Hardware-friendly network quantization (e.g., binary/uniform quantization) can efficiently accelerate the inference and meanwhile reduce memory consumption of the deep neural networks, which is crucial for model deployment on resource-limited devices like mobile phones. However, due to the discreteness of low-bit quantization, existing quantization methods often face the unstable training process and severe performance degradation. To address this problem, in this paper we propose Differentiable Soft Quantization (DSQ) to bridge the gap between the full-precision and low-bit networks. DSQ can automatically evolve during training to gradually approximate the standard quantization. Owing to its differentiable property, DSQ can help pursue the accurate gradients in backward propagation, and reduce the quantization loss in forward process with an appropriate clipping range. Extensive experiments over several popular network structures show that training lowbit neural networks with DSQ can consistently outperform state-of-the-art quantization methods. Besides, our first efficient implementation for deploying 2 to 4-bit DSQ on devices with ARM architecture achieves up to 1.7× speed up, compared with the open-source 8-bit high-performance inference framework NCNN [31].

Model binarization is an effective method of compressing neural networks and accelerating their inference process, which enables state-of-the-art models to run on resource-limited devices. Recently, advanced binarization methods have been greatly improved by minimizing the quantization error directly in the forward process. However, a significant performance gap still exists between the 1-bit model and the 32-bit one. The empirical study shows that binarization causes a great loss of information in the forward and backward propagation which harms the performance of binary neural networks (BNNs), and the limited information representation ability of binarized parameter is one of the bottlenecks of BNN performance. We present a novel Distributionsensitive Information Retention Network (DIR-Net) to retain the information of the forward activations and backward gradients, which improves BNNs

The binary neural network, largely saving the storage and computation, serves as a promising technique for deploying deep models on resource-limited devices.However, the binarization inevitably causes severe information loss, and even worse, its discontinuity brings difficulty to the optimization of the deep network.To address these issues, a variety of algorithms have been proposed, and achieved satisfying progress in recent years. In this paper, we present a comprehensive survey of these algorithms, mainly categorized into the native solutions directly conducting binarization, and the optimized ones using techniques like minimizing the quantization error, improving the network loss function, and reducing the gradient error. We also investigate other practical aspects of binary neural networks such as the hardware-friendly design and the training tricks. Then, we give the evaluation and discussions on different tasks, including image classification, object detection and semantic segmentation. Finally, the challenges that may be faced in future research are prospected.the heavy computation and storage still inevitably limit the applications of the deep CNNs in practice. Besides, due to the huge model parameter space, the prediction of the neural networks is usually viewed as a black-box, which brings great challenges to the interpretability of CNNs. Some works like [21,22,23] empirically explore the function of each layer in the network. They visualize the feature maps extracted by different filters and view each filter as a visual unit focusing on different visual components.of the ResNet-50 [28], and meanwhile save more than 75% of parameters and 50% computational time. In the literature, approaches for compressing the deep networks can be classified into five categories: parameter pruning [26,29,30,31], parameter quantizing [32,33,34,35,36,37,38,39,40,41], low-rank parameter factorization [42,43,44,45,46], transferred/compact convolutional filters [47,48,49,50], and knowledge distillation [51,52,53,54,55,56]. The parameter pruning and quantizing mainly focus on eliminating the redundancy in the model parameters respectively by removing the redundant/uncritical ones or compressing the parameter space (e.g. , from the floating-point weights to the integer ones). Low-rank factorization applies the matrix/tensor decomposition techniques to estimate the informative parameters using the proxy ones of small size. The compact convolutional filter based approaches rely on the carefullydesigned structural convolutional filters to reduce the storage and computation complexity. The knowledge distillation methods try to distill a more compact model to reproduce the output of a larger network.Among the existing network compression techniques, quantization based one serves as a promising and fast solution that yields highly compact models compared to their floating-point counterparts, by representing the network weights with very low precision. Along this direction, the most extreme quantization is binarization, the interest...

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We study the challenging task of neural network quantization without end-toend retraining, called Post-training Quantization (PTQ). PTQ usually requires a small subset of training data but produces less powerful quantized models than Quantization-Aware Training (QAT). In this work, we propose a novel PTQ framework, dubbed BRECQ, which pushes the limits of bitwidth in PTQ down to INT2 for the first time. BRECQ leverages the basic building blocks in neural networks and reconstructs them one-by-one. In a comprehensive theoretical study of the second-order error, we show that BRECQ achieves a good balance between crosslayer dependency and generalization error. To further employ the power of quantization, the mixed precision technique is incorporated in our framework by approximating the inter-layer and intra-layer sensitivity. Extensive experiments on various handcrafted and searched neural architectures are conducted for both image classification and object detection tasks. And for the first time we prove that, without bells and whistles, PTQ can attain 4-bit ResNet and MobileNetV2 comparable with QAT and enjoy 240× faster production of quantized models. Codes are available at https://github.com/yhhhli/BRECQ.

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