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Low-bit quantization of network weights and activations can drasticallyreduce the memory footprint, complexity, energy consumption and latency of DeepNeural Networks (DNNs). However, low-bit quantization can also cause aconsiderable drop in accuracy, in particular when we apply it to complexlearning tasks or lightweight DNN architectures. In this paper, we propose atraining procedure that relaxes the low-bit quantization. We call thisprocedure \textit{DNN Quantization with Attention} (DQA). The relaxation isachieved by using a learnable linear combination of high, medium and low-bitquantizations. Our learning procedure converges step by step to a low-bitquantization using an attention mechanism with temperature scheduling. Inexperiments, our approach outperforms other low-bit quantization techniques onvarious object recognition benchmarks such as CIFAR10, CIFAR100 and ImageNetILSVRC 2012, achieves almost the same accuracy as a full precision DNN, andconsiderably reduces the accuracy drop when quantizing lightweight DNNarchitectures.