We propose a novel value-aware quantization which applies aggressively reduced precision to the majority of data while separately handling a small amount of large data in high precision, which reduces total quantization errors under very low precision. We present new techniques to apply the proposed quantization to training and inference. The experiments show that our method with 3-bit activations (with 2 of large ones) can give the same training accuracy as full-precision one while offering significant (41.6 and 53.7 ) reductions in the memory cost of activations in ResNet-152 and Inception-v3 compared with the state-of-the-art method. Our experiments also show that deep networks such as Inception-v3, ResNet-101 and DenseNet-121 can be quantized for inference with 4-bit weights and activations (with 1 16-bit data) within 1 top-1 accuracy drop.
Recent advances in convolutional neural networks have considered model complexity and hardware efficiency to enable deployment onto embedded systems and mobile devices. For example, it is now well-known that the arithmetic operations of deep networks can be encoded down to 8-bit fixed-point without significant deterioration in performance. However, further reduction in precision down to as low as 3-bit fixed-point results in significant losses in performance. In this paper we propose a new data representation that enables state-of-the-art networks to be encoded to 3 bits with negligible loss in classification performance. To perform this, we take advantage of the fact that the weights and activations in a trained network naturally have non-uniform distributions. Using non-uniform, base-2 logarithmic representation to encode weights, communicate activations, and perform dot-products enables networks to 1) achieve higher classification accuracies than fixed-point at the same resolution and 2) eliminate bulky digital multipliers. Finally, we propose an end-to-end training procedure that uses log representation at 5-bits, which achieves higher final test accuracy than linear at 5-bits. Deep neural networks (DNNs) continue to make significant advances, solving tasks from image classification to translation or reinforcement learning. One aspect of the field receiving considerable attention is efficiently executing deep models in resource-constrained environments, such as mobile or embedded devices. This paper focuses on this problem, and proposes two new compression methods, which jointly leverage weight quantization and distillation of larger teacher networks into smaller student networks. The first method we propose is called quantized distillation and leverages distillation during the training process, by incorporating distillation loss, expressed with respect to the teacher, into the training of a student network whose weights are quantized to a limited set of levels. The second method, differentiable quantization, optimizes the location of quantization points through stochastic gradient descent, to better fit the behavior of the teacher model. We validate both methods through experiments on convolutional and recurrent architectures. We show that quantized shallow students can reach similar accuracy levels to full-precision teacher models, while providing order of magnitude compression, and inference speedup that is linear in the depth reduction. In sum, our results enable DNNs for resource-constrained environments to leverage architecture and accuracy advances developed on more powerful devices. Quantization is considered as one of the most effective methods to optimize the inference cost of neural network models for their deployment to mobile and embedded systems, which have tight resource constraints. In such approaches, it is critical to provide low-cost quantization under a tight accuracy loss constraint (e.g., 1 ). In this paper, we propose a novel method for quantizing weights and activations based on the concept of weighted entropy. Unlike recent work on binary-weight neural networks, our approach is multi-bit quantization, in which weights and activations can be quantized by any number of bits depending on the target accuracy. This facilitates much more flexible exploitation of accuracy-performance trade-off provided by different levels of quantization. Moreover, our scheme provides an automated quantization flow based on conventional training algorithms, which greatly reduces the design-time effort to quantize the network. According to our extensive evaluations based on practical neural network models for image classification (AlexNet, GoogLeNet and ResNet-50 101), object detection (R-FCN with 50-layer ResNet), and language modeling (an LSTM network), our method achieves significant reductions in both the model size and the amount of computation with minimal accuracy loss. Also, compared to existing quantization schemes, ours provides higher accuracy with a similar resource constraint and requires much lower design effort. For computer vision applications, prior works have shown the efficacy of reducing numeric precision of model parameters (network weights) in deep neural networks. Activation maps, however, occupy a large memory footprint during both the training and inference step when using mini-batches of inputs. One way to reduce this large memory footprint is to reduce the precision of activations. However, past works have shown that reducing the precision of activations hurts model accuracy. We study schemes to train networks from scratch using reduced-precision activations without hurting accuracy. We reduce the precision of activation maps (along with model parameters) and increase the number of filter maps in a layer, and find that this scheme matches or surpasses the accuracy of the baseline full-precision network. As a result, one can significantly improve the execution efficiency (e.g. reduce dynamic memory footprint, memory bandwidth and computational energy) and speed up the training and inference process with appropriate hardware support. We call our scheme WRPN - wide reduced-precision networks. We report results and show that WRPN scheme is better than previously reported accuracies on ILSVRC-12 dataset while being computationally less expensive compared to previously reported reduced-precision networks. Deep learning networks have achieved state-of-the-art accuracies on computer vision workloads like image classification and object detection. The performant systems, however, typically involve big models with numerous parameters. Once trained, a challenging aspect for such top performing models is deployment on resource constrained inference systems -- the models (often deep networks or wide networks or both) are compute and memory intensive. Low precision numerics and model compression using knowledge distillation are popular techniques to lower both the compute requirements and memory footprint of these deployed models. In this paper, we study the combination of these two techniques and show that the performance of low precision networks can be significantly improved by using knowledge distillation techniques. We call our approach Apprentice and show state-of-the-art accuracies using ternary precision and 4-bit precision for many variants of ResNet architecture on ImageNet dataset. We study three schemes in which one can apply knowledge distillation techniques to various stages of the train-and-deploy pipeline. 