As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient. This motivated the introduction of various normalization techniques such as Batch Normalization and Layer Normalization. The aforementioned normalization methods use arithmetic operations to compute an approximation statistics (mainly the first and second moments) of the layer's data and use it to normalize it. The aforementioned methods use plain Monte Carlo method to approximate the statistics and such method fails when approximating the statistics whose distribution is complex. Here, we propose an approach that uses weighted sum, implemented using depth-wise convolutional neural networks, to not only approximate the statistics, but to learn the coefficients of the sum.
Rice University（莱斯大学）；Technical University of Munich（慕尼黑工业大学）
Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem arises in recent approaches for solving inverse problems such as the deep image prior or the deep decoder. We show that for this setup, channel normalization, which centers and normalizes each channel individually, avoids vanishing gradients, whereas, without normalization, gradients vanish which prevents efficient optimization. This effect prevails in deep singl…
LIRIS - UMR 5205 CNRS（法国国家科学研究中心LIRIS联合研究单位5205）；Ecole Centrale de Lyon（里昂中央理工学院）；LVMH Recherche - Parfums et cosmetiques（路威酩轩香水化妆品研究中心）
The lack of transparency of neural networks stays a major break for their use. The Layerwise Relevance Propagation technique builds heat-maps representing the relevance of each input in the model s decision. The relevance spreads backward from the last to the first layer of the Deep Neural Network. Layer-wise Relevance Propagation does not manage normalization layers, in this work we suggest a method to include normalization layers. Specifically, we build an equivalent network fusing normalization layers and convolutional or fully connected layers. Heatmaps obtained with our method on MNIST an…
Baze University（巴泽大学）；The University of the West of England（西英格兰大学）
Deep networks have achieved huge successes in application domains like object and face recognition. The performance gain is attributed to different facets of the network architecture such as: depth of the convolutional layers, activation function, pooling, batch normalization, forward and back propagation and many more. However, very little emphasis is made on the preprocessors. Therefore, in this paper, the network's preprocessing module is varied across different preprocessing approaches while keeping constant other facets of the network architecture, to investigate the contribution preproce…
University of South Australia（南澳大学）；University of California, San Diego（加州大学圣地亚哥分校）；Western Sydney University（西悉尼大学）
Batch-normalization (BN) layers are thought to be an integrally important layer type in today's state-of-the-art deep convolutional neural networks for computer vision tasks such as classification and detection. However, BN layers introduce complexity and computational overheads that are highly undesirable for training and/or inference on low-power custom hardware implementations of real-time embedded vision systems such as UAVs, robots and Internet of Things (IoT) devices. They are also problematic when batch sizes need to be very small during training, and innovations such as residual connec…
NTT Communication Science Laboratories（NTT通信科学实验室）；Nippon Telegraph and Telephone Corporation（日本电报电话公司）
This paper proposes a voice conversion (VC) method using sequence-to-sequence (seq2seq or S2S) learning, which flexibly converts not only the voice characteristics but also the pitch contour and duration of input speech. The proposed method, called ConvS2S-VC, has three key features. First, it uses a model with a fully convolutional architecture. This is particularly advantageous in that it is suitable for parallel computations using GPUs. It is also beneficial since it enables effective normalization techniques such as batch normalization to be used for all the hidden layers in the networks. …
Ecole des Ponts（巴黎桥路学院）；Univ Gustave Eiffel（古斯塔夫·埃菲尔大学）；Département d’informatique de l’ENS, PSL（巴黎高等师范学院计算机系（巴黎文理研究大学））；Inria（法国国家信息与自动化研究所）
Normalization Layers (NLs) are widely used in modern deep-learning architectures. Despite their apparent simplicity, their effect on optimization is not yet fully understood. This paper introduces a spherical framework to study the optimization of neural networks with NLs from a geometric perspective. Concretely, the radial invariance of groups of parameters, such as filters for convolutional neural networks, allows to translate the optimization steps on the $L_2$ unit hypersphere. This formulation and the associated geometric interpretation shed new light on the training dynamics. Firstly, th…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Beijing Academy of Frontier Science and Technology（北京前沿科学技术研究院）
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change of input distribution, thus results in poor generalization, and aggravates the internal covariate shift which slows down the training. To bound dot product and decrease the variance, we propose to use cosine similarity or centered cosine similarity (Pearson Correlation Coefficient…
University of Michigan（密歇根大学）；Beihang University（北京航空航天大学）
Batch Normalization (BN) is capable of accelerating the training of deep models by centering and scaling activations within mini-batches. In this work, we propose Decorrelated Batch Normalization (DBN), which not just centers and scales activations but whitens them. We explore multiple whitening techniques, and find that PCA whitening causes a problem we call stochastic axis swapping, which is detrimental to learning. We show that ZCA whitening does not suffer from this problem, permitting successful learning. DBN retains the desirable qualities of BN and further improves BN's optimization eff…
Beihang University（北京航空航天大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous convolutional neural networks on graphs, we first design a motif-matching guided subgraph normalization method to capture neighborhood information. Then we implement subgraph-level self-attentional layers to learn different importances from different subgraphs to solve graph classification problems. Analogous to image-based attentional convolution networks that oper…
Centrum Wiskunde & Informatica (CWI)（荷兰数学与计算机科学研究中心）；Holst Centre / IMEC（霍尔斯特中心/比利时微电子研究中心）；Technical University Eindhoven（埃因霍温理工大学）；University of Amsterdam（阿姆斯特丹大学）；Rijksuniversiteit Groningen（格罗宁根大学）
While modern convolutional neural networks achieve outstanding accuracy on many image classification tasks, they are, compared to humans, much more sensitive to image degradation. Here, we describe a variant of Batch Normalization, LocalNorm, that regularizes the normalization layer in the spirit of Dropout while dynamically adapting to the local image intensity and contrast at test-time. We show that the resulting deep neural networks are much more resistant to noise-induced image degradation, improving accuracy by up to three times, while achieving the same or slightly better accuracy on non…
This study introduces a new normalization layer termed Batch Layer Normalization (BLN) to reduce the problem of internal covariate shift in deep neural network layers. As a combined version of batch and layer normalization, BLN adaptively puts appropriate weight on mini-batch and feature normalization based on the inverse size of mini-batches to normalize the input to a layer during the learning process. It also performs the exact computation with a minor change at inference times, using either mini-batch statistics or population statistics. The decision process to either use statistics of min…
Imperial College London（帝国理工学院）；Shanghai Jiao Tong University（上海交通大学）
Normalization layers are essential in a Deep Convolutional Neural Network (DCNN). Various normalization methods have been proposed. The statistics used to normalize the feature maps can be computed at batch, channel, or instance level. However, in most of existing methods, the normalization for each layer is fixed. Batch-Instance Normalization (BIN) is one of the first proposed methods that combines two different normalization methods and achieve diverse normalization for different layers. However, two potential issues exist in BIN: first, the Clip function is not differentiable at input value…
The Chinese University of Hong Kong（香港中文大学）；SenseTime Research（商汤科技研究院）
Yes, they do. This work investigates a perspective for deep learning: whether different normalization layers in a ConvNet require different normalizers. This is the first step towards understanding this phenomenon. We allow each convolutional layer to be stacked before a switchable normalization (SN) that learns to choose a normalizer from a pool of normalization methods. Through systematic experiments in ImageNet, COCO, Cityscapes, and ADE20K, we answer three questions: (a) Is it useful to allow each normalization layer to select its own normalizer? (b) What impacts the choices of normalizers…
University of Kentucky（肯塔基大学）；Ohio Wesleyan University（俄亥俄卫斯理大学）
Batch normalization (BN) is a popular and ubiquitous method in deep learning that has been shown to decrease training time and improve generalization performance of neural networks. Despite its success, BN is not theoretically well understood. It is not suitable for use with very small mini-batch sizes or online learning. In this paper, we propose a new method called Batch Normalization Preconditioning (BNP). Instead of applying normalization explicitly through a batch normalization layer as is done in BN, BNP applies normalization by conditioning the parameter gradients directly during traini…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Deep neural networks can suffer from the exploding and vanishing activation problem, in which the networks fail to train properly because the neural signals either amplify or attenuate across the layers and become saturated. While other normalization methods aim to fix the stated problem, most of them have inference speed penalties in those applications that require running averages of the neural activations. Here we extend the unitary framework based on Lie algebra to neural networks of any dimensionalities, overcoming the major constraints of the prior arts that limit synaptic weights to be …
University of Technology Sydney（悉尼科技大学）；Qamcom Research and Technology AB（Qamcom研究与技术公司）
This paper considers object detection and 3D estimation using an FMCW radar. The state-of-the-art deep learning framework is employed instead of using traditional signal processing. In preparing the radar training data, the ground truth of an object orientation in 3D space is provided by conducting image analysis, of which the images are obtained through a coupled camera to the radar device. To ensure successful training of a fully convolutional network (FCN), we propose a normalization method, which is found to be essential to be applied to the radar signal before feeding into the neural netw…
We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with up to 144 layers, and show that bipolar activation functions help learning in this setting. On the Penn Treebank and Text8 language modeling tasks we obtain competitive results, improving on the best reported results for non-gated networks. In experiments with convolutional neur…
Comparative Analysis of CNN and Transformer Architectures with Heart Cycle Normalization for Automated Phonocardiogram Classification
Fraunhofer Institute for Software and Systems Engineering ISST（弗劳恩霍夫软件与系统工程研究所）；Department of Computer Science, University of Applied Sciences and Arts Dortmund（应用科学大学多特蒙德计算机科学系）；Department of Computer Science, TU Dortmund University（图尔努恩大学计算机科学系）；Department of Health Informatics, School of Medicine, Witten/Herdecke University（医学学院健康信息学系，维滕/赫尔德克大学）；Institute for Medical Informatics, Biometry and Epidemiology (IMIBE), University Hospital Essen（医学信息学、生物统计与流行病学研究所（IMIBE），埃森大学医院）
Deep neural networks (DNNs) have set benchmarks on a wide array of supervised learning tasks. Trained DNNs, however, often lack robustness to minor adversarial perturbations to the input, which undermines their true practicality. Recent works have increased the robustness of DNNs by fitting networks using adversarially-perturbed training samples, but the improved performance can still be far below the performance seen in non-adversarial settings. A significant portion of this gap can be attributed to the decrease in generalization performance due to adversarial training. In this work, we exten…
Radboud University Medical Center（拉德堡德大学医学中心）；Laboratorium Pathologie Oost Nederland（东荷兰病理学实验室）
The development of reliable imaging biomarkers for the analysis of colorectal cancer (CRC) in hematoxylin and eosin (H&E) stained histopathology images requires an accurate and reproducible classification of the main tissue components in the image. In this paper, we propose a system for CRC tissue classification based on convolutional networks (ConvNets). We investigate the importance of stain normalization in tissue classification of CRC tissue samples in H&E-stained images. Furthermore, we report the performance of ConvNets on a cohort of rectal cancer samples and on an independent publicly …
TU Kaiserslautern（凯泽斯劳滕工业大学）；MindGarage；Imperial College London（帝国理工学院）；NeuralSpace；Luleå University of Technology（吕勒奥理工大学）
We introduce a novel uncertainty estimation for classification tasks for Bayesian convolutional neural networks with variational inference. By normalizing the output of a Softplus function in the final layer, we estimate aleatoric and epistemic uncertainty in a coherent manner. The intractable posterior probability distributions over weights are inferred by Bayes by Backprop. Firstly, we demonstrate how this reliable variational inference method can serve as a fundamental construct for various network architectures. On multiple datasets in supervised learning settings (MNIST, CIFAR-10, CIFAR-1…
Performance of deep learning algorithms decreases drastically if the data distributions of the training and testing sets are different. Due to variations in staining protocols, reagent brands, and habits of technicians, color variation in digital histopathology images is quite common. Color variation causes problems for the deployment of deep learning-based solutions for automatic diagnosis system in histopathology. Previously proposed color normalization methods consider a small patch as a reference for normalization, which creates artifacts on out-of-distribution source images. These methods…
We systematically explored a spectrum of normalization algorithms related to Batch Normalization (BN) and propose a generalized formulation that simultaneously solves two major limitations of BN: (1) online learning and (2) recurrent learning. Our proposal is simpler and more biologically-plausible. Unlike previous approaches, our technique can be applied out of the box to all learning scenarios (e.g., online learning, batch learning, fully-connected, convolutional, feedforward, recurrent and mixed --- recurrent and convolutional) and compare favorably with existing approaches. We also propose…
Center for Data Science, New York University（纽约大学数据科学中心）；Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）；Department of EECS, UC Berkeley（加州大学伯克利分校电气工程与计算机科学系）；Electrical and Computer Engineering, University of Denver（丹佛大学电气与计算机工程系）；Department of EECS, University of Michigan（密歇根大学电气工程与计算机科学系）
Normalization techniques have become a basic component in modern convolutional neural networks (ConvNets). In particular, many recent works demonstrate that promoting the orthogonality of the weights helps train deep models and improve robustness. For ConvNets, most existing methods are based on penalizing or normalizing weight matrices derived from concatenating or flattening the convolutional kernels. These methods often destroy or ignore the benign convolutional structure of the kernels; therefore, they are often expensive or impractical for deep ConvNets. In contrast, we introduce a simple…
Ulm University（乌尔姆大学）；University College London（伦敦大学学院）
Appropriate weight initialization has been of key importance to successfully train neural networks. Recently, batch normalization has diminished the role of weight initialization by simply normalizing each layer based on batch statistics. Unfortunately, batch normalization has several drawbacks when applied to small batch sizes, as they are required to cope with memory limitations when learning on point clouds. While well-founded weight initialization strategies can render batch normalization unnecessary and thus avoid these drawbacks, no such approaches have been proposed for point convolutio…
To build light-weight network, we propose a new normalization, Fine-grained Batch Normalization (FBN). Different from Batch Normalization (BN), which normalizes the final summation of the weighted inputs, FBN normalizes the intermediate state of the summation. We propose a novel light-weight network based on FBN, called Finet. At training time, the convolutional layer with FBN can be seen as an inverted bottleneck mechanism. FBN can be fused into convolution at inference time. After fusion, Finet uses the standard convolution with equal channel width, thus makes the inference more efficient. O…
University of Toronto（多伦多大学）；Baylor College of Medicine（贝勒医学院）；Canadian Institute for Advanced Research (CIFAR)（加拿大高等研究院（CIFAR））
Normalization techniques have only recently begun to be exploited in supervised learning tasks. Batch normalization exploits mini-batch statistics to normalize the activations. This was shown to speed up training and result in better models. However its success has been very limited when dealing with recurrent neural networks. On the other hand, layer normalization normalizes the activations across all activities within a layer. This was shown to work well in the recurrent setting. In this paper we propose a unified view of normalization techniques, as forms of divisive normalization, which in…
Hochschule Bonn-Rhein-Sieg（波恩-莱茵-锡格应用技术大学）；Fraunhofer Center for Machine Learning and SCAI（弗劳恩霍夫机器学习中心与算法与科学计算研究所）；University of Bonn（波恩大学）
We introduce canonical weight normalization for convolutional neural networks. Inspired by the canonical tensor decomposition, we express the weight tensors in so-called canonical networks as scaled sums of outer vector products. In particular, we train network weights in the decomposed form, where scale weights are optimized separately for each mode. Additionally, similarly to weight normalization, we include a global scaling parameter. We study the initialization of the canonical form by running the power method and by drawing randomly from Gaussian or uniform distributions. Our results indi…
Universitas Indonesia（印度尼西亚大学）；Bogor Agricultural University（茂物农业大学）
In 2015, stroke was the number one cause of death in Indonesia. The majority type of stroke is ischemic. The standard tool for diagnosing stroke is CT-Scan. For developing countries like Indonesia, the availability of CT-Scan is very limited and still relatively expensive. Because of the availability, another device that potential to diagnose stroke in Indonesia is EEG. Ischemic stroke occurs because of obstruction that can make the cerebral blood flow (CBF) on a person with stroke has become lower than CBF on a normal person (control) so that the EEG signal have a deceleration. On this study,…
We characterize the singular values of the linear transformation associated with a standard 2D multi-channel convolutional layer, enabling their efficient computation. This characterization also leads to an algorithm for projecting a convolutional layer onto an operator-norm ball. We show that this is an effective regularizer; for example, it improves the test error of a deep residual network using batch normalization on CIFAR-10 from 6.2\% to 5.3\%.
Coventry University（考文垂大学）；American University of Beirut（贝鲁特美国大学）
In this work, we propose a novel Generative Adversarial Stacked Autoencoder that learns to map facial expressions, with up to plus or minus 60 degrees, to an illumination invariant facial representation of 0 degrees. We accomplish this by using a novel convolutional layer that exploits both local and global spatial information, and a convolutional layer with a reduced number of parameters that exploits facial symmetry. Furthermore, we introduce a generative adversarial gradual greedy layer-wise learning algorithm designed to train Adversarial Autoencoders in an efficient and incremental manner…
Parallel Layer Normalization for Universal Approximation
State Key Laboratory of Complex and Critical Software Environment (SKLCCSE)（复杂与关键软件环境国家重点实验室）；Beihang University（北京航空航天大学）；Hangzhou International Innovation Institute（杭州国际创新研究院）
New York University（纽约大学）；New York University Langone Medical Center（纽约大学朗格尼医学中心）
Early detection is a crucial goal in the study of Alzheimer's Disease (AD). In this work, we describe several techniques to boost the performance of 3D deep convolutional neural networks (CNNs) trained to detect AD using structural brain MRI scans. Specifically, we provide evidence that (1) instance normalization outperforms batch normalization, (2) early spatial downsampling negatively affects performance, (3) widening the model brings consistent gains while increasing the depth does not, and (4) incorporating age information yields moderate improvement. Together, these insights yield an incr…
We propose a novel unsupervised domain adaptation framework based on domain-specific batch normalization in deep neural networks. We aim to adapt to both domains by specializing batch normalization layers in convolutional neural networks while allowing them to share all other model parameters, which is realized by a two-stage algorithm. In the first stage, we estimate pseudo-labels for the examples in the target domain using an external unsupervised domain adaptation algorithm---for example, MSTN or CPUA---integrating the proposed domain-specific batch normalization. The second stage learns th…
We introduce a novel approach, requiring only mild assumptions, for the characterization of deep neural networks at initialization. Our approach applies both to fully-connected and convolutional networks and easily incorporates batch normalization and skip-connections. Our key insight is to consider the evolution with depth of statistical moments of signal and noise, thereby characterizing the presence or absence of pathologies in the hypothesis space encoded by the choice of hyperparameters. We establish: (i) for feedforward networks, with and without batch normalization, the multiplicativity…
Northwestern University（西北大学）；Tunnel；The Graduate Center（研究生院）；The City University of New York（纽约市立大学）
Batch Normalization (BatchNorm) is an extremely useful component of modern neural network architectures, enabling optimization using higher learning rates and achieving faster convergence. In this paper, we use mean-field theory to analytically quantify the impact of BatchNorm on the geometry of the loss landscape for multi-layer networks consisting of fully-connected and convolutional layers. We show that it has a flattening effect on the loss landscape, as quantified by the maximum eigenvalue of the Fisher Information Matrix. These findings are then used to justify the use of larger learning…
Action recognition greatly benefits motion understanding in video analysis. Recurrent networks such as long short-term memory (LSTM) networks are a popular choice for motion-aware sequence learning tasks. Recently, a convolutional extension of LSTM was proposed, in which input-to-hidden and hidden-to-hidden transitions are modeled through convolution with a single kernel. This implies an unavoidable trade-off between effectiveness and efficiency. Herein, we propose a new enhancement to convolutional LSTM networks that supports accommodation of multiple convolutional kernels and layers. This re…
University of New South Wales（新南威尔士大学）；University of Technology Sydney（悉尼科技大学）
As an alcoholic beverage, wine has remained prevalent for thousands of years, and the quality assessment of wines has been significant in wine production and trade. Scholars have proposed various deep learning and machine learning algorithms for wine quality prediction, such as Support vector machine (SVM), Random Forest (RF), K-nearest neighbors (KNN), Deep neural network (DNN), and Logistic regression (LR). However, these methods ignore the inner relationship between the physical and chemical properties of the wine, for example, the correlations between pH values, fixed acidity, citric acid,…
Google Brain（谷歌大脑）；Stanford University（斯坦福大学）；Google（谷歌）
An emerging design principle in deep learning is that each layer of a deep artificial neural network should be able to easily express the identity transformation. This idea not only motivated various normalization techniques, such as \emph{batch normalization}, but was also key to the immense success of \emph{residual networks}. In this work, we put the principle of \emph{identity parameterization} on a more solid theoretical footing alongside further empirical progress. We first give a strikingly simple proof that arbitrarily deep linear residual networks have no spurious local optima. The sa…
IBM Research（IBM研究院）；Princeton Neuroscience Institute（普林斯顿神经科学研究所）；Princeton University（普林斯顿大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）
Local Hebbian learning is believed to be inferior in performance to end-to-end training using a backpropagation algorithm. We question this popular belief by designing a local algorithm that can learn convolutional filters at scale on large image datasets. These filters combined with patch normalization and very steep non-linearities result in a good classification accuracy for shallow networks trained locally, as opposed to end-to-end. The filters learned by our algorithm contain both orientation selective units and unoriented color units, resembling the responses of pyramidal neurons located…
Very deep CNNs with small 3x3 kernels have recently been shown to achieve very strong performance as acoustic models in hybrid NN-HMM speech recognition systems. In this paper we investigate how to efficiently scale these models to larger datasets. Specifically, we address the design choice of pooling and padding along the time dimension which renders convolutional evaluation of sequences highly inefficient. We propose a new CNN design without timepadding and without timepooling, which is slightly suboptimal for accuracy, but has two significant advantages: it enables sequence training and dep…
Center for Data Science（数据科学中心）；New York University（纽约大学）；Center for Neural Science（神经科学中心）；Howard Hughes Medical Institute（霍华德·休斯医学研究所）；Courant Inst. of Mathematical Sciences（库朗数学科学研究所）
Deep convolutional networks often append additive constant ("bias") terms to their convolution operations, enabling a richer repertoire of functional mappings. Biases are also used to facilitate training, by subtracting mean response over batches of training images (a component of "batch normalization"). Recent state-of-the-art blind denoising methods (e.g., DnCNN) seem to require these terms for their success. Here, however, we show that these networks systematically overfit the noise levels for which they are trained: when deployed at noise levels outside the training range, performance degr…
Deep convolutional neural networks are known to be unstable during training at high learning rate unless normalization techniques are employed. Normalizing weights or activations allows the use of higher learning rates, resulting in faster convergence and higher test accuracy. Batch normalization requires minibatch statistics that approximate the dataset statistics but this incurs additional compute and memory costs and causes a communication bottleneck for distributed training. Weight normalization and initialization-only schemes do not achieve comparable test accuracy. We introduce a new und…
University of Maryland, College Park（马里兰大学帕克分校）；Facebook（脸书）；Harbin Institute of Technology（哈尔滨工业大学）
We propose a novel deep neural network architecture for the challenging problem of single image dehazing, which aims to recover the clear image from a degraded hazy image. Instead of relying on hand-crafted image priors or explicitly estimating the components of the widely used atmospheric scattering model, our end-to-end system directly generates the clear image from an input hazy image. The proposed network has an encoder-decoder architecture with skip connections and instance normalization. We adopt the convolutional layers of the pre-trained VGG network as encoder to exploit the representa…
ENS de Lyon（里昂高等师范学校）；MILA（MILA（蒙特利尔学习算法研究所））；IMT Atlantique（大西洋国立高等矿业电信学校）；Université Côte d’Azur（蔚蓝海岸大学）
Typical deep convolutional architectures present an increasing number of feature maps as we go deeper in the network, whereas spatial resolution of inputs is decreased through downsampling operations. This means that most of the parameters lay in the final layers, while a large portion of the computations are performed by a small fraction of the total parameters in the first layers. In an effort to use every parameter of a network at its maximum, we propose a new convolutional neural network architecture, called ThriftyNet. In ThriftyNet, only one convolutional layer is defined and used recurs…
