We study characteristics of receptive fields of units in deep convolutional networks. The receptive field size is a crucial issue in many visual tasks, as the output must respond to large enough areas in the image to capture information about large objects. We introduce the notion of an effective receptive field, and show that it both has a Gaussian distribution and only occupies a fraction of the full theoretical receptive field. We analyze the effective receptive field in several architecture designs, and the effect of nonlinear activations, dropout, sub-sampling and skip connections on it. This leads to suggestions for ways to address its tendency to be too small.

在本文中，我们提出了解决稳定性和卷积神经网络（CNN）的稳定性和视野的问题的神经网络。作为提高网络深度或宽度以提高性能的替代方案，我们提出了与全球加权拉普拉斯，分数拉普拉斯和逆分数拉普拉斯算子有关的基于积分的空间非识别算子，其在物理科学中的几个问题中出现。这种网络的前向传播由部分积分微分方程（PIDE）启发。我们在自动驾驶中测试基准图像分类数据集和语义分段任务的提出神经架构的有效性。此外，我们调查了这些密集的运营商的额外计算成本以及提出神经网络的前向传播的稳定性。

批量标准化是所有最先进的神经网络架构的必要组件。然而，由于引入了许多实际问题，最近的研究已经致力于设计无规范化的架构。在本文中，我们表明权重初始化是培训Reset的归一化网络的关键。特别是，我们提出了对跳过连接分支的块输出的求和操作的略微修改，从而正确初始化整个网络。我们表明，这种修改的体系结构在CiFar-10上实现了竞争结果，而无需进一步正常化，也不是算法修改。

$ $With recent advances in CNNs, exceptional improvements have been made in semantic segmentation of high resolution images in terms of accuracy and latency. However, challenges still remain in detecting objects in crowded scenes, large scale variations, partial occlusion, and distortions, while still maintaining mobility and latency. We introduce a fast and efficient convolutional neural network, ASBU-Net, for semantic segmentation of high resolution images that addresses these problems and uses no novelty layers for ease of quantization and embedded hardware support. ASBU-Net is based on a new feature extraction module, atrous space bender layer (ASBL), which is efficient in terms of computation and memory. The ASB layers form a building block that is used to make ASBNet. Since this network does not use any special layers it can be easily implemented, quantized and deployed on FPGAs and other hardware with limited memory. We present experiments on resource and accuracy trade-offs and show strong performance compared to other popular models.

These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics. The main objective of these notes is to introduce a student who is familiar with concepts in linear algebra and partial differential equations to select topics in deep learning. These lecture notes exploit the strong connections between deep learning algorithms and the more conventional techniques of computational physics to achieve two goals. First, they use concepts from computational physics to develop an understanding of deep learning algorithms. Not surprisingly, many concepts in deep learning can be connected to similar concepts in computational physics, and one can utilize this connection to better understand these algorithms. Second, several novel deep learning algorithms can be used to solve challenging problems in computational physics. Thus, they offer someone who is interested in modeling a physical phenomena with a complementary set of tools.

Rectified activation units (rectifiers) are essential for state-of-the-art neural networks. In this work, we study rectifier neural networks for image classification from two aspects. First, we propose a Parametric Rectified Linear Unit (PReLU) that generalizes the traditional rectified unit. PReLU improves model fitting with nearly zero extra computational cost and little overfitting risk. Second, we derive a robust initialization method that particularly considers the rectifier nonlinearities. This method enables us to train extremely deep rectified models directly from scratch and to investigate deeper or wider network architectures. Based on our PReLU networks (PReLU-nets), we achieve 4.94% top-5 test error on the ImageNet 2012 classification dataset. This is a 26% relative improvement over the ILSVRC 2014 winner (GoogLeNet, 6.66% [29]). To our knowledge, our result is the first to surpass human-level performance (5.1%, [22]) on this visual recognition challenge.

适当的重量初始化是成功培训神经网络的重要意义。最近，批量归一化通过基于批处理统计数据量化每层来判定权重初始化的作用。遗憾的是，批量归一化在应用于小批量尺寸时具有多个缺点，因为在点云上学习时需要应对内存限制。虽然良好的重量初始化策略可以不需要呈现批量归一化，从而避免这些缺点，没有提出这种方法对于点卷积网络。为了填补这一差距，我们提出了一个框架来统一众多持续卷积。这实现了我们的主要贡献，方差感知权重初始化。我们表明，此初始化可以避免批量标准化，同时实现相似，并且在某些情况下更好的性能。

扩张的卷积基本上是通过定期插入内核元素之间的空格而创建的更宽内核的卷积。在本文中，我们提出了一种新版本的扩张卷积，其中通过通过插值技术通过反向化进行了学习的间距。我们称这种方法“通过学习间距扩张卷积”（DCLS），并推广其对N维卷积案例的方法。但是，我们这里的主要焦点将是我们开发了两种实现的2D案例：一个天真的外壳：一个天真的一个，它构建了适合小的扩张率的扩张内核，以及使用“IM2COL的修改版本的时间/记忆有效的内核” “ 算法。然后，我们通过DCLS ONE通过简单的替换，我们如何通过简单的替换DCLS替换该技术如何通过简单的替换置换古典扩张的卷积层对Pascal VOC 2012 DataSet上的现有架构的准确性。此外，我们表明DCLS允许减少最近Convmixer架构中使用的深度卷曲的学习参数的数量，其因子3具有NO或非常低的准确性，并且通过用稀疏DCLS替换大型密集内核。该方法的代码基于Pytorch，可用于：https://github.com/k-h-imail/dilated-convolution-with-learnable-pacings-pytorch。

Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks. Following this finding -and building on other recent work for finding simple network structures -we propose a new architecture that consists solely of convolutional layers and yields competitive or state of the art performance on several object recognition datasets (CIFAR-10, CIFAR-100, ImageNet). To analyze the network we introduce a new variant of the "deconvolution approach" for visualizing features learned by CNNs, which can be applied to a broader range of network structures than existing approaches.

The study of feature propagation at initialization in neural networks lies at the root of numerous initialization designs. An assumption very commonly made in the field states that the pre-activations are Gaussian. Although this convenient Gaussian hypothesis can be justified when the number of neurons per layer tends to infinity, it is challenged by both theoretical and experimental works for finite-width neural networks. Our major contribution is to construct a family of pairs of activation functions and initialization distributions that ensure that the pre-activations remain Gaussian throughout the network's depth, even in narrow neural networks. In the process, we discover a set of constraints that a neural network should fulfill to ensure Gaussian pre-activations. Additionally, we provide a critical review of the claims of the Edge of Chaos line of works and build an exact Edge of Chaos analysis. We also propose a unified view on pre-activations propagation, encompassing the framework of several well-known initialization procedures. Finally, our work provides a principled framework for answering the much-debated question: is it desirable to initialize the training of a neural network whose pre-activations are ensured to be Gaussian?

Neural networks require careful weight initialization to prevent signals from exploding or vanishing. Existing initialization schemes solve this problem in specific cases by assuming that the network has a certain activation function or topology. It is difficult to derive such weight initialization strategies, and modern architectures therefore often use these same initialization schemes even though their assumptions do not hold. This paper introduces AutoInit, a weight initialization algorithm that automatically adapts to different neural network architectures. By analytically tracking the mean and variance of signals as they propagate through the network, AutoInit appropriately scales the weights at each layer to avoid exploding or vanishing signals. Experiments demonstrate that AutoInit improves performance of convolutional, residual, and transformer networks across a range of activation function, dropout, weight decay, learning rate, and normalizer settings, and does so more reliably than data-dependent initialization methods. This flexibility allows AutoInit to initialize models for everything from small tabular tasks to large datasets such as ImageNet. Such generality turns out particularly useful in neural architecture search and in activation function discovery. In these settings, AutoInit initializes each candidate appropriately, making performance evaluations more accurate. AutoInit thus serves as an automatic configuration tool that makes design of new neural network architectures more robust. The AutoInit package provides a wrapper around TensorFlow models and is available at https://github.com/cognizant-ai-labs/autoinit.

Computational units in artificial neural networks follow a simplified model of biological neurons. In the biological model, the output signal of a neuron runs down the axon, splits following the many branches at its end, and passes identically to all the downward neurons of the network. Each of the downward neurons will use their copy of this signal as one of many inputs dendrites, integrate them all and fire an output, if above some threshold. In the artificial neural network, this translates to the fact that the nonlinear filtering of the signal is performed in the upward neuron, meaning that in practice the same activation is shared between all the downward neurons that use that signal as their input. Dendrites thus play a passive role. We propose a slightly more complex model for the biological neuron, where dendrites play an active role: the activation in the output of the upward neuron becomes optional, and instead the signals going through each dendrite undergo independent nonlinear filterings, before the linear combination. We implement this new model into a ReLU computational unit and discuss its biological plausibility. We compare this new computational unit with the standard one and describe it from a geometrical point of view. We provide a Keras implementation of this unit into fully connected and convolutional layers and estimate their FLOPs and weights change. We then use these layers in ResNet architectures on CIFAR-10, CIFAR-100, Imagenette, and Imagewoof, obtaining performance improvements over standard ResNets up to 1.73%. Finally, we prove a universal representation theorem for continuous functions on compact sets and show that this new unit has more representational power than its standard counterpart.

Semantic image segmentation is a basic street scene understanding task in autonomous driving, where each pixel in a high resolution image is categorized into a set of semantic labels. Unlike other scenarios, objects in autonomous driving scene exhibit very large scale changes, which poses great challenges for high-level feature representation in a sense that multi-scale information must be correctly encoded. To remedy this problem, atrous convolution [14] was introduced to generate features with larger receptive fields without sacrificing spatial resolution. Built upon atrous convolution, Atrous Spatial Pyramid Pooling (ASPP) [2] was proposed to concatenate multiple atrous-convolved features using different dilation rates into a final feature representation. Although ASPP is able to generate multi-scale features, we argue the feature resolution in the scale-axis is not dense enough for the autonomous driving scenario. To this end, we propose Densely connected Atrous Spatial Pyramid Pooling (DenseASPP), which connects a set of atrous convolutional layers in a dense way, such that it generates multi-scale features that not only cover a larger scale range, but also cover that scale range densely, without significantly increasing the model size. We evaluate DenseASPP on the street scene benchmark Cityscapes [4] and achieve state-of-the-art performance.

接收场的大小和形状决定了网络如何聚集本地信息并极大地影响模型的整体性能。神经网络中的许多组件，例如内核大小和用于卷积和汇总操作的大步，都会影响接受场的配置。但是，它们仍然依靠超参数，现有模型的接受场导致了次优的形状和尺寸。因此，我们提出了一个简单而有效的动态优化的合并操作，称为Dynopool，该操作通过学习每一层中其接受场的理想大小和形状来优化特征地图的比例因子。深层神经网络中的任何调整模块都可以用Dynopool的操作取代，而成本最低。此外，Dynopool通过引入限制计算成本的附加损失项来控制模型的复杂性。我们的实验表明，配备了拟议的可学习调整模块的模型优于图像分类和语义分割中多个数据集上的基线网络。

In standard Convolutional Neural Networks (CNNs), the receptive fields of artificial neurons in each layer are designed to share the same size. It is well-known in the neuroscience community that the receptive field size of visual cortical neurons are modulated by the stimulus, which has been rarely considered in constructing CNNs. We propose a dynamic selection mechanism in CNNs that allows each neuron to adaptively adjust its receptive field size based on multiple scales of input information. A building block called Selective Kernel (SK) unit is designed, in which multiple branches with different kernel sizes are fused using softmax attention that is guided by the information in these branches. Different attentions on these branches yield different sizes of the effective receptive fields of neurons in the fusion layer. Multiple SK units are stacked to a deep network termed Selective Kernel Networks (SKNets). On the ImageNet and CIFAR benchmarks, we empirically show that SKNet outperforms the existing state-of-the-art architectures with lower model complexity. Detailed analyses show that the neurons in SKNet can capture target objects with different scales, which verifies the capability of neurons for adaptively adjusting their receptive field sizes according to the input. The code and models are available at https://github.com/implus/SKNet.

Convolutional neural networks (CNNs) are inherently limited to model geometric transformations due to the fixed geometric structures in their building modules. In this work, we introduce two new modules to enhance the transformation modeling capability of CNNs, namely, deformable convolution and deformable RoI pooling. Both are based on the idea of augmenting the spatial sampling locations in the modules with additional offsets and learning the offsets from the target tasks, without additional supervision. The new modules can readily replace their plain counterparts in existing CNNs and can be easily trained end-to-end by standard back-propagation, giving rise to deformable convolutional networks. Extensive experiments validate the performance of our approach. For the first time, we show that learning dense spatial transformation in deep CNNs is effective for sophisticated vision tasks such as object detection and semantic segmentation. The code is released at https://github.com/ msracver/Deformable-ConvNets.

神经架构的创新促进了语言建模和计算机视觉中的重大突破。不幸的是，如果网络参数未正确初始化，新颖的架构通常会导致挑战超参数选择和培训不稳定。已经提出了许多架构特定的初始化方案，但这些方案并不总是可移植到新体系结构。本文介绍了毕业，一种用于初始化神经网络的自动化和架构不可知论由方法。毕业基础是一个简单的启发式;调整每个网络层的规范，使得具有规定的超参数的SGD或ADAM的单个步骤导致可能的损耗值最小。通过在每个参数块前面引入标量乘数变量，然后使用简单的数字方案优化这些变量来完成此调整。 GradInit加速了许多卷积架构的收敛性和测试性能，无论是否有跳过连接，甚至没有归一化层。它还提高了机器翻译的原始变压器架构的稳定性，使得在广泛的学习速率和动量系数下使用ADAM或SGD来训练它而无需学习速率预热。代码可在https://github.com/zhuchen03/gradinit上获得。

这是一门专门针对STEM学生开发的介绍性机器学习课程。我们的目标是为有兴趣的读者提供基础知识，以在自己的项目中使用机器学习，并将自己熟悉术语作为进一步阅读相关文献的基础。在这些讲义中，我们讨论受监督，无监督和强化学习。注释从没有神经网络的机器学习方法的说明开始，例如原理分析，T-SNE，聚类以及线性回归和线性分类器。我们继续介绍基本和先进的神经网络结构，例如密集的进料和常规神经网络，经常性的神经网络，受限的玻尔兹曼机器，（变性）自动编码器，生成的对抗性网络。讨论了潜在空间表示的解释性问题，并使用梦和对抗性攻击的例子。最后一部分致力于加强学习，我们在其中介绍了价值功能和政策学习的基本概念。

图像分类的深卷卷神经网络（CNN）依次交替交替进行卷积和下采样操作，例如合并层或陷入困境的卷积，从而导致较低的分辨率特征网络越深。这些降采样操作节省了计算资源，并在下一层提供了一些翻译不变性以及更大的接收领域。但是，这样做的固有副作用是，在网络深端产生的高级特征始终以低分辨率特征图捕获。逆也是如此，因为浅层总是包含小规模的特征。在生物医学图像分析中，工程师通常负责对仅包含有限信息的非常小的图像贴片进行分类。从本质上讲，这些补丁甚至可能不包含对象，而分类取决于图像纹理中未知量表的微妙基础模式的检测。在这些情况下，每一个信息都是有价值的。因此，重要的是要提取最大数量的信息功能。在这些考虑因素的推动下，我们引入了一种新的CNN体​​系结构，该体系结构可通过利用跳过连接以及连续的收缩和特征图的扩展来保留深，中间和浅层层的多尺度特征。使用来自胰腺导管腺癌（PDAC）CT扫描的非常低分辨率斑块的数据集，我们证明我们的网络可以超越最新模型的当前状态。

可解释的人工智能（XAI）的新兴领域旨在为当今强大但不透明的深度学习模型带来透明度。尽管本地XAI方法以归因图的形式解释了个体预测，从而确定了重要特征的发生位置（但没有提供有关其代表的信息），但全局解释技术可视化模型通常学会的编码的概念。因此，两种方法仅提供部分见解，并留下将模型推理解释的负担。只有少数当代技术旨在将本地和全球XAI背后的原则结合起来，以获取更多信息的解释。但是，这些方法通常仅限于特定的模型体系结构，或对培训制度或数据和标签可用性施加其他要求，这实际上使事后应用程序成为任意预训练的模型。在这项工作中，我们介绍了概念相关性传播方法（CRP）方法，该方法结合了XAI的本地和全球观点，因此允许回答“何处”和“ where”和“什么”问题，而没有其他约束。我们进一步介绍了相关性最大化的原则，以根据模型对模型的有用性找到代表性的示例。因此，我们提高了对激活最大化及其局限性的共同实践的依赖。我们证明了我们方法在各种环境中的能力，展示了概念相关性传播和相关性最大化导致了更加可解释的解释，并通过概念图表，概念组成分析和概念集合和概念子区和概念子区和概念子集和定量研究对模型的表示和推理提供了深刻的见解。它们在细粒度决策中的作用。