Deep Convolutional Neural Networks (DCNNs) is currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $Π$-Nets, a new class of DCNNs. $Π$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. $Π$-Nets can be implemented using special kind of skip connections and their parameters can be represented via high-order tensors. We empirically demonstrate that $Π$-Nets have better representation power than standard DCNNs and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, $Π$-Nets produce state-of-the-art results in challenging tasks, such as image generation. Lastly, our framework elucidates why recent generative models, such as StyleGAN, improve upon their predecessors, e.g., ProGAN.
Imperial College London（帝国理工学院）；Ecole Polytechnique Federale de Lausanne (EPFL)（洛桑联邦理工学院）；University of Athens（雅典大学）
Deep Convolutional Neural Networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose $Π$-Nets, a new class of function approximators based on polynomial expansions. $Π$-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which a…
Imperial College London（帝国理工学院）；Columbia University（哥伦比亚大学）；Shanghai Jiao Tong University（上海交通大学）
Deep generative models have been successfully applied to many applications. However, existing works experience limitations when generating large images (the literature usually generates small images, e.g. 32 * 32 or 128 * 128). In this paper, we propose a novel scheme, called deep tensor adversarial generative nets (TGAN), that generates large high-quality images by exploring tensor structures. Essentially, the adversarial process of TGAN takes place in a tensor space. First, we impose tensor structures for concise image representation, which is superior in capturing the pixel proximity inform…
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Descartes Labs, Inc（笛卡尔实验室公司）
In this work we demonstrate that generative adversarial networks (GANs) can be used to generate realistic pervasive changes in remote sensing imagery, even in an unpaired training setting. We investigate some transformation quality metrics based on deep embedding of the generated and real images which enable visualization and understanding of the training dynamics of the GAN, and may provide a useful measure in terms of quantifying how distinguishable the generated images are from real images. We also identify some artifacts introduced by the GAN in the generated images, which are likely to co…
Dalle Molle Institute for Artificial Intelligence（达莱·莫勒人工智能研究所）；University of Lugano（卢加诺大学）；University of Applied Sciences of Southern Switzerland（瑞士南部应用科学大学）
The competitive MNIST handwritten digit recognition benchmark has a long history of broken records since 1998. The most recent substantial improvement by others dates back 7 years (error rate 0.4%) . Recently we were able to significantly improve this result, using graphics cards to greatly speed up training of simple but deep MLPs, which achieved 0.35%, outperforming all the previous more complex methods. Here we report another substantial improvement: 0.31% obtained using a committee of MLPs.
University of California, Irvine（加州大学欧文分校）；University of California, Los Angeles（加州大学洛杉矶分校）
Deep neural nets (DNNs) compression is crucial for adaptation to mobile devices. Though many successful algorithms exist to compress naturally trained DNNs, developing efficient and stable compression algorithms for robustly trained DNNs remains widely open. In this paper, we focus on a co-design of efficient DNN compression algorithms and sparse neural architectures for robust and accurate deep learning. Such a co-design enables us to advance the goal of accommodating both sparsity and robustness. With this objective in mind, we leverage the relaxed augmented Lagrangian based algorithms to pr…
Neural tangent kernel (NTK) is a powerful tool to analyze training dynamics of neural networks and their generalization bounds. The study on NTK has been devoted to typical neural network architectures, but it is incomplete for neural networks with Hadamard products (NNs-Hp), e.g., StyleGAN and polynomial neural networks (PNNs). In this work, we derive the finite-width NTK formulation for a special class of NNs-Hp, i.e., polynomial neural networks. We prove their equivalence to the kernel regression predictor with the associated NTK, which expands the application scope of NTK. Based on our res…
Michigan Technological University（密歇根理工大学）；Symbiosis Centre for Medical Image Analysis（共生医学图像分析中心）；Symbiosis Institute of Technology（共生技术学院）
This work introduces a novel activation unit that can be efficiently employed in deep neural nets (DNNs) and performs significantly better than the traditional Rectified Linear Units (ReLU). The function developed is a two parameter version of the specialized Richard's Curve and we call it Adaptive Richard's Curve weighted Activation (ARiA). This function is non-monotonous, analogous to the newly introduced Swish, however allows a precise control over its non-monotonous convexity by varying the hyper-parameters. We first demonstrate the mathematical significance of the two parameter ARiA follo…
This paper considers the power of deep neural networks (deep nets for short) in realizing data features. Based on refined covering number estimates, we find that, to realize some complex data features, deep nets can improve the performances of shallow neural networks (shallow nets for short) without requiring additional capacity costs. This verifies the advantage of deep nets in realizing complex features. On the other hand, to realize some simple data feature like the smoothness, we prove that, up to a logarithmic factor, the approximation rate of deep nets is asymptotically identical to that…
University of California, Los Angeles（加州大学洛杉矶分校）；Hong Kong University of Science and Technology（香港科技大学）；Duke University（杜克大学）；Tsinghua University（清华大学）
We replace the output layer of deep neural nets, typically the softmax function, by a novel interpolating function. And we propose end-to-end training and testing algorithms for this new architecture. Compared to classical neural nets with softmax function as output activation, the surrogate with interpolating function as output activation combines advantages of both deep and manifold learning. The new framework demonstrates the following major advantages: First, it is better applicable to the case with insufficient training data. Second, it significantly improves the generalization accuracy o…
While the class of Polynomial Nets demonstrates comparable performance to neural networks (NN), it currently has neither theoretical generalization characterization nor robustness guarantees. To this end, we derive new complexity bounds for the set of Coupled CP-Decomposition (CCP) and Nested Coupled CP-decomposition (NCP) models of Polynomial Nets in terms of the $\ell_\infty$-operator-norm and the $\ell_2$-operator norm. In addition, we derive bounds on the Lipschitz constant for both models to establish a theoretical certificate for their robustness. The theoretical results enable us to pro…
University of California, Davis（加州大学戴维斯分校）；Stanford University（斯坦福大学）
Despite the success of neural networks (NNs), there is still a concern among many over their "black box" nature. Why do they work? Here we present a simple analytic argument that NNs are in fact essentially polynomial regression models. This view will have various implications for NNs, e.g. providing an explanation for why convergence problems arise in NNs, and it gives rough guidance on avoiding overfitting. In addition, we use this phenomenon to predict and confirm a multicollinearity property of NNs not previously reported in the literature. Most importantly, given this loose correspondence…
Bar-Ilan University（巴伊兰大学）；Technion（以色列理工学院）；University of Illinois（伊利诺伊大学）
Generalization bounds which assess the difference between the true risk and the empirical risk have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz loss function. To avoid these assumptions, in this paper, we propose a new generalization bound for Bayesian deep nets by exploiting the contractivity of the Log-Sobolev inequalities. Using these inequalities adds an additional loss-gradient norm term to the generalization bound, which is intuitively a surrogate of the model complexity. Empirically, we analyze…
The University of Western Australia（西澳大利亚大学）；The University of New South Wales（新南威尔士大学）
In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a single hidden layer. The transformations of both deep rectifier nets and deep residual nets are conducted to demonstrate the advantages of the residual nets over the conventional neural nets and the advantages of the deep neural nets over the shallow neural nets. In summary, for …
Along with the rapid development of deep learning in practice, the theoretical explanations for its success become urgent. Generalization and expressivity are two widely used measurements to quantify theoretical behaviors of deep learning. The expressivity focuses on finding functions expressible by deep nets but cannot be approximated by shallow nets with the similar number of neurons. It usually implies the large capacity. The generalization aims at deriving fast learning rate for deep nets. It usually requires small capacity to reduce the variance. Different from previous studies on deep le…
Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of parameters and over a thousand layers. The trade-off is that these large architectures require an enormous amount of memory, storage, and computation, thus limiting their usability. Inspired by the recent tensor ring factorization, we introduce Tensor Ring Networks (TR-Nets), which significantly compress both the fully connected layers and the convolutional layers o…
Waterloo Artificial Intelligence Institute, University of Waterloo（滑铁卢大学滑铁卢人工智能研究所）；DarwinAI Corp.（DarwinAI公司）
Much of the focus in the design of deep neural networks has been on improving accuracy, leading to more powerful yet highly complex network architectures that are difficult to deploy in practical scenarios, particularly on edge devices such as mobile and other consumer devices given their high computational and memory requirements. As a result, there has been a recent interest in the design of quantitative metrics for evaluating deep neural networks that accounts for more than just model accuracy as the sole indicator of network performance. In this study, we continue the conversation towards …
UC Irvine（加州大学欧文分校）；University of Edinburgh（爱丁堡大学）；Ecole Polytechnique de Montreal（蒙特利尔理工学院）；University of Alberta（阿尔伯塔大学）；University of Washington（华盛顿大学）；Microsoft Research（微软研究院）
Yes, they do. This paper provides the first empirical demonstration that deep convolutional models really need to be both deep and convolutional, even when trained with methods such as distillation that allow small or shallow models of high accuracy to be trained. Although previous research showed that shallow feed-forward nets sometimes can learn the complex functions previously learned by deep nets while using the same number of parameters as the deep models they mimic, in this paper we demonstrate that the same methods cannot be used to train accurate models on CIFAR-10 unless the student m…
As machine learning is applied to an increasing variety of complex problems, which are defined by high dimensional and complex data sets, the necessity for task oriented feature learning grows in importance. With the advancement of Deep Learning algorithms, various successful feature learning techniques have evolved. In this paper, we present a novel way of learning discriminative features by training Deep Neural Nets which have Encoder or Decoder type architecture similar to an Autoencoder. We demonstrate that our approach can learn discriminative features which can perform better at pattern …
Hong Kong Baptist University（香港浸会大学）；CityU（香港城市大学）
Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal function approximation in an arbitrarily high dimensional Euclidian space. It is shown that deep nets have much better performance than shallow nets (with only one hidden layer) in terms of approximation accuracy and learning capabilities. In particular, for learning radial functions, it is shown that near-optimal rate can be achieved by deep nets but not by shal…
University of Toronto（多伦多大学）；Microsoft Research（微软研究院）
Currently, deep neural networks are the state of the art on problems such as speech recognition and computer vision. In this extended abstract, we show that shallow feed-forward networks can learn the complex functions previously learned by deep nets and achieve accuracies previously only achievable with deep models. Moreover, in some cases the shallow neural nets can learn these deep functions using a total number of parameters similar to the original deep model. We evaluate our method on the TIMIT phoneme recognition task and are able to train shallow fully-connected nets that perform simila…
Duke University（杜克大学）；Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）
Mode connectivity is a surprising phenomenon in the loss landscape of deep nets. Optima -- at least those discovered by gradient-based optimization -- turn out to be connected by simple paths on which the loss function is almost constant. Often, these paths can be chosen to be piece-wise linear, with as few as two segments. We give mathematical explanations for this phenomenon, assuming generic properties (such as dropout stability and noise stability) of well-trained deep nets, which have previously been identified as part of understanding the generalization properties of deep nets. Our expla…
While stochastic gradient descent (SGD) and variants have been surprisingly successful for training deep nets, several aspects of the optimization dynamics and generalization are still not well understood. In this paper, we present new empirical observations and theoretical results on both the optimization dynamics and generalization behavior of SGD for deep nets based on the Hessian of the training loss and associated quantities. We consider three specific research questions: (1) what is the relationship between the Hessian of the loss and the second moment of stochastic gradients (SGs)? (2) …
In this paper, we study the generalization performance of global minima for implementing empirical risk minimization (ERM) on over-parameterized deep ReLU nets. Using a novel deepening scheme for deep ReLU nets, we rigorously prove that there exist perfect global minima achieving almost optimal generalization error bounds for numerous types of data under mild conditions. Since over-parameterization is crucial to guarantee that the global minima of ERM on deep ReLU nets can be realized by the widely used stochastic gradient descent (SGD) algorithm, our results indeed fill a gap between optimiza…
We propose two bounded comparison metrics that may be implemented to arbitrary dimensions in regression tasks. One quantifies the structure of uncertainty and the other quantifies the distribution of uncertainty. The structure metric assesses the similarity in shape and location of uncertainty with the true error, while the distribution metric quantifies the supported magnitudes between the two. We apply these metrics to Gaussian Processes (GPs), Ensemble Deep Neural Nets (DNNs), and Ensemble Deep Neural Operators (DNOs) on high-dimensional and nonlinear test cases. We find that comparing a mo…
State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences（中国科学院沈阳自动化研究所机器人学国家重点实验室）
Deep learning is recognized to be capable of discovering deep features for representation learning and pattern recognition without requiring elegant feature engineering techniques by taking advantage of human ingenuity and prior knowledge. Thus it has triggered enormous research activities in machine learning and pattern recognition. One of the most important challenge of deep learning is to figure out relations between a feature and the depth of deep neural networks (deep nets for short) to reflect the necessity of depth. Our purpose is to quantify this feature-depth correspondence in feature…
Stanford University（斯坦福大学）；City University of Hong Kong（香港城市大学）
The great success of deep learning poses urgent challenges for understanding its working mechanism and rationality. The depth, structure, and massive size of the data are recognized to be three key ingredients for deep learning. Most of the recent theoretical studies for deep learning focus on the necessity and advantages of depth and structures of neural networks. In this paper, we aim at rigorous verification of the importance of massive data in embodying the out-performance of deep learning. To approximate and learn spatially sparse and smooth functions, we establish a novel sampling theore…
University of Maryland, College Park（马里兰大学帕克分校）；Cornell University（康奈尔大学）
Currently, deep neural networks are deployed on low-power portable devices by first training a full-precision model using powerful hardware, and then deriving a corresponding low-precision model for efficient inference on such systems. However, training models directly with coarsely quantized weights is a key step towards learning on embedded platforms that have limited computing resources, memory capacity, and power consumption. Numerous recent publications have studied methods for training quantized networks, but these studies have mostly been empirical. In this work, we investigate training…
Fudan University（复旦大学）；Rochester Institute of Technology（罗切斯特理工学院）
Meta-learning is a promising method to achieve efficient training method towards deep neural net and has been attracting increases interests in recent years. But most of the current methods are still not capable to train complex neuron net model with long-time training process. In this paper, a novel second-order meta-optimizer, named Meta-learning with Hessian-Free(MLHF) approach, is proposed based on the Hessian-Free approach. Two recurrent neural networks are established to generate the damping and the precondition matrix of this Hessian-Free framework. A series of techniques to meta-train …
Princeton University（普林斯顿大学）；Duke University（杜克大学）；Institute for Advanced Study（高等研究院）
Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better than naive parameter counting. The current paper shows generalization bounds that're orders of magnitude better in practice. These rely upon new succinct reparametrizations of the trained net --- a compression that is explicit and efficient. These yield generalization bounds via a simple compression-based framework introduced here. Our results also provide some…
Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural networks (CNN) style architectures are being looked at: (1) transparency of the intermediate layers to the overall classification; (2) discriminativeness and robustness of learned features, especially in the early layers; (3) effectiveness in training due to the presence of the explod…
We introduce SE3-Nets, which are deep neural networks designed to model and learn rigid body motion from raw point cloud data. Based only on sequences of depth images along with action vectors and point wise data associations, SE3-Nets learn to segment effected object parts and predict their motion resulting from the applied force. Rather than learning point wise flow vectors, SE3-Nets predict SE3 transformations for different parts of the scene. Using simulated depth data of a table top scene and a robot manipulator, we show that the structure underlying SE3-Nets enables them to generate a fa…
Most of today's popular deep architectures are hand-engineered to be generalists. However, this design procedure usually leads to massive redundant, useless, or even harmful features for specific tasks. Unnecessarily high complexities render deep nets impractical for many real-world applications, especially those without powerful GPU support. In this paper, we attempt to derive task-dependent compact models from a deep discriminant analysis perspective. We propose an iterative and proactive approach for classification tasks which alternates between (1) a pushing step, with an objective to simu…
Applying traditional collaborative filtering to digital publishing is challenging because user data is very sparse due to the high volume of documents relative to the number of users. Content based approaches, on the other hand, is attractive because textual content is often very informative. In this paper we describe large-scale content based collaborative filtering for digital publishing. To solve the digital publishing recommender problem we compare two approaches: latent Dirichlet allocation (LDA) and deep belief nets (DBN) that both find low-dimensional latent representations for document…
University of Oxford（牛津大学）；OATML, Department of Computer Science（OATML计算机科学系）
We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distributions in function-space to those induced by shallower networks with complex weight posteriors. We validate our theoretical contributions empirically, both through examination of the weight posterior using Hamiltonian Monte Carlo in small models and by comparing diagonal- to structure…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose Chirality Nets, a family of deep nets that is equivariant to the "chirality transform," i.e., the transformation to create a chiral pair. Through parameter sharing, odd and even symmetry, we propose and prove variants of standard building blocks of deep nets that satisfy the equivariance property, including fully connected layers, convolutional layers, batch-normalization, and LSTM/GRU cells. The proposed layers lead to a more data efficient representation and a reduction in computation by exploiting symmetry. We evaluate chirality nets on the task of human pose regression, which na…
Feature Qualification by Deep Nets: A Constructive Approach
School of Mathematics, Zhejiang Normal University（浙江师范大学数学学院）；Institute of Mathematics and Cross-disciplinary Science, Zhejiang Normal University（浙江师范大学数学与交叉科学研究院）；Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University（西安交通大学管理学院智能决策与机器学习中心）
Neural networks should be interpretable to humans. In particular, there is a growing interest in concepts learned in a layer and similarity between layers. In this work, a tool, UMAP Tour, is built to visually inspect and compare internal behavior of real-world neural network models using well-aligned, instance-level representations. The method used in the visualization also implies a new similarity measure between neural network layers. Using the visual tool and the similarity measure, we find concepts learned in state-of-the-art models and dissimilarities between them, such as GoogLeNet and …
Accurate segmentation of medical images is essential for diagnosis and treatment of diseases. These problems are solved by highly complex models, such as deep networks (DN), requiring a large amount of labeled data for training. Thereby, many DNs possess task- or imaging modality specific architectures with a decision-making process that is often hard to explain and interpret. Here, we propose a framework that embeds existing DNs into a low-dimensional subspace induced by the learnable explicit feature map (LEFM) layer. Compared to the existing DN, the framework adds one hyperparameter and onl…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Gradient-based meta-learning (GBML) with deep neural nets (DNNs) has become a popular approach for few-shot learning. However, due to the non-convexity of DNNs and the bi-level optimization in GBML, the theoretical properties of GBML with DNNs remain largely unknown. In this paper, we first aim to answer the following question: Does GBML with DNNs have global convergence guarantees? We provide a positive answer to this question by proving that GBML with over-parameterized DNNs is guaranteed to converge to global optima at a linear rate. The second question we aim to address is: How does GBML a…
Recent theoretical work has demonstrated that deep neural networks have superior performance over shallow networks, but their training is more difficult, e.g., they suffer from the vanishing gradient problem. This problem can be typically resolved by the rectified linear unit (ReLU) activation. However, here we show that even for such activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability. Deep and narrow NNs are encountered in solving partial differential equations with high-order de…
Despite the phenomenal success of deep learning in recent years, there remains a gap in understanding the fundamental mechanics of neural nets. More research is focussed on handcrafting complex and larger networks, and the design decisions are often ad-hoc and based on intuition. Some recent research has aimed to demystify the learning dynamics in neural nets by attempting to build a theory from first principles, such as characterising the non-linear dynamics of specialised \textit{linear} deep neural nets (such as orthogonal networks). In this work, we expand and derive properties of learning…
Generative models for deep learning are promising both to improve understanding of the model, and yield training methods requiring fewer labeled samples. Recent works use generative model approaches to produce the deep net's input given the value of a hidden layer several levels above. However, there is no accompanying "proof of correctness" for the generative model, showing that the feedforward deep net is the correct inference method for recovering the hidden layer given the input. Furthermore, these models are complicated. The current paper takes a more theoretical tack. It presents a very …
Department of Mathematics, Texas A\&M, College Station, United States
This article concerns the expressive power of depth in neural nets with ReLU activations and bounded width. We are particularly interested in the following questions: what is the minimal width $w_{\text{min}}(d)$ so that ReLU nets of width $w_{\text{min}}(d)$ (and arbitrary depth) can approximate any continuous function on the unit cube $[0,1]^d$ aribitrarily well? For ReLU nets near this minimal width, what can one say about the depth necessary to approximate a given function? Our approach to this paper is based on the observation that, due to the convexity of the ReLU activation, ReLU nets a…
Institute of Physics（物理研究所）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Understanding why deep nets can classify data in large dimensions remains a challenge. It has been proposed that they do so by becoming stable to diffeomorphisms, yet existing empirical measurements support that it is often not the case. We revisit this question by defining a maximum-entropy distribution on diffeomorphisms, that allows to study typical diffeomorphisms of a given norm. We confirm that stability toward diffeomorphisms does not strongly correlate to performance on benchmark data sets of images. By contrast, we find that the stability toward diffeomorphisms relative to that of gen…
This is an opinion paper about the strengths and weaknesses of Deep Nets for vision. They are at the heart of the enormous recent progress in artificial intelligence and are of growing importance in cognitive science and neuroscience. They have had many successes but also have several limitations and there is limited understanding of their inner workings. At present Deep Nets perform very well on specific visual tasks with benchmark datasets but they are much less general purpose, flexible, and adaptive than the human visual system. We argue that Deep Nets in their current form are unlikely to…
Yale University（耶鲁大学）；Rutgers University – New Brunswick（罗格斯大学新不伦瑞克分校）
For any ReLU network there is a representation in which the sum of the absolute values of the weights into each node is exactly $1$, and the input layer variables are multiplied by a value $V$ coinciding with the total variation of the path weights. Implications are given for Gaussian complexity, Rademacher complexity, statistical risk, and metric entropy, all of which are shown to be proportional to $V$. There is no dependence on the number of nodes per layer, except for the number of inputs $d$. For estimation with sub-Gaussian noise, the mean square generalization error bounds that can be o…
Jiangxi Normal University（江西师范大学）；City University of Hong Kong（香港城市大学）；Hong Kong University of Science and Technology（香港科技大学）
In this paper, we develop an alternating direction method of multipliers (ADMM) for deep neural networks training with sigmoid-type activation functions (called \textit{sigmoid-ADMM pair}), mainly motivated by the gradient-free nature of ADMM in avoiding the saturation of sigmoid-type activations and the advantages of deep neural networks with sigmoid-type activations (called deep sigmoid nets) over their rectified linear unit (ReLU) counterparts (called deep ReLU nets) in terms of approximation. In particular, we prove that the approximation capability of deep sigmoid nets is not worse than t…
In this paper, we build an organization of high-dimensional datasets that cannot be cleanly embedded into a low-dimensional representation due to missing entries and a subset of the features being irrelevant to modeling functions of interest. Our algorithm begins by defining coarse neighborhoods of the points and defining an expected empirical function value on these neighborhoods. We then generate new non-linear features with deep net representations tuned to model the approximate function, and re-organize the geometry of the points with respect to the new representation. Finally, the points …
Towards Size-Independent Generalization Bounds for Deep Operator Nets
Indian Institute of Technology Kanpur (IIT Kanpur)（印度理工学院坎普尔分校（IIT坎普尔））；University of Michigan（密歇根大学）；University of Florida（佛罗里达大学）；The University of Manchester（曼彻斯特大学）
Deep learning model developers often use cloud GPU resources to experiment with large data and models that need expensive setups. However, this practice raises privacy concerns. Adversaries may be interested in: 1) personally identifiable information or objects encoded in the training images, and 2) the models trained with sensitive data to launch model-based attacks. Learning deep neural networks (DNN) from encrypted data is still impractical due to the large training data and the expensive learning process. A few recent studies have tried to provide efficient, practical solutions to protect …
This paper presents a new state-of-the-art for document image classification and retrieval, using features learned by deep convolutional neural networks (CNNs). In object and scene analysis, deep neural nets are capable of learning a hierarchical chain of abstraction from pixel inputs to concise and descriptive representations. The current work explores this capacity in the realm of document analysis, and confirms that this representation strategy is superior to a variety of popular hand-crafted alternatives. Experiments also show that (i) features extracted from CNNs are robust to compression…
University of California, Irvine（加州大学尔湾分校）；Baidu Research（百度研究院）
In this work, we present a fully automated lung CT cancer diagnosis system, DeepLung. DeepLung contains two parts, nodule detection and classification. Considering the 3D nature of lung CT data, two 3D networks are designed for the nodule detection and classification respectively. Specifically, a 3D Faster R-CNN is designed for nodule detection with a U-net-like encoder-decoder structure to effectively learn nodule features. For nodule classification, gradient boosting machine (GBM) with 3D dual path network (DPN) features is proposed. The nodule classification subnetwork is validated on a pub…
Unsupervised neural networks, such as restricted Boltzmann machines (RBMs) and deep belief networks (DBNs), are powerful tools for feature selection and pattern recognition tasks. We demonstrate that overfitting occurs in such models just as in deep feedforward neural networks, and discuss possible regularization methods to reduce overfitting. We also propose a "partial" approach to improve the efficiency of Dropout/DropConnect in this scenario, and discuss the theoretical justification of these methods from model convergence and likelihood bounds. Finally, we compare the performance of these …
Motivated by the idea that criticality and universality of phase transitions might play a crucial role in achieving and sustaining learning and intelligent behaviour in biological and artificial networks, we analyse a theoretical and a pragmatic experimental set up for critical phenomena in deep learning. On the theoretical side, we use results from statistical physics to carry out critical point calculations in feed-forward/fully connected networks, while on the experimental side we set out to find traces of criticality in deep neural networks. This is our first step in a series of upcoming i…
We study large-scale kernel methods for acoustic modeling and compare to DNNs on performance metrics related to both acoustic modeling and recognition. Measuring perplexity and frame-level classification accuracy, kernel-based acoustic models are as effective as their DNN counterparts. However, on token-error-rates DNN models can be significantly better. We have discovered that this might be attributed to DNN's unique strength in reducing both the perplexity and the entropy of the predicted posterior probabilities. Motivated by our findings, we propose a new technique, entropy regularized perp…
University of Maryland, College Park（马里兰大学帕克分校）；United States Naval Academy（美国海军学院）；Cornell University（康奈尔大学）
Clean-label poisoning attacks inject innocuous looking (and "correctly" labeled) poison images into training data, causing a model to misclassify a targeted image after being trained on this data. We consider transferable poisoning attacks that succeed without access to the victim network's outputs, architecture, or (in some cases) training data. To achieve this, we propose a new "polytope attack" in which poison images are designed to surround the targeted image in feature space. We also demonstrate that using Dropout during poison creation helps to enhance transferability of this attack. We …
