Despite the recent advances in optical character recognition (OCR), mathematical expressions still face a great challenge to recognize due to their two-dimensional graphical layout. In this paper, we propose a convolutional sequence modeling network, ConvMath, which converts the mathematical expression description in an image into a LaTeX sequence in an end-to-end way. The network combines an image encoder for feature extraction and a convolutional decoder for sequence generation. Compared with other Long Short Term Memory(LSTM) based encoder-decoder models, ConvMath is entirely based on convolution, thus it is easy to perform parallel computation. Besides, the network adopts multi-layer attention mechanism in the decoder, which allows the model to align output symbols with source feature vectors automatically, and alleviates the problem of lacking coverage while training the model. The performance of ConvMath is evaluated on an open dataset named IM2LATEX-100K, including 103556 samples. The experimental results demonstrate that the proposed network achieves state-of-the-art accuracy and much better efficiency than previous methods.
This work attempts to address two fundamental questions about the structure of the convolutional neural networks (CNN): 1) why a non-linear activation function is essential at the filter output of every convolutional layer? 2) what is the advantage of the two-layer cascade system over the one-layer system? A mathematical model called the "REctified-COrrelations on a Sphere" (RECOS) is proposed to answer these two questions. After the CNN training process, the converged filter weights define a set of anchor vectors in the RECOS model. Anchor vectors represent the frequently occurring patterns (…
In this paper, we address the task of Optical Character Recognition(OCR) for the Telugu script. We present an end-to-end framework that segments the text image, classifies the characters and extracts lines using a language model. The segmentation is based on mathematical morphology. The classification module, which is the most challenging task of the three, is a deep convolutional neural network. The language is modelled as a third degree markov chain at the glyph level. Telugu script is a complex alphasyllabary and the language is agglutinative, making the problem hard. In this paper we apply…
National Institutes of Health Clinical Center（美国国立卫生研究院临床中心）；National Cancer Institute（美国国家癌症研究所）
Tumor growth is associated with cell invasion and mass-effect, which are traditionally formulated by mathematical models, namely reaction-diffusion equations and biomechanics. Such models can be personalized based on clinical measurements to build the predictive models for tumor growth. In this paper, we investigate the possibility of using deep convolutional neural networks (ConvNets) to directly represent and learn the cell invasion and mass-effect, and to predict the subsequent involvement regions of a tumor. The invasion network learns the cell invasion from information related to metaboli…
Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computations of invariants involve multiscale contractions, the linearization of hierarchical symmetries, and sparse separations. Applications are discussed.
This paper proposes a fusion strategy for multistream convolutional networks, the Lattice Cross Fusion. This approach crosses signals from convolution layers performing mathematical operation-based fusions right before pooling layers. Results on a purposely worsened CIFAR-10, a popular image classification data set, with a modified AlexNet-LCNN version show that this novel method outperforms by 46% the baseline single stream network, with faster convergence, stability, and robustness.
University of Science and Technology of China（中国科学技术大学）
Handwritten mathematical expression recognition is a challenging problem due to the complicated two-dimensional structures, ambiguous handwriting input and variant scales of handwritten math symbols. To settle this problem, we utilize the attention based encoder-decoder model that recognizes mathematical expression images from two-dimensional layouts to one-dimensional LaTeX strings. We improve the encoder by employing densely connected convolutional networks as they can strengthen feature extraction and facilitate gradient propagation especially on a small training set. We also present a nove…
University of Chinese Academy of Sciences（中国科学院大学）
This paper proposes a novel model, named Continuity-Discrimination Convolutional Neural Network (CD-CNN), for visual object tracking. Existing state-of-the-art tracking methods do not deal with temporal relationship in video sequences, which leads to imperfect feature representations. To address this problem, CD-CNN models temporal appearance continuity based on the idea of temporal slowness. Mathematically, we prove that, by introducing temporal appearance continuity into tracking, the upper bound of target appearance representation error can be sufficiently small with high probability. Furth…
University of Chinese Academy of Sciences（中国科学院大学）
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networks). Here, we think three factors in each layer of it including the initialization, the dictionary design and the number of iterations greatly affect the performance of ML-CSC. Inspired by these considerations, we propose two novel multi-layer models--residual convolutional spars…
We study performance characteristics of convolutional neural networks (CNN) for mobile computer vision systems. CNNs have proven to be a powerful and efficient approach to implement such systems. However, the system performance depends largely on the utilization of hardware accelerators, which are able to speed up the execution of the underlying mathematical operations tremendously through massive parallelism. Our contribution is performance characterization of multiple CNN-based models for object recognition and detection with several different hardware platforms and software frameworks, usin…
Convolution Neural Networks, known as ConvNets exceptionally perform well in many complex machine learning tasks. The architecture of ConvNets demands the huge and rich amount of data and involves with a vast number of parameters that leads the learning takes to be computationally expensive, slow convergence towards the global minima, trap in local minima with poor predictions. In some cases, architecture overfits the data and make the architecture difficult to generalise for new samples that were not in the training set samples. To address these limitations, many regularization and optimizati…
Computer Vision Lab, ETH Zürich（苏黎世联邦理工学院计算机视觉实验室）；ETH Zürich（苏黎世联邦理工学院）；Johns Hopkins University（约翰斯·霍普金斯大学）；Microsoft（微软）；National University of Singapore（新加坡国立大学）；KU Leuven（鲁汶大学）
In this paper, we aim at improving the computational efficiency of graph convolutional networks (GCNs) for learning on point clouds. The basic graph convolution that is typically composed of a $K$-nearest neighbor (KNN) search and a multilayer perceptron (MLP) is examined. By mathematically analyzing the operations there, two findings to improve the efficiency of GCNs are obtained. (1) The local geometric structure information of 3D representations propagates smoothly across the GCN that relies on KNN search to gather neighborhood features. This motivates the simplification of multiple KNN sea…
Intelligent Transportation Systems (ITS) have become an important pillar in modern "smart city" framework which demands intelligent involvement of machines. Traffic load recognition can be categorized as an important and challenging issue for such systems. Recently, Convolutional Neural Network (CNN) models have drawn considerable amount of interest in many areas such as weather classification, human rights violation detection through images, due to its accurate prediction capabilities. This work tackles real-life traffic load recognition problem on System-On-a-Programmable-Chip (SOPC) platfor…
School of Instrumentation Science and Optoelectronics Engineering, Beihang University（北京航空航天大学仪器科学与光电工程学院）；Institute of Electronics, Chinese Academy of Sciences（中国科学院电子学研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Offline handwritten mathematical expression recognition is a challenging task, because handwritten mathematical expressions mainly have two problems in the process of recognition. On one hand, it is how to correctly recognize different mathematical symbols. On the other hand, it is how to correctly recognize the two-dimensional structure existing in mathematical expressions. Inspired by recent work in deep learning, a new neural network model that combines a Multi-Scale convolutional neural network (CNN) with an Attention recurrent neural network (RNN) is proposed to identify two-dimensional h…
Indian Institute of Technology Hyderabad（印度理工学院海得拉巴分校）；Cisco Systems（思科系统公司）
Over the last decade, Convolutional Neural Network (CNN) models have been highly successful in solving complex vision problems. However, these deep models are perceived as "black box" methods considering the lack of understanding of their internal functioning. There has been a significant recent interest in developing explainable deep learning models, and this paper is an effort in this direction. Building on a recently proposed method called Grad-CAM, we propose a generalized method called Grad-CAM++ that can provide better visual explanations of CNN model predictions, in terms of better obje…
Recognition of Handwritten Mathematical Expressions (HMEs) is a challenging problem because of the ambiguity and complexity of two-dimensional handwriting. Moreover, the lack of large training data is a serious issue, especially for academic recognition systems. In this paper, we propose pattern generation strategies that generate shape and structural variations to improve the performance of recognition systems based on a small training set. For data generation, we employ the public databases: CROHME 2014 and 2016 of online HMEs. The first strategy employs local and global distortions to gener…
New York University Abu Dhabi（纽约大学阿布扎比分校）；Inception Institute of Artificial Intelligence（起源人工智能研究院）；New York University（纽约大学）
Analyzing the structure of proteins is a key part of understanding their functions and thus their role in biology at the molecular level. In addition, design new proteins in a methodical way is a major engineering challenge. In this work, we introduce a joint geometric-neural networks approach for comparing, deforming and generating 3D protein structures. Viewing protein structures as 3D open curves, we adopt the Square Root Velocity Function (SRVF) representation and leverage its suitable geometric properties along with Deep Residual Networks (ResNets) for a joint registration and comparison.…
University College London（伦敦大学学院）；King’s College London（伦敦国王学院）；University of Electronic Science and Technology of China（电子科技大学）；University Hospitals Leuven（鲁汶大学医院）；Institute for Women’s Health（妇女健康研究所）
Despite the state-of-the-art performance for medical image segmentation, deep convolutional neural networks (CNNs) have rarely provided uncertainty estimations regarding their segmentation outputs, e.g., model (epistemic) and image-based (aleatoric) uncertainties. In this work, we analyze these different types of uncertainties for CNN-based 2D and 3D medical image segmentation tasks. We additionally propose a test-time augmentation-based aleatoric uncertainty to analyze the effect of different transformations of the input image on the segmentation output. Test-time augmentation has been previo…
The Hong Kong University of Science and Technology（香港科技大学）
There is a rising need for computational models that can complementarily leverage data of different modalities while investigating associations between subjects for population-based disease analysis. Despite the success of convolutional neural networks in representation learning for imaging data, it is still a very challenging task. In this paper, we propose a generalizable framework that can automatically integrate imaging data with non-imaging data in populations for uncertainty-aware disease prediction. At its core is a learnable adaptive population graph with variational edges, which we ma…
The growing demand for the internet of things (IoT) makes it necessary to implement computer vision tasks such as object recognition in low-power devices. Convolutional neural networks (CNNs) are a potential approach for object recognition and detection. However, the convolutional layer in CNN consumes significant energy compared to the fully connected layers. To mitigate this problem, a new approach based on the Hadamard transformation as an alternative to the convolution operation is demonstrated using two fundamental datasets, MNIST and CIFAR10. The mathematical expression of the Hadamard m…
University of Science and Technology Beijing（北京科技大学）
This paper develops a novel self-training U-net (STU-net) based method for the automated WPC model generation without requiring data pre-processing. The self-training (ST) process of STU-net has two steps. First, different from traditional studies regarding the WPC modeling as a curve fitting problem, in this paper, we renovate the WPC modeling formulation from a machine vision aspect. To develop sufficiently diversified training samples, we synthesize supervisory control and data acquisition (SCADA) data based on a set of S-shape functions depicting WPCs. These synthesized SCADA data and WPC …
Convolutional Neural Network is known as ConvNet have been extensively used in many complex machine learning tasks. However, hyperparameters optimization is one of a crucial step in developing ConvNet architectures, since the accuracy and performance are reliant on the hyperparameters. This multilayered architecture parameterized by a set of hyperparameters such as the number of convolutional layers, number of fully connected dense layers & neurons, the probability of dropout implementation, learning rate. Hence the searching the hyperparameter over the hyperparameter space are highly difficul…
In the field of medical image, deep convolutional neural networks(ConvNets) have achieved great success in the classification, segmentation, and registration tasks thanks to their unparalleled capacity to learn image features. However, these tasks often require large amounts of manually annotated data and are labor-intensive. Therefore, it is of significant importance for us to study unsupervised semantic feature learning tasks. In our work, we propose to learn features in medical images by training ConvNets to recognize the geometric transformation applied to images and present a simple self-…
Convolutional neural networks (ConvNets) have demonstrated an exceptional capacity to discern visual patterns from digital images and signals. Unfortunately, such powerful ConvNets do not generalize well to arbitrary-shaped manifolds, where data representation does not fit into a tensor-like grid. Hence, many fields of science and engineering, where data points possess some manifold structure, cannot enjoy the full benefits of the recent advances in ConvNets. The aneurysm wall stress estimation problem introduced in this paper is one of many such problems. The problem is well-known to be of a …
PAII Inc.（PAII公司）；Johns Hopkins University（约翰斯·霍普金斯大学）；Nvidia Corporation（英伟达公司）；National Institutes of Health Clinical Center（美国国立卫生研究院临床中心）；Tencent Holdings Limited（腾讯控股有限公司）
Prognostic tumor growth modeling via volumetric medical imaging observations can potentially lead to better outcomes of tumor treatment and surgical planning. Recent advances of convolutional networks have demonstrated higher accuracy than traditional mathematical models in predicting future tumor volumes. This indicates that deep learning-based techniques may have great potentials on addressing such problem. However, current 2D patch-based modeling approaches cannot make full use of the spatio-temporal imaging context of the tumor's longitudinal 4D (3D + time) data. Moreover, they are incapab…
Georgetown University Medical Center（乔治城大学医学中心）；Virginia Tech（弗吉尼亚理工大学）；Harbin Institute of Technology（哈尔滨工业大学）
Mathematically speaking, a transformationally invariant operator, such as a transformationally identical (TI) matrix kernel (i.e., K= T{K}), commutes with the transformation (T{.}) itself when they operate on the first operand matrix. We found that by consistently applying the same type of TI kernels in a convolutional neural networks (CNN) system, the commutative property holds throughout all layers of convolution processes with and without involving an activation function and/or a 1D convolution across channels within a layer. We further found that any CNN possessing the same TI kernel prope…
Ahsanullah University of Science and Technology（阿萨努拉科技大学）；Bangladesh University of Engineering and Technology（孟加拉国工程技术大学）
Recently, recognition of handwritten Bengali letters and digits have captured a lot of attention among the researchers of the AI community. In this work, we propose a Convolutional Neural Network (CNN) based object detection model which can recognize and evaluate handwritten Bengali mathematical expressions. This method is able to detect multiple Bengali digits and operators and locate their positions in the image. With that information, it is able to construct numbers from series of digits and perform mathematical operations on them. For the object detection task, the state-of-the-art YOLOv3 …
The success of deep convolutional neural network (CNN) in computer vision especially image classification problems requests a new information theory for function of image, instead of image itself. In this article, after establishing a deep mathematical connection between image classification problem and quantum spin model, we propose to use entanglement entropy, a generalization of classical Boltzmann-Shannon entropy, as a powerful tool to characterize the information needed for representation of general function of image. We prove that there is a sub-volume-law bound for entanglement entropy …
First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and Bölcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathematical framework for their analysis. Specifically, we establish deformation and translation sensitivity results of local and global nature, and we investigate how certain structural properties of the input signal are reflected in the corresponding feature vectors. Our theory applies…
Georgetown University Medical Center（乔治城大学医学中心）；Virginia Tech（弗吉尼亚理工大学）
Transformationally invariant processors constructed by transformed input vectors or operators have been suggested and applied to many applications. In this study, transformationally identical processing based on combining results of all sub-processes with corresponding transformations at one of the processing steps or at the beginning step were found to be equivalent for a given condition. This property can be applied to most convolutional neural network (CNN) systems. Specifically, a transformationally identical CNN can be constructed by arranging internally symmetric operations in parallel w…
Base and Exponent Prediction in Mathematical Expressions using Multi-Output CNN
Department of Electrical Engineering（电气工程系）；Delhi Technological University（德里技术大学）；Department of Information Technology（信息技术系）；School of Engineering and Technology（工程与技术学院）；DYPU；Department of Aerospace Engineering（航空航天工程系）；IIST（印度理工学院泰米尔纳德分校）
Twisted Convolutional Networks (TCNs): Enhancing Feature Interactions for Non-Spatial Data Classification
McCormick School of Engineering, Northwestern University（西北大学工程学院）；School of Mathematics, University of Science and Technology of China（中国科学技术大学数学系）；College of New Energy, Jingchu University of Technology（荆楚科技学院新能源学院）；Information Initiative Center, Hokkaido University（北海道大学信息初始化中心）；School of Computer Science and Artificial Intelligence, Wenzhou University（温州大学计算机科学与人工智能学院）
Beijing Normal University（北京师范大学）；Hong Kong Baptist University（香港浸会大学）
We use Deep Convolutional Neural Networks (DCNNs) for image segmentation problems. DCNNs can well extract the features from natural images. However, the classification functions in the existing network architecture of CNNs are simple and lack capabilities to handle important spatial information in a way that have been done for many well-known traditional variational models. Prior such as spatial regularity, volume prior and object shapes cannot be well handled by existing DCNNs. We propose a novel Soft Threshold Dynamics (STD) framework which can easily integrate many spatial priors of the cla…
Nanyang Technological University（南洋理工大学）；University of Southern California（南加州大学）
Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this study, we show that tensor networks can systematically partition structured data, e.g. color images, for distributed storage and communication in privacy-preserving manner. Leveraging the sea of big data and metadata privacy, empirical results show that neighbouring subtensors with implicit information stored in tensor network formats cannot be identified f…
Perceptual misalignment of texture representations in convolutional neural networks
Neuroscience area International School for Advanced Studies (SISSA) Trieste Italy（国际先进研究学院（SISSA）神经科学部，特里埃斯特，意大利）；Department of Mathematics Informatics and Geosciences Università degli Studi di Trieste Trieste Italy（特里埃斯特大学数学、信息学和地球科学系，特里埃斯特，意大利）；Department of Data Engineering Area Science Park Trieste Italy（数据工程系，Area Science Park，特里埃斯特，意大利）
KANICE: Kolmogorov-Arnold Networks with Interactive Convolutional Elements
the University of New Orleans（新奥尔良大学）；Naval Research Laboratory（美国海军研究实验室）；US Army Corps of Engineers, Engineer Research and Development Center（美国陆军工程兵团工程研究与发展中心）
Ecole Supérieure Polytechnique, Université cheikh Anta Diop（谢赫·安塔·迪奥普大学高等理工学院）；Institut national Supérieur de l’Education Populaire et du Sport, Université cheikh Anta Diop（谢赫·安塔·迪奥普大学国家高等民众教育与体育学院）；Faculté de Médecine, de Pharmacie et d’Odonto-Stomatologie, Université cheikh Anta Diop（谢赫·安塔·迪奥普大学医学、药学与牙科学院）
Identifying and characterizing the patient's blood samples is indispensable in diagnostics of malignance suspicious. A painstaking and sometimes subjective task is used in laboratories to manually classify white blood cells. Neural mathematical methods as deep learnings can be very useful in the automated recognition of blood cells. This study uses a particular type of deep learning i.e., convolutional neural networks (CNNs or ConvNets) for image recognition of the four (4) blood cell types (neutrophil, eosinophil, lymphocyte and monocyte) and to enable it to tag them employing a dataset of bl…
CSEM SA（瑞士电子与微技术中心）；Swiss Federal Institute of Technology, ETH Zurich（苏黎世联邦理工学院）；University of Bologna（博洛尼亚大学）
While the accuracy of convolutional neural networks has achieved vast improvements by introducing larger and deeper network architectures, also the memory footprint for storing their parameters and activations has increased. This trend especially challenges power- and resource-limited accelerator designs, which are often restricted to store all network data in on-chip memory to avoid interfacing energy-hungry external memories. Maximizing the network size that fits on a given accelerator thus requires to maximize its memory utilization. While the traditionally used ping-pong buffering techniqu…
DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）；University of Wisconsin Madison（威斯康星大学麦迪逊分校）
Automated anatomical labeling plays a vital role in coronary artery disease diagnosing procedure. The main challenge in this problem is the large individual variability inherited in human anatomy. Existing methods usually rely on the position information and the prior knowledge of the topology of the coronary artery tree, which may lead to unsatisfactory performance when the main branches are confusing. Motivated by the wide application of the graph neural network in structured data, in this paper, we propose a conditional partial-residual graph convolutional network (CPR-GCN), which takes bot…
Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems. However, it is still difficult to obtain coherent geometric view why such an architecture gives the desired performance. Inspired by recent theoretical understanding on generalizability, expressivity and optimization landscape of neural networks, as well as the theory of convolutional framelets, here we provide a unified theoretical framework that leads to a better understanding of geometry of en…
MathNet: A Data-Centric Approach for Printed Mathematical Expression Recognition
Institute of Computer Science, ZHAW（苏黎世应用科技大学计算机科学学院）；People and Computing Laboratory, University of Zurich（苏黎世大学人与计算实验室）；Centre for Artificial Intelligence, ZHAW（苏黎世应用科技大学人工智能中心）；European Centre for Living Technology (ECLT)（欧洲生命技术中心）
Georgia Tech（佐治亚理工学院）；Oregon State University（俄勒冈州立大学）
Deep learning's great success motivates many practitioners and students to learn about this exciting technology. However, it is often challenging for beginners to take their first step due to the complexity of understanding and applying deep learning. We present CNN Explainer, an interactive visualization tool designed for non-experts to learn and examine convolutional neural networks (CNNs), a foundational deep learning model architecture. Our tool addresses key challenges that novices face while learning about CNNs, which we identify from interviews with instructors and a survey with past st…
Northeast Yucai Foreign Language School（东北育才外国语学校）；Northwestern University（西北大学）；Shenyang Pharmaceutical University（沈阳药科大学）
Because of their abundance of amino acids, polysaccharides, and many other nutrients that benefit human beings, mushrooms are deservedly popular as dietary cuisine both worldwide and in China. However, if people eat poisonous fungi by mistake, they may suffer from nausea, vomiting, mental disorder, acute anemia, or even death. Each year in China, there are around 8000 people became sick, and 70 died as a result of eating toxic mushrooms by mistake. It is counted that there are thousands of kinds of mushrooms among which only around 900 types are edible, thus without specialized knowledge, the …
