To realize the promise of ubiquitous embedded deep network inference, it is essential to seek limits of energy and area efficiency. To this end, low-precision networks offer tremendous promise because both energy and area scale down quadratically with the reduction in precision. Here, for the first time, we demonstrate ResNet-18, ResNet-34, ResNet-50, ResNet-152, Inception-v3, densenet-161, and VGG-16bn networks on the ImageNet classification benchmark that, at 8-bit precision exceed the accuracy of the full-precision baseline networks after one epoch of finetuning, thereby leveraging the availability of pretrained models. We also demonstrate for the first time ResNet-18, ResNet-34, and ResNet-50 4-bit models that match the accuracy of the full-precision baseline networks. Surprisingly, the weights of the low-precision networks are very close (in cosine similarity) to the weights of the corresponding baseline networks, making training from scratch unnecessary. The number of iterations required by stochastic gradient descent to achieve a given training error is related to the square of (a) the distance of the initial solution from the final plus (b) the maximum variance of the gradient estimates. By drawing inspiration from this observation, we (a) reduce solution distance by starting with pretrained fp32 precision baseline networks and fine-tuning, and (b) combat noise introduced by quantizing weights and activations during training, by using larger batches along with matched learning rate annealing. Together, these two techniques offer a promising heuristic to discover low-precision networks, if they exist, close to fp32 precision baseline networks.

通过调整激活函数范围并使用精细调整的预训练模型来组合简单技术，可以发现与fp32模型接近的低精度模型，同时提高了效率，本文证明了4位精度足以进行分类。

为高效嵌入式推断发现接近全精度网络的低精度网络