Mixed-precision quantization has received increasing attention for its capability of reducing the computational burden and speeding up the inference time. Existing methods usually focus on the sensitivity of different network layers, which requires a time-consuming search or training process. To this end, a novel mixed-precision quantization method, termed CSMPQ, is proposed. Specifically, the TF-IDF metric that is widely used in natural language processing (NLP) is introduced to measure the class separability of layer-wise feature maps. Furthermore, a linear programming problem is designed to derive the optimal bit configuration for each layer. Without any iterative process, the proposed CSMPQ achieves better compression trade-offs than the state-of-the-art quantization methods. Specifically, CSMPQ achieves 73.03$\%$ Top-1 acc on ResNet-18 with only 59G BOPs for QAT, and 71.30$\%$ top-1 acc with only 1.5Mb on MobileNetV2 for PTQ.

为了弥合深度神经网络的复杂性和硬件能力之间不断增加的差距，网络量化引起了越来越多的研究关注。混合精度量化的最新趋势利用硬件的多个位宽度算术运算来释放网络量化的全部潜力。然而，这也导致困难的整数编程配方，并且即使使用各种放松，大多数现有方法也能使用极其耗时的搜索过程。我们建议优化一个代理度量，而不是解决原始整数编程的问题，而是与整数编程的丢失高度相关的网络正交性的概念，而是用线性编程易于优化。该方法通过数量级的秩序减少了搜索时间和所需的数据量，符合量化精度几乎没有妥协。具体而言，我们在Reset-18上获得72.08％的前1个精度，6.7MB不需要任何搜索迭代。鉴于我们的算法的高效率和低数据依赖性，我们将其用于训练后量化，该量化仅在MobileNetv2上实现71.27％的前1个精度，只有1.5MB。我们的代码可在https://github.com/mac-automl/oppq上获得。

Mixed-precision quantization has been widely applied on deep neural networks (DNNs) as it leads to significantly better efficiency-accuracy tradeoffs compared to uniform quantization. Meanwhile, determining the exact precision of each layer remains challenging. Previous attempts on bit-level regularization and pruning-based dynamic precision adjustment during training suffer from noisy gradients and unstable convergence. In this work, we propose Continuous Sparsification Quantization (CSQ), a bit-level training method to search for mixed-precision quantization schemes with improved stability. CSQ stabilizes the bit-level mixed-precision training process with a bi-level gradual continuous sparsification on both the bit values of the quantized weights and the bit selection in determining the quantization precision of each layer. The continuous sparsification scheme enables fully-differentiable training without gradient approximation while achieving an exact quantized model in the end.A budget-aware regularization of total model size enables the dynamic growth and pruning of each layer's precision towards a mixed-precision quantization scheme of the desired size. Extensive experiments show CSQ achieves better efficiency-accuracy tradeoff than previous methods on multiple models and datasets.

Model quantization enables the deployment of deep neural networks under resource-constrained devices. Vector quantization aims at reducing the model size by indexing model weights with full-precision embeddings, i.e., codewords, while the index needs to be restored to 32-bit during computation. Binary and other low-precision quantization methods can reduce the model size up to 32$\times$, however, at the cost of a considerable accuracy drop. In this paper, we propose an efficient framework for ternary quantization to produce smaller and more accurate compressed models. By integrating hyperspherical learning, pruning and reinitialization, our proposed Hyperspherical Quantization (HQ) method reduces the cosine distance between the full-precision and ternary weights, thus reducing the bias of the straight-through gradient estimator during ternary quantization. Compared with existing work at similar compression levels ($\sim$30$\times$, $\sim$40$\times$), our method significantly improves the test accuracy and reduces the model size.

量化图像超分辨率的深卷积神经网络大大降低了它们的计算成本。然而，现有的作品既不患有4个或低位宽度的超低精度的严重性能下降，或者需要沉重的微调过程以恢复性能。据我们所知，这种对低精度的漏洞依赖于特征映射值的两个统计观察。首先，特征贴图值的分布每个通道和每个输入图像都变化显着变化。其次，特征映射具有可以主导量化错误的异常值。基于这些观察，我们提出了一种新颖的分布感知量化方案（DAQ），其促进了超低精度的准确训练量化。 DAQ的简单功能确定了具有低计算负担的特征图和权重的动态范围。此外，我们的方法通过计算每个通道的相对灵敏度来实现混合精度量化，而无需涉及任何培训过程。尽管如此，量化感知培训也适用于辅助性能增益。我们的新方法优于最近的培训甚至基于培训的量化方法，以超低精度为最先进的图像超分辨率网络。

网络量化是一种有效的压缩方法，以降低模型大小和计算成本。尽管压缩比高，但训练低精度模型由于量化的离散和不可分散的性质，难以实现相当大的性能下降。最近，提出了清晰度感知最小化（SAM），以通过同时最小化损耗值和损耗曲率来改善模型的泛化性能。在本文中，我们设计了锐度感知量化（SAQ）方法来培训量化模型，从而导致更好的泛化性能。此外，由于每个层与网络的损耗和损耗锐度有不同的贡献，我们进一步设计了一种有效的方法，该方法学习配置生成器以自动确定每层的位宽度配置，鼓励平面区域的较低位，反之亦然尖锐的景观，同时促进最小值的平整度，以实现更积极的量化。对CiFar-100和Imagenet的广泛实验显示了所提出的方法的优越性。例如，我们的量化Reset-18具有55.1X比特操作（BOP）减少甚至在前1个精度方面均匀地优于0.7％。代码可在https://github.com/zhuang-group/saq获得。

混合精确的深神经网络达到了硬件部署所需的能源效率和吞吐量，尤其是在资源有限的情况下，而无需牺牲准确性。但是，不容易找到保留精度的最佳每层钻头精度，尤其是在创建巨大搜索空间的大量模型，数据集和量化技术中。为了解决这一困难，最近出现了一系列文献，并且已经提出了一些实现有希望的准确性结果的框架。在本文中，我们首先总结了文献中通常使用的量化技术。然后，我们对混合精液框架进行了彻底的调查，该调查是根据其优化技术进行分类的，例如增强学习和量化技术，例如确定性舍入。此外，讨论了每个框架的优势和缺点，我们在其中呈现并列。我们最终为未来的混合精液框架提供了指南。

深神经网络（DNN）的庞大计算和记忆成本通常排除了它们在资源约束设备中的使用。将参数和操作量化为较低的位精确，为神经网络推断提供了可观的记忆和能量节省，从而促进了在边缘计算平台上使用DNN。量化DNN的最新努力采用了一系列技术，包括渐进式量化，步进尺寸的适应性和梯度缩放。本文提出了一种针对边缘计算的混合精度卷积神经网络（CNN）的新量化方法。我们的方法在模型准确性和内存足迹上建立了一个新的Pareto前沿，展示了一系列量化模型，可提供低于4.3 MB的权重（WGTS。）和激活（ACTS。）。我们的主要贡献是：（i）用张量学的学习精度，（ii）WGTS的靶向梯度修饰，（i）硬件感知的异质可区分量化。和行为。为了减轻量化错误，以及（iii）多相学习时间表，以解决从更新到学习的量化器和模型参数引起的学习不稳定性。我们证明了我们的技术在Imagenet数据集上的有效性，包括高效网络lite0（例如，WGTS。的4.14MB和ACTS。以67.66％的精度）和MobilenEtV2（例如3.51MB WGTS。 ％ 准确性）。

量化被疯狂地作为模型压缩技术，该技术通过将神经网络中的浮点重量和激活转换为低位整数来获得有效的模型。量化已被证明可以很好地在卷积神经网络和基于变压器的模型上运行。尽管这些模型具有符合性的典型性，但最近的工作表明，基于MLP的模型能够在从计算机视觉，NLP到3D点云等各种任务上取得可比的结果，同时由于并行性和网络简单性，可以实现更高的吞吐量。但是，正如我们在论文中所显示的那样，将量化直接应用于基于MLP的模型将导致明显的准确性降解。基于我们的分析，两个主要问题说明了准确性差距：1）基于MLP的模型中的激活范围可能太大而无法量化，而2）基于MLP的模型中的特定组件对量化很敏感。因此，我们建议1）应用分层以控制激活的量化范围，2）使用有界的激活功能，3）在激活上应用百分位量化，4）使用我们的改进的模块，称为多个令牌混合MLP，5）应用线性态度敏感操作的不对称量化器。我们的Q-MLP模型配备了上述技术，可以使用8位均匀量化（型号30 MB）和78.47％的Imagenet获得79.68％的精度，而4位量化（15 MB）。

目前，神经网络模型的量化方法主要分为训练后量化（PTQ）和量化意识培训（QAT）。培训后量化仅需要一小部分数据即可完成量化过程，但是其定量模型的性能不如量化意识培训。本文提出了一种新颖的量化方法，称为注意弹。该方法给出了参数w有机会映射到所有可能的量化值，而不仅仅是在量化过程中w附近的两个量化值。被映射到不同量化值的概率与量化值和W之间的距离负相关，并随高斯函数衰减。此外，本文使用有损耗的编码长度作为衡量标准，将位宽度分配给模型的不同层以解决混合精度量化的问题，从而有效避免了解决组合优化问题。本文还对不同模型进行了定量实验，结果证实了该方法的有效性。对于RESNET18和MOBILENETV2，本文提出的后培训量化仅需要1,024个培训数据和10分钟即可完成量化过程，这可以在量化意识培训的情况下实现量化性能。

尽管在许多计算机视觉任务上具有卓越的性能，但深度卷积神经网络众所周知，在具有资源限制的设备上被压缩。大多数现有的网络修剪方法需要艰苦的人类努力和禁止的计算资源，特别是当约束改变时。当需要部署在各种设备上时，这实际上限制了模型压缩的应用。此外，现有的方法仍然受到缺失的理论指导挑战。在本文中，我们提出了一种信息理论启发的自动模型压缩策略。我们的方法背后的原理是信息瓶颈理论，即隐藏的表示应该彼此压缩信息。因此，我们在网络激活中介绍了标准化的Hilbert-Schmidt独立性标准（NHSIC），作为层重要性的稳定和广义指标。当给出某个资源约束时，我们将HSIC指示器与约束将架构搜索问题转换为具有二次约束的线性编程问题。这种问题很容易通过几秒钟的凸优化方法解决。我们还提供严格的证据，揭示优化归一化的HSIC同时最小化不同层之间的相互信息。没有任何搜索过程，我们的方法实现了与最先进的压缩算法相比的更好的压缩权衡。例如，通过Reset-50，我们达到了45.3％的杂志，在想象中有75.75前1个精度。代码是在https://github.com/mac-automl/itpruner/tree/master上的途径。

Although considerable progress has been obtained in neural network quantization for efficient inference, existing methods are not scalable to heterogeneous devices as one dedicated model needs to be trained, transmitted, and stored for one specific hardware setting, incurring considerable costs in model training and maintenance. In this paper, we study a new vertical-layered representation of neural network weights for encapsulating all quantized models into a single one. With this representation, we can theoretically achieve any precision network for on-demand service while only needing to train and maintain one model. To this end, we propose a simple once quantization-aware training (QAT) scheme for obtaining high-performance vertical-layered models. Our design incorporates a cascade downsampling mechanism which allows us to obtain multiple quantized networks from one full precision source model by progressively mapping the higher precision weights to their adjacent lower precision counterparts. Then, with networks of different bit-widths from one source model, multi-objective optimization is employed to train the shared source model weights such that they can be updated simultaneously, considering the performance of all networks. By doing this, the shared weights will be optimized to balance the performance of different quantized models, thus making the weights transferable among different bit widths. Experiments show that the proposed vertical-layered representation and developed once QAT scheme are effective in embodying multiple quantized networks into a single one and allow one-time training, and it delivers comparable performance as that of quantized models tailored to any specific bit-width. Code will be available.

Although weight and activation quantization is an effective approach for Deep Neural Network (DNN) compression and has a lot of potentials to increase inference speed leveraging bit-operations, there is still a noticeable gap in terms of prediction accuracy between the quantized model and the full-precision model. To address this gap, we propose to jointly train a quantized, bit-operation-compatible DNN and its associated quantizers, as opposed to using fixed, handcrafted quantization schemes such as uniform or logarithmic quantization. Our method for learning the quantizers applies to both network weights and activations with arbitrary-bit precision, and our quantizers are easy to train. The comprehensive experiments on CIFAR-10 and ImageNet datasets show that our method works consistently well for various network structures such as AlexNet, VGG-Net, GoogLeNet, ResNet, and DenseNet, surpassing previous quantization methods in terms of accuracy by an appreciable margin. Code available at https://github.com/Microsoft/LQ-Nets

为了以计算有效的方式部署深层模型，经常使用模型量化方法。此外，由于新的硬件支持混合的位算术操作，最近对混合精度量化（MPQ）的研究开始通过搜索网络中不同层和模块的优化位低宽，从而完全利用表示的能力。但是，先前的研究主要是在使用强化学习，神经体系结构搜索等的昂贵方案中搜索MPQ策略，或者简单地利用部分先验知识来进行位于刻度分配，这可能是有偏见和优势的。在这项工作中，我们提出了一种新颖的随机量化量化（SDQ）方法，该方法可以在更灵活，更全球优化的空间中自动学习MPQ策略，并具有更平滑的梯度近似。特别是，可区分的位宽参数（DBP）被用作相邻位意选择之间随机量化的概率因素。在获取最佳MPQ策略之后，我们将进一步训练网络使用熵感知的bin正则化和知识蒸馏。我们广泛评估了不同硬件（GPU和FPGA）和数据集的多个网络的方法。 SDQ的表现优于所有最先进的混合或单个精度量化，甚至比较低的位置量化，甚至比各种重新网络和Mobilenet家族的全精度对应物更好，这表明了我们方法的有效性和优势。

In deep neural networks (DNNs), there are a huge number of weights and multiply-and-accumulate (MAC) operations. Accordingly, it is challenging to apply DNNs on resource-constrained platforms, e.g., mobile phones. Quantization is a method to reduce the size and the computational complexity of DNNs. Existing quantization methods either require hardware overhead to achieve a non-uniform quantization or focus on model-wise and layer-wise uniform quantization, which are not as fine-grained as filter-wise quantization. In this paper, we propose a class-based quantization method to determine the minimum number of quantization bits for each filter or neuron in DNNs individually. In the proposed method, the importance score of each filter or neuron with respect to the number of classes in the dataset is first evaluated. The larger the score is, the more important the filter or neuron is and thus the larger the number of quantization bits should be. Afterwards, a search algorithm is adopted to exploit the different importance of filters and neurons to determine the number of quantization bits of each filter or neuron. Experimental results demonstrate that the proposed method can maintain the inference accuracy with low bit-width quantization. Given the same number of quantization bits, the proposed method can also achieve a better inference accuracy than the existing methods.

具有混合精度量化的大DNN可以实现超高压缩，同时保持高分类性能。但是，由于找到了可以引导优化过程的准确度量的挑战，与32位浮点（FP-32）基线相比，这些方法牺牲了显着性能，或者依赖于计算昂贵的迭代培训政策这需要预先训练的基线的可用性。要解决此问题，本文提出了BMPQ，一种使用位梯度来分析层敏感性的训练方法，并产生混合精度量化模型。 BMPQ需要单一的训练迭代，但不需要预先训练的基线。它使用整数线性程序（ILP）来动态调整培训期间层的精度，但经过固定的硬件预算。为了评估BMPQ的功效，我们对CiFar-10，CiFar-100和微小想象数据集的VGG16和Reset18进行了广泛的实验。与基线FP-32型号相比，BMPQ可以产生具有15.4倍的参数比特的模型，精度可忽略不计。与SOTA“在培训期间”相比，混合精确训练方案，我们的模型分别在CiFar-10，CiFar-100和微小想象中分别为2.1倍，2.2倍2.9倍，具有提高的精度高达14.54％。

Considering the computation complexity, we propose a Guided Hybrid Quantization with One-to-one Self-Teaching (GHOST}) framework. More concretely, we first design a structure called guided quantization self-distillation (GQSD), which is an innovative idea for realizing lightweight through the synergy of quantization and distillation. The training process of the quantization model is guided by its full-precision model, which is time-saving and cost-saving without preparing a huge pre-trained model in advance. Second, we put forward a hybrid quantization (HQ) module to obtain the optimal bit width automatically under a constrained condition where a threshold for distribution distance between the center and samples is applied in the weight value search space. Third, in order to improve information transformation, we propose a one-to-one self-teaching (OST) module to give the student network a ability of self-judgment. A switch control machine (SCM) builds a bridge between the student network and teacher network in the same location to help the teacher to reduce wrong guidance and impart vital knowledge to the student. This distillation method allows a model to learn from itself and gain substantial improvement without any additional supervision. Extensive experiments on a multimodal dataset (VEDAI) and single-modality datasets (DOTA, NWPU, and DIOR) show that object detection based on GHOST outperforms the existing detectors. The tiny parameters (<9.7 MB) and Bit-Operations (BOPs) (<2158 G) compared with any remote sensing-based, lightweight or distillation-based algorithms demonstrate the superiority in the lightweight design domain. Our code and model will be released at https://github.com/icey-zhang/GHOST.

As a neural network compression technique, post-training quantization (PTQ) transforms a pre-trained model into a quantized model using a lower-precision data type. However, the prediction accuracy will decrease because of the quantization noise, especially in extremely low-bit settings. How to determine the appropriate quantization parameters (e.g., scaling factors and rounding of weights) is the main problem facing now. Many existing methods determine the quantization parameters by minimizing the distance between features before and after quantization. Using this distance as the metric to optimize the quantization parameters only considers local information. We analyze the problem of minimizing local metrics and indicate that it would not result in optimal quantization parameters. Furthermore, the quantized model suffers from overfitting due to the small number of calibration samples in PTQ. In this paper, we propose PD-Quant to solve the problems. PD-Quant uses the information of differences between network prediction before and after quantization to determine the quantization parameters. To mitigate the overfitting problem, PD-Quant adjusts the distribution of activations in PTQ. Experiments show that PD-Quant leads to better quantization parameters and improves the prediction accuracy of quantized models, especially in low-bit settings. For example, PD-Quant pushes the accuracy of ResNet-18 up to 53.08% and RegNetX-600MF up to 40.92% in weight 2-bit activation 2-bit. The code will be released at https://github.com/hustvl/PD-Quant.

由于神经网络变得更加强大，因此在现实世界中部署它们的愿望是一个上升的愿望;然而，神经网络的功率和准确性主要是由于它们的深度和复杂性，使得它们难以部署，尤其是在资源受限的设备中。最近出现了神经网络量化，以满足这种需求通过降低网络的精度来降低神经网络的大小和复杂性。具有较小和更简单的网络，可以在目标硬件的约束中运行神经网络。本文调查了在过去十年中开发的许多神经网络量化技术。基于该调查和神经网络量化技术的比较，我们提出了该地区的未来研究方向。

强大的量化提高了网络对各种实现的公差，从而允许在不同的位宽度或零散的低精度算术中可靠的输出。在这项工作中，我们进行了广泛的分析以确定量化误差的来源，并提出了三个见解以鲁棒化的网络，以防止量化：减少误差传播，范围夹紧误差最小化以及遗传的稳健性，以抗量化。基于这些见解，我们提出了两种称为对称正则化（Symreg）和饱和非线性（SATNL）的新方法。在培训期间应用提出的方法可以增强对现有训练后量化（PTQ）和量化感知培训（QAT）算法的量化的任意神经网络的鲁棒性各种条件。我们对CIFAR和Imagenet数据集进行了广泛的研究，并验证了所提出的方法的有效性。