Two-Step Quantization for Low-bit Neural Networks

Every bit matters in the hardware design of quantized neural networks. However, extremely-low-bit representation usually causes large accuracy drop. Thus, how to train extremely-low-bit neural networks with high accuracy is of central importance. Most existing network quantization approaches learn transformations (low-bit weights) as well as encodings (low-bit activations) simultaneously. This tight coupling makes the optimization problem difficult, and thus prevents the network from learning optimal representations. In this paper, we propose a simple yet effective Two-Step Quantization (TSQ) framework, by decomposing the network quantization problem into two steps: code learning and transformation function learning based on the learned codes. For the first step, we propose the sparse quantization method for code learning. The second step can be formulated as a non-linear least square regression problem with low-bit constraints, which can be solved efficiently in an iterative manner. Extensive experiments on CIFAR-10 and ILSVRC-12 datasets demonstrate that the proposed TSQ is effective and outperforms the state-of-the-art by a large margin. Especially, for 2-bit activation and ternary weight quantization of AlexNet, the accuracy of our TSQ drops only about 0.5 points compared with the full-precision counterpart, outperforming current state-of-the-art by more than 5 points.