We give the first provably efficient algorithm for learning a one hidden layer convolutional network with respect to a general class of (potentially overlapping) patches. Additionally, our algorithm requires only mild conditions on the underlying distribution. We prove that our framework captures commonly used schemes from computer vision, including one-dimensional and two-dimensional "patch and stride" convolutions.
Our algorithm-- $Convotron$ -- is inspired by recent work applying isotonic regression to learning neural networks. Convotron uses a simple, iterative update rule that is stochastic in nature and tolerant to noise (requires only that the conditional mean function is a one layer convolutional network, as opposed to the realizable setting). In contrast to gradient descent, Convotron requires no special initialization or learning-rate tuning to converge to the global optimum.
We also point out that learning one hidden convolutional layer with respect to a Gaussian distribution and just $one$ disjoint patch $P$ (the other patches may be arbitrary) is $easy$ in the following sense: Convotron can efficiently recover the hidden weight vector by updating $only$ in the direction of $P$.
In this paper, we consider parameter recovery for non-overlapping convolutional neural networks (CNNs) with multiple kernels. We show that when the inputs follow Gaussian distribution and the sample size is sufficiently large, the squared loss of such CNNs is $\mathit{~locally~strongly~convex}$ in a basin of attraction near the global optima for most popular activation functions, like ReLU, Leaky ReLU, Squared ReLU, Sigmoid and Tanh. The required sample complexity is proportional to the dimension of the input and polynomial in the number of kernels and a condition number of the parameters. We …
The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we study this through the lens of kernel methods, by considering simple hierarchical kernels with two or three convolution and pooling layers, inspired by convolutional kernel networks. These achieve good empirical performance on standard vision datasets, while providing a precise description of their functional space that yields new insights on their inductive b…
Carnegie Mellon University（卡内基梅隆大学）；University of Southern California（南加州大学）；Facebook AI Research（Facebook人工智能研究）
We analyze the convergence of (stochastic) gradient descent algorithm for learning a convolutional filter with Rectified Linear Unit (ReLU) activation function. Our analysis does not rely on any specific form of the input distribution and our proofs only use the definition of ReLU, in contrast with previous works that are restricted to standard Gaussian input. We show that (stochastic) gradient descent with random initialization can learn the convolutional filter in polynomial time and the convergence rate depends on the smoothness of the input distribution and the closeness of patches. To the…
University of Oxford（牛津大学）；NIHR Oxford Biomedical Research Centre（英国国家健康研究所牛津生物医学研究中心）
We propose a multi-label multi-task framework based on a convolutional recurrent neural network to unify detection of isolated and overlapping audio events. The framework leverages the power of convolutional recurrent neural network architectures; convolutional layers learn effective features over which higher recurrent layers perform sequential modelling. Furthermore, the output layer is designed to handle arbitrary degrees of event overlap. At each time step in the recurrent output sequence, an output triple is dedicated to each event category of interest to jointly model event occurrence an…
Universite Paris Est（巴黎东大学）；Ecole des Ponts ParisTech（巴黎高科桥路学院）
In this paper we show how to learn directly from image data (i.e., without resorting to manually-designed features) a general similarity function for comparing image patches, which is a task of fundamental importance for many computer vision problems. To encode such a function, we opt for a CNN-based model that is trained to account for a wide variety of changes in image appearance. To that end, we explore and study multiple neural network architectures, which are specifically adapted to this task. We show that such an approach can significantly outperform the state-of-the-art on several probl…
Département d’Informatique de l’ENS（巴黎高等师范学院计算机系）；ENS（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL University（巴黎文理研究大学）；Gatsby Computational Neuroscience Unit（盖茨比计算神经科学中心）；University College London（伦敦大学学院）；Concordia University（康考迪亚大学）；Mila（米拉人工智能研究所）；LIP6（巴黎第六大学计算机实验室）；Sorbonne University（索邦大学）
A recent line of work showed that various forms of convolutional kernel methods can be competitive with standard supervised deep convolutional networks on datasets like CIFAR-10, obtaining accuracies in the range of 87-90% while being more amenable to theoretical analysis. In this work, we highlight the importance of a data-dependent feature extraction step that is key to the obtain good performance in convolutional kernel methods. This step typically corresponds to a whitened dictionary of patches, and gives rise to a data-driven convolutional kernel methods. We extensively study its effect, …
Faculty of Computer and Information Science（计算机与信息科学学院）；University of Ljubljana（卢布尔雅那大学）；Courant Institute of Mathematical Sciences（库朗数学科学研究所）；New York University（纽约大学）；Facebook AI Research（脸书人工智能研究院）
We present a method for extracting depth information from a rectified image pair. Our approach focuses on the first stage of many stereo algorithms: the matching cost computation. We approach the problem by learning a similarity measure on small image patches using a convolutional neural network. Training is carried out in a supervised manner by constructing a binary classification data set with examples of similar and dissimilar pairs of patches. We examine two network architectures for this task: one tuned for speed, the other for accuracy. The output of the convolutional neural network is u…
University of Helsinki（赫尔辛基大学）；Finnish Environment Institute（芬兰环境研究所）
Semantic segmentation by convolutional neural networks (CNN) has advanced the state of the art in pixel-level classification of remote sensing images. However, processing large images typically requires analyzing the image in small patches, and hence features that have large spatial extent still cause challenges in tasks such as cloud masking. To support a wider scale of spatial features while simultaneously reducing computational requirements for large satellite images, we propose an architecture of two cascaded CNN model components successively processing undersampled and full resolution ima…
In this paper we present a class of convolutional neural networks (CNNs) called non-overlapping CNNs in the study of approximation capabilities of CNNs. We prove that such networks with sigmoidal activation function are capable of approximating arbitrary continuous function defined on compact input sets with any desired degree of accuracy. This result extends existing results where only multilayer feedforward networks are a class of approximators. Evaluations elucidate the accuracy and efficiency of our result and indicate that the proposed non-overlapping CNNs are less sensitive to noise.
Institut de Robòtica i Informàtica Industrial, UPC-CSIC（加泰罗尼亚理工大学-西班牙国家研究委员会机器人与工业信息技术研究所）；Institut Pediàtric de Malalties Rares, Hospital de Sant Joan de Déu（罕见病儿科研究所，圣若安·德乌医院）；Hospital de Sant Joan de Déu（圣若安·德乌医院）
The development of machine learning systems for the diagnosis of rare diseases is challenging mainly due the lack of data to study them. Despite this challenge, this paper proposes a system for the Computer Aided Diagnosis (CAD) of low-prevalence, congenital muscular dystrophies from confocal microscopy images. The proposed CAD system relies on a Convolutional Neural Network (CNN) which performs an independent classification for non-overlapping patches tiling the input image, and generates an overall decision summarizing the individual decisions for the patches on the query image. This decisio…
Tampere University of Technology（坦佩雷理工大学）；Aalto University（阿尔托大学）
In this paper, we propose a stacked convolutional and recurrent neural network (CRNN) with a 3D convolutional neural network (CNN) in the first layer for the multichannel sound event detection (SED) task. The 3D CNN enables the network to simultaneously learn the inter- and intra-channel features from the input multichannel audio. In order to evaluate the proposed method, multichannel audio datasets with different number of overlapping sound sources are synthesized. Each of this dataset has a four-channel first-order Ambisonic, binaural, and single-channel versions, on which the performance of…
Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）；Department of Computer Science, University of Texas at Austin（德克萨斯大学奥斯汀分校计算机科学系）
We propose a new algorithm to learn a one-hidden-layer convolutional neural network where both the convolutional weights and the outputs weights are parameters to be learned. Our algorithm works for a general class of (potentially overlapping) patches, including commonly used structures for computer vision tasks. Our algorithm draws ideas from (1) isotonic regression for learning neural networks and (2) landscape analysis of non-convex matrix factorization problems. We believe these findings may inspire further development in designing provable algorithms for learning neural networks and other…
New York University（纽约大学）；Bosch Center for AI（博世人工智能中心）
Randomized smoothing (RS) has been shown to be a fast, scalable technique for certifying the robustness of deep neural network classifiers. However, methods based on RS require augmenting data with large amounts of noise, which leads to significant drops in accuracy. We propose a training-free, modified smoothing approach, Smooth-Reduce, that leverages patching and aggregation to provide improved classifier certificates. Our algorithm classifies overlapping patches extracted from an input image, and aggregates the predicted logits to certify a larger radius around the input. We study two aggre…
Expressive efficiency refers to the relation between two architectures A and B, whereby any function realized by B could be replicated by A, but there exists functions realized by A, which cannot be replicated by B unless its size grows significantly larger. For example, it is known that deep networks are exponentially efficient with respect to shallow networks, in the sense that a shallow network must grow exponentially large in order to approximate the functions represented by a deep network of polynomial size. In this work, we extend the study of expressive efficiency to the attribute of ne…
National Technical University of Athens（雅典国立技术大学）；National and Kapodistrian University of Athens（雅典国立卡波迪斯特里安大学）；Aretaieion Hospital（阿雷泰翁医院）
Deep Convolutional Neural Networks (CNNs) for image classification successively alternate convolutions and downsampling operations, such as pooling layers or strided convolutions, resulting in lower resolution features the deeper the network gets. These downsampling operations save computational resources and provide some translational invariance as well as a bigger receptive field at the next layers. However, an inherent side-effect of this is that high-level features, produced at the deep end of the network, are always captured in low resolution feature maps. The inverse is also true, as sha…
We introduce a pretraining technique called Selfie, which stands for SELFie supervised Image Embedding. Selfie generalizes the concept of masked language modeling of BERT (Devlin et al., 2019) to continuous data, such as images, by making use of the Contrastive Predictive Coding loss (Oord et al., 2018). Given masked-out patches in an input image, our method learns to select the correct patch, among other "distractor" patches sampled from the same image, to fill in the masked location. This classification objective sidesteps the need for predicting exact pixel values of the target patches. The…
Arizona State University（亚利桑那州立大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Microsoft Research（微软研究院）；StylingAI Inc.（StylingAI公司）
We present a novel method of compression of deep Convolutional Neural Networks (CNNs) by weight sharing through a new representation of convolutional filters. The proposed method reduces the number of parameters of each convolutional layer by learning a 1D vector termed Filter Summary (FS). The convolutional filters are located in FS as overlapping 1D segments, and nearby filters in FS share weights in their overlapping regions in a natural way. The resultant neural network based on such weight sharing scheme, termed Filter Summary CNNs or FSNet, has a FS in each convolution layer instead of a…
North South University（北南大学）；Bangladesh University of Engineering and Technology（孟加拉国工程技术大学）；Military Institute of Science and Technology（军事科学技术学院）
Malaria is a female anopheles mosquito-bite inflicted life-threatening disease which is considered endemic in many parts of the world. This article focuses on improving malaria detection from patches segmented from microscopic images of red blood cell smears by introducing a deep convolutional neural network. Compared to the traditional methods that use tedious hand engineering feature extraction, the proposed method uses deep learning in an end-to-end arrangement that performs both feature extraction and classification directly from the raw segmented patches of the red blood smears. The datas…
To build the connectomics map of the brain, we developed a new algorithm that can automatically refine the Membrane Detection Probability Maps (MDPM) generated to perform automatic segmentation of electron microscopy (EM) images. To achieve this, we executed supervised training of a convolutional neural network to recover the removed center pixel label of patches sampled from a MDPM. MDPM can be generated from other machine learning based algorithms recognizing whether a pixel in an image corresponds to the cell membrane. By iteratively applying this network over MDPM for multiple rounds, we w…
University of California, Riverside（加州大学河滨分校）；University of Southern California（南加利福尼亚大学）
In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our approach dubbed Deep Tensor Decomposition (DeepTD) is based on a rank-1 tensor decomposition. We theoretically investigate DeepTD under a realizable model for the training data where the inputs are chosen i.i.d. from a Gaussian distribution and the labels are generated according to …
With the success of deep learning, recent efforts have been focused on analyzing how learned networks make their classifications. We are interested in analyzing the network output based on the network structure and information flow through the network layers. We contribute an algorithm for 1) analyzing a deep network to find neurons that are 'important' in terms of the network classification outcome, and 2)automatically labeling the patches of the input image that activate these important neurons. We propose several measures of importance for neurons and demonstrate that our technique can be u…
University of Ljubljana（卢布尔雅那大学）；New York University（纽约大学）
We present a method for extracting depth information from a rectified image pair. We train a convolutional neural network to predict how well two image patches match and use it to compute the stereo matching cost. The cost is refined by cross-based cost aggregation and semiglobal matching, followed by a left-right consistency check to eliminate errors in the occluded regions. Our stereo method achieves an error rate of 2.61 % on the KITTI stereo dataset and is currently (August 2014) the top performing method on this dataset.
We propose an unsupervised method using self-clustering convolutional adversarial autoencoders to classify prostate tissue as tumor or non-tumor without any labeled training data. The clustering method is integrated into the training of the autoencoder and requires only little post-processing. Our network trains on hematoxylin and eosin (H&E) input patches and we tested two different reconstruction targets, H&E and immunohistochemistry (IHC). We show that antibody-driven feature learning using IHC helps the network to learn relevant features for the clustering task. Our network achieves a F1 s…
Most current speech technology systems are designed to operate well even in the presence of multiple active speakers. However, most solutions assume that the number of co-current speakers is known. Unfortunately, this information might not always be available in real-world applications. In this study, we propose a real-time, single-channel attention-guided Convolutional Neural Network (CNN) to estimate the number of active speakers in overlapping speech. The proposed system extracts higher-level information from the speech spectral content using a CNN model. Next, the attention mechanism summa…
The Institute of Cancer Research（癌症研究院）；University College London（伦敦大学学院）
In digital pathology, cell detection and classification are often prerequisites to quantify cell abundance and explore tissue spatial heterogeneity. However, these tasks are particularly challenging for multiplex immunohistochemistry (mIHC) images due to high levels of variability in staining, expression intensity, and inherent noise as a result of preprocessing artefacts. We proposed a deep learning method to detect and classify cells in mIHC whole-tumour slide images of breast cancer. Inspired by inception-v3, we developed Cell COunt RegularizeD Convolutional neural Network (ConCORDe-Net) wh…
Idiap Research Institute（伊迪亚普研究所）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
We present a semi-blind, spatially-variant deconvolution technique aimed at optical microscopy that combines a local estimation step of the point spread function (PSF) and deconvolution using a spatially variant, regularized Richardson-Lucy algorithm. To find the local PSF map in a computationally tractable way, we train a convolutional neural network to perform regression of an optical parametric model on synthetically blurred image patches. We deconvolved both synthetic and experimentally-acquired data, and achieved an improvement of image SNR of 1.00 dB on average, compared to other deconvo…
Charles University（查理大学）；Faculty of Mathematics and Physics（数学与物理学院）；Institute of Formal and Applied Linguistics（形式与应用语言学研究所）
Filters of convolutional networks used in computer vision are often visualized as image patches that maximize the response of the filter. We use the same approach to interpret weight matrices in simple architectures for natural language processing tasks. We interpret a convolutional network for sentiment classification as word-based rules. Using the rule, we recover the performance of the original model.
École Polytechnique（巴黎综合理工学院）；Athens University of Economics and Business（雅典经济与商业大学）
Graph kernels have been successfully applied to many graph classification problems. Typically, a kernel is first designed, and then an SVM classifier is trained based on the features defined implicitly by this kernel. This two-stage approach decouples data representation from learning, which is suboptimal. On the other hand, Convolutional Neural Networks (CNNs) have the capability to learn their own features directly from the raw data during training. Unfortunately, they cannot handle irregular data such as graphs. We address this challenge by using graph kernels to embed meaningful local neig…
University of Central Florida（中佛罗里达大学）；Purdue University（普渡大学）
Classification and clustering have been studied separately in machine learning and computer vision. Inspired by the recent success of deep learning models in solving various vision problems (e.g., object recognition, semantic segmentation) and the fact that humans serve as the gold standard in assessing clustering algorithms, here, we advocate for a unified treatment of the two problems and suggest that hierarchical frameworks that progressively build complex patterns on top of the simpler ones (e.g., convolutional neural networks) offer a promising solution. We do not dwell much on the learni…
We address the problem of contour detection via per-pixel classifications of edge point. To facilitate the process, the proposed approach leverages with DenseNet, an efficient implementation of multiscale convolutional neural networks (CNNs), to extract an informative feature vector for each pixel and uses an SVM classifier to accomplish contour detection. The main challenge lies in adapting a pre-trained per-image CNN model for yielding per-pixel image features. We propose to base on the DenseNet architecture to achieve pixelwise fine-tuning and then consider a cost-sensitive strategy to furt…
Institut National des Sciences Appliquées Centre Val de Loire（卢瓦尔河谷中心国立应用科学学院）；Université de Tours（图尔大学）；LIFAT EA 6300（LIFAT EA 6300实验室）
Deep learning based models, generally, require a large number of samples for appropriate training, a requirement that is difficult to satisfy in the medical field. This issue can usually be avoided with a proper initialization of the weights. On the task of medical image segmentation in general, two techniques are oftentimes employed to tackle the training of a deep network $f_T$. The first one consists in reusing some weights of a network $f_S$ pre-trained on a large scale database ($e.g.$ ImageNet). This procedure, also known as $transfer$ $learning$, happens to reduce the flexibility when i…
Univ. Bordeaux（波尔多大学）；Bordeaux INP（波尔多国立理工学院）；CNRS（法国国家科学研究中心）；Université de Paris（巴黎大学）
In this work, we propose a framework to learn a local regularization model for solving general image restoration problems. This regularizer is defined with a fully convolutional neural network that sees the image through a receptive field corresponding to small image patches. The regularizer is then learned as a critic between unpaired distributions of clean and degraded patches using a Wasserstein generative adversarial networks based energy. This yields a regularization function that can be incorporated in any image restoration problem. The efficiency of the framework is finally shown on den…
[-15pt]1 Federal University of Technology - Paran\' a , Curitiba, Brazil 2 Federal University of Paran\'a, Curitiba, Brazil [0.5ex]
This work addresses the problem of vehicle identification through non-overlapping cameras. As our main contribution, we introduce a novel dataset for vehicle identification, called Vehicle-Rear, that contains more than three hours of high-resolution videos, with accurate information about the make, model, color and year of nearly 3,000 vehicles, in addition to the position and identification of their license plates. To explore our dataset we design a two-stream CNN that simultaneously uses two of the most distinctive and persistent features available: the vehicle's appearance and its license p…
This paper investigates the joint localization, detection, and tracking of sound events using a convolutional recurrent neural network (CRNN). We use a CRNN previously proposed for the localization and detection of stationary sources, and show that the recurrent layers enable the spatial tracking of moving sources when trained with dynamic scenes. The tracking performance of the CRNN is compared with a stand-alone tracking method that combines a multi-source (DOA) estimator and a particle filter. Their respective performance is evaluated in various acoustic conditions such as anechoic and reve…
