} (DQA). It relaxes the training problem, using a learnable linear combination of high, medium and low-bit quantization at the beginning, while converging to a single low-bit quantization at the end of the training. We show empirically that this relaxation effectively smooths the loss function and therefore helps convergence. Moreover, we conduct experiments and show that our procedure improves the performance of many state-of-the-art quantization methods on various object recognition tasks. In particular, we apply DQA with min-max, SAWB and BWN to train $2$bit quantized DNNs on the CIFAR10, CIFAR100 and ImageNet ILSVRC 2012 datasets, achieving a very good accuracy comparing to other conterparts.