Quantization is a promising technique to reduce the computation and storage costs of DNNs. Low-bit ( ≤ 8 bits) precision training remains an open problem due to the difficulty of gradient quantization. In this paper, we find two long-standing misunderstandings of the bias of gradient quantization noise. First, the large bias of gradient quantization noise, instead of the variance, is the key factor of training accuracy loss. Second, the widely used stochastic rounding cannot solve the training crash problem caused by the gradient quantization bias in practice. Moreover, we find that the asymmetric distribution of gradients causes a large bias of gradient quantization noise. Based on our findings, we propose a novel adaptive piecewise quantization method to effectively limit the bias of gradient quantization noise. Accordingly, we propose a new data format, Piecewise Fixed Point (PWF), to present data after quantization. We apply our method to different applications including image classification, machine translation, optical character recognition, and text classification. We achieve approximately 1.9 ∼ 3.5× speedup compared with full precision training with an accuracy loss of less than 0.5%. To the best of our knowledge, this is the first work to quantize gradients of all layers to 8 bits in both large-scale CNN and RNN training with negligible accuracy loss.

Recent emerged quantization technique (i.e., using low bit-width fixed-point data instead of high bit-width floating-point data) has been applied to inference of deep neural networks for fast and efficient execution. However, directly applying quantization in training can cause significant accuracy loss, thus remaining an open challenge. In this paper, we propose a novel training approach, which applies a layer-wise precision-adaptive quantization in deep neural networks. The new training approach leverages our key insight that the degradation of training accuracy is attributed to the dramatic change of data distribution. Therefore, by keeping the data distribution stable through a layer-wise precision-adaptive quantization, we are able to directly train deep neural networks using low bit-width fixed-point data and achieve guaranteed accuracy, without changing hyper parameters. Experimental results on a wide variety of network architectures (e.g., convolution and recurrent networks) and applications (e.g., image classification, object detection, segmentation and machine translation) show that the proposed approach can train these neural networks with negligible accuracy losses (-1.40%-1.3%, 0.02% on average), and speed up training by 252% on a state-of-the-art Intel CPU.