The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks (PINNs). For an accurate representation of the field variables, a multi-objective loss function is proposed. It consists of terms corresponding to the residual of the governing partial differential equations (PDE), constitutive relations derived from the governing physics, various boundary conditions, and data-driven physical knowledge fitting terms across randomly selected collocation points in the problem domain. To this end, multiple densely connected independent artificial neural networks (ANNs), each approximating a field variable, are trained to obtain accurate solutions. Several benchmark problems including the Airy solution to elasticity and the Kirchhoff-Love plate problem are solved. Performance in terms of accuracy and robustness illustrates the superiority of the current framework showing excellent agreement with analytical solutions. The present work combines the benefits of the classical methods depending on the physical information available in analytical relations with the superior capabilities of the DL techniques in the data-driven construction of lightweight, yet accurate and robust neural networks. The models developed herein can significantly boost computational speed using minimal network parameters with easy adaptability in different computational platforms.
Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed, different sources of predictive uncertainty cannot be distinguished properly. We present Credal Bayesian Deep Learning (CBDL). Heuristically, CBDL allows to train an (uncountably) infinite ensemble of BNNs, using only finitely many elements. This is possible thanks to prior and likelihood finitely generated credal sets (FGCSs), a concept from the imprecise probability literature. Intuitively, convex combinations of a finite collection of prior-likelihood pairs are able to represent infinitely many such pairs. After training, CBDL outputs a set of posteriors on the parameters of the neural network. At inference time, such posterior set is used to derive a set of predictive distributions that is in turn utilized to distinguish between (predictive) aleatoric and epistemic uncertainties, and to quantify them. The predictive set also produces either (i) a collection of outputs enjoying desirable probabilistic guarantees, or (ii) the single output that is deemed the best, that is, the one having the highest predictive lower probability -- another imprecise-probabilistic concept. CBDL is more robust than single BNNs to prior and likelihood misspecification, and to distribution shift. We show that CBDL is better at quantifying and disentangling different types of (predictive) uncertainties than single BNNs and ensemble of BNNs. In addition, we apply CBDL to two case studies to demonstrate its downstream tasks capabilities: one, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. We show that CBDL performs better when compared to an ensemble of BNNs baseline.
In recent years, deep learning has achieved remarkable success in various fields such as image recognition, natural language processing, and speech recognition. The effectiveness of deep learning largely depends on the optimization methods used to train deep neural networks. In this paper, we provide an overview of first-order optimization methods such as Stochastic Gradient Descent, Adagrad, Adadelta, and RMSprop, as well as recent momentum-based and adaptive gradient methods such as Nesterov accelerated gradient, Adam, Nadam, AdaMax, and AMSGrad. We also discuss the challenges associated with optimization in deep learning and explore techniques for addressing these challenges, including weight initialization, batch normalization, and layer normalization. Finally, we provide recommendations for selecting optimization methods for different deep learning tasks and datasets. This paper serves as a comprehensive guide to optimization methods in deep learning and can be used as a reference for researchers and practitioners in the field.
We consider the problem of simultaneously approximating the conditional distribution of market prices and their log returns with a single machine learning model. We show that an instance of the GDN model of Kratsios and Papon (2022) solves this problem without having prior assumptions on the market's "clipped" log returns, other than that they follow a generalized Ornstein-Uhlenbeck process with a priori unknown dynamics. We provide universal approximation guarantees for these conditional distributions and contingent claims with a Lipschitz payoff function.
In this technical report we compare different deep learning models for prediction of water depth rasters at high spatial resolution. Efficient, accurate, and fast methods for water depth prediction are nowadays important as urban floods are increasing due to higher rainfall intensity caused by climate change, expansion of cities and changes in land use. While hydrodynamic models models can provide reliable forecasts by simulating water depth at every location of a catchment, they also have a high computational burden which jeopardizes their application to real-time prediction in large urban areas at high spatial resolution. Here, we propose to address this issue by using data-driven techniques. Specifically, we evaluate deep learning models which are trained to reproduce the data simulated by the CADDIES cellular-automata flood model, providing flood forecasts that can occur at different future time horizons. The advantage of using such models is that they can learn the underlying physical phenomena a priori, preventing manual parameter setting and computational burden. We perform experiments on a dataset consisting of two catchments areas within Switzerland with 18 simpler, short rainfall patterns and 4 long, more complex ones. Our results show that the deep learning models present in general lower errors compared to the other methods, especially for water depths $>0.5m$. However, when testing on more complex rainfall events or unseen catchment areas, the deep models do not show benefits over the simpler ones.
Skin cancer is the most common type of cancer. Specifically, melanoma is the cause of 75% of skin cancer deaths, although it is the least common skin cancer. Better detection of melanoma could have a positive impact on millions of people. The ISIC archive contains the largest publicly available collection of dermatoscopic images of skin lesions. In this research, we investigate the efficacy of applying advanced deep learning techniques in computer vision to identify melanoma in images of skin lesions. Through reviewing previous methods, including pre-trained models, deep-learning classifiers, transfer learning, etc., we demonstrate the applicability of the popular deep learning methods on critical clinical problems such as identifying melanoma. Finally, we proposed a processing flow with a validation AUC greater than 94% and a sensitivity greater than 90% on ISIC 2016 - 2020 datasets.
Introduction: Multiple Sclerosis (MS) is a chronic disease that affects millions of people across the globe. MS can critically affect different organs of the central nervous system such as the eyes, the spinal cord, and the brain. Background: To help physicians in diagnosing MS lesions, computer-aided methods are widely used. In this regard, a considerable research has been carried out in the area of automatic detection and segmentation of MS lesions in magnetic resonance images (MRIs). Methodology: In this study, we review the different approaches that have been used in computer-aided detection and segmentation of MS lesions. Our review resulted in categorizing MS lesion segmentation approaches into six broad categories: data-driven, statistical, supervised machine learning, unsupervised machine learning, fuzzy, and deep learning-based techniques. We critically analyze the different techniques under these approaches and highlight their strengths and weaknesses. Results: From the study, we observe that a considerable amount of work, around 25% of related literature, is focused on statistical-based MS lesion segmentation techniques, followed by 21.15% for data-driven based methods, 19.23% for deep learning and 15.38% for supervised methods. Implication: The study points out the challenges/gaps to be addressed in future research. The study shows the work which has been done in last one decade in detection and segmentation of MS lesions. The results show that, in recent years, deep learning methods are outperforming all the others methods.
Deep learning is becoming increasingly adopted in business and industry due to its ability to transform large quantities of data into high-performing models. These models, however, are generally regarded as black boxes, which, in spite of their performance, could prevent their use. In this context, the field of eXplainable AI attempts to develop techniques that temper the impenetrable nature of the models and promote a level of understanding of their behavior. Here we present our contribution to XAI methods in the form of a framework that we term SpecXAI, which is based on the spectral characterization of the entire network. We show how this framework can be used to not only understand the network but also manipulate it into a linear interpretable symbolic representation.
We propose a non-representationalist framework for deep learning relying on a novel method: computational phenomenology, a dialogue between the first-person perspective (relying on phenomenology) and the mechanisms of computational models. We thereby reject the modern cognitivist interpretation of deep learning, according to which artificial neural networks encode representations of external entities. This interpretation mainly relies on neuro-representationalism, a position that combines a strong ontological commitment towards scientific theoretical entities and the idea that the brain operates on symbolic representations of these entities. We proceed as follows: after offering a review of cognitivism and neuro-representationalism in the field of deep learning, we first elaborate a phenomenological critique of these positions; we then sketch out computational phenomenology and distinguish it from existing alternatives; finally we apply this new method to deep learning models trained on specific tasks, in order to formulate a conceptual framework of deep-learning, that allows one to think of artificial neural networks' mechanisms in terms of lived experience.
Several websites improve their security and avoid dangerous Internet attacks by implementing CAPTCHAs (Completely Automated Public Turing test to tell Computers and Humans Apart), a type of verification to identify whether the end-user is human or a robot. The most prevalent type of CAPTCHA is text-based, designed to be easily recognized by humans while being unsolvable towards machines or robots. However, as deep learning technology progresses, development of convolutional neural network (CNN) models that predict text-based CAPTCHAs becomes easier. The purpose of this research is to investigate the flaws and vulnerabilities in the CAPTCHA generating systems in order to design more resilient CAPTCHAs. To achieve this, we created CapNet, a Convolutional Neural Network. The proposed platform can evaluate both numerical and alphanumerical CAPTCHAs
We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) preserve geometric features on manifolds by utilizing an equivariant embedding from the manifold to its image in the Euclidean space. Moreover, intrinsic deep neural networks (iDNNs) incorporate the underlying intrinsic geometry of manifolds via exponential and log maps with respect to a Riemannian structure. Consequently, we prove that the empirical risk of the empirical risk minimizers (ERM) of eDNNs and iDNNs converge in optimal rates. Overall, The eDNNs framework is simple and easy to compute, while the iDNNs framework is accurate and fast converging. To demonstrate the utilities of our framework, various simulation studies, and real data analyses are presented with eDNNs and iDNNs.
Event cameras are bio-inspired sensors that capture the per-pixel intensity changes asynchronously and produce event streams encoding the time, pixel position, and polarity (sign) of the intensity changes. Event cameras possess a myriad of advantages over canonical frame-based cameras, such as high temporal resolution, high dynamic range, low latency, etc. Being capable of capturing information in challenging visual conditions, event cameras have the potential to overcome the limitations of frame-based cameras in the computer vision and robotics community. In very recent years, deep learning (DL) has been brought to this emerging field and inspired active research endeavors in mining its potential. However, there is still a lack of taxonomies in DL techniques for event-based vision. We first scrutinize the typical event representations with quality enhancement methods as they play a pivotal role as inputs to the DL models. We then provide a comprehensive survey of existing DL-based methods by structurally grouping them into two major categories: 1) image/video reconstruction and restoration; 2) event-based scene understanding and 3D vision. We conduct benchmark experiments for the existing methods in some representative research directions, i.e., image reconstruction, deblurring, and object recognition, to identify some critical insights and problems. Finally, we have discussions regarding the challenges and provide new perspectives for inspiring more research studies.
Deep neural networks (DNNs) are the de facto standard for essential use cases, such as image classification, computer vision, and natural language processing. As DNNs and datasets get larger, they require distributed training on increasingly larger clusters. A main bottleneck is the resulting communication overhead where workers exchange model updates (i.e., gradients) on a per-round basis. To address this bottleneck and accelerate training, a widely-deployed approach is compression. However, previous deployments often apply bi-directional compression schemes by simply using a uni-directional gradient compression scheme in each direction. This results in significant computational overheads at the parameter server and increased compression error, leading to longer training and lower accuracy. We introduce Tensor Homomorphic Compression (THC), a novel bi-directional compression framework that enables the direct aggregation of compressed values and thus eliminating the aforementioned computational overheads. Moreover, THC is compatible with in-network aggregation (INA), which allows for further acceleration. Our evaluation shows that training representative vision and language models with THC reaches target accuracy by 1.40x to 1.47x faster using INA and 1.28x to 1.33x faster using a software PS compared with state-of-the-art systems.
Handwritten digit recognition is a basic and important problem in computer vision. While it has been studied intensively, the newer datasets keep bring new challenges to existed solutions. A new Kannada-MNIST dataset is mainly digital images of the Kannada language, which contains 70,000 28×28 gray-scale sample images and 10 classes. It also contains a Dig-MNIST dataset, which is an out-of domain test sample dataset and a more challenging test dataset for recognition. In this paper, we evaluate the state-of-art deep learning models for Kannada-MNIST and improve their performance with data augmentation and transfer learning techniques. We manage to achieve a best accuracy of 90.27% for Dig-MNIST in the literature with Inception Model.
We propose a new approach to volatility modeling by combining deep learning (LSTM) and realized volatility measures. This LSTM-enhanced realized GARCH framework incorporates and distills modeling advances from financial econometrics, high frequency trading data and deep learning. Bayesian inference via the Sequential Monte Carlo method is employed for statistical inference and forecasting. The new framework can jointly model the returns and realized volatility measures, has an excellent in-sample fit and superior predictive performance compared to several benchmark models, while being able to adapt well to the stylized facts in volatility. The performance of the new framework is tested using a wide range of metrics, from marginal likelihood, volatility forecasting, to tail risk forecasting and option pricing. We report on a comprehensive empirical study using 31 widely traded stock indices over a time period that includes COVID-19 pandemic.
Technological advances have enabled the generation of unique and complementary types of data or views (e.g. genomics, proteomics, metabolomics) and opened up a new era in multiview learning research with the potential to lead to new biomedical discoveries. We propose iDeepViewLearn (Interpretable Deep Learning Method for Multiview Learning) for learning nonlinear relationships in data from multiple views while achieving feature selection. iDeepViewLearn combines deep learning flexibility with the statistical benefits of data and knowledge-driven feature selection, giving interpretable results. Deep neural networks are used to learn view-independent low-dimensional embedding through an optimization problem that minimizes the difference between observed and reconstructed data, while imposing a regularization penalty on the reconstructed data. The normalized Laplacian of a graph is used to model bilateral relationships between variables in each view, therefore, encouraging selection of related variables. iDeepViewLearn is tested on simulated and two real-world data, including breast cancer-related gene expression and methylation data. iDeepViewLearn had competitive classification results and identified genes and CpG sites that differentiated between individuals who died from breast cancer and those who did not. The results of our real data application and simulations with small to moderate sample sizes suggest that iDeepViewLearn may be a useful method for small-sample-size problems compared to other deep learning methods for multiview learning.
The use of AI systems in healthcare for the early screening of diseases is of great clinical importance. Deep learning has shown great promise in medical imaging, but the reliability and trustworthiness of AI systems limit their deployment in real clinical scenes, where patient safety is at stake. Uncertainty estimation plays a pivotal role in producing a confidence evaluation along with the prediction of the deep model. This is particularly important in medical imaging, where the uncertainty in the model's predictions can be used to identify areas of concern or to provide additional information to the clinician. In this paper, we review the various types of uncertainty in deep learning, including aleatoric uncertainty and epistemic uncertainty. We further discuss how they can be estimated in medical imaging. More importantly, we review recent advances in deep learning models that incorporate uncertainty estimation in medical imaging. Finally, we discuss the challenges and future directions in uncertainty estimation in deep learning for medical imaging. We hope this review will ignite further interest in the community and provide researchers with an up-to-date reference regarding applications of uncertainty estimation models in medical imaging.
Biogenic Volatile Organic Compounds (BVOCs) play a critical role in biosphere-atmosphere interactions, being a key factor in the physical and chemical properties of the atmosphere and climate. Acquiring large and fine-grained BVOC emission maps is expensive and time-consuming, so most available BVOC data are obtained on a loose and sparse sampling grid or on small regions. However, high-resolution BVOC data are desirable in many applications, such as air quality, atmospheric chemistry, and climate monitoring. In this work, we investigate the possibility of enhancing BVOC acquisitions, further explaining the relationships between the environment and these compounds. We do so by comparing the performances of several state-of-the-art neural networks proposed for image Super-Resolution (SR), adapting them to overcome the challenges posed by the large dynamic range of the emission and reduce the impact of outliers in the prediction. Moreover, we also consider realistic scenarios, considering both temporal and geographical constraints. Finally, we present possible future developments regarding SR generalization, considering the scale-invariance property and super-resolving emissions from unseen compounds.
Deep learning based on unrolled algorithm has served as an effective method for accelerated magnetic resonance imaging (MRI). However, many methods ignore the direct use of edge information to assist MRI reconstruction. In this work, we present the edge-weighted pFISTA-Net that directly applies the detected edge map to the soft-thresholding part of pFISTA-Net. The soft-thresholding value of different regions will be adjusted according to the edge map. Experimental results of a public brain dataset show that the proposed yields reconstructions with lower error and better artifact suppression compared with the state-of-the-art deep learning-based methods. The edge-weighted pFISTA-Net also shows robustness for different undersampling masks and edge detection operators. In addition, we extend the edge weighted structure to joint reconstruction and segmentation network and obtain improved reconstruction performance and more accurate segmentation results.
This paper considers deep neural networks for learning weakly dependent processes in a general framework that includes, for instance, regression estimation, time series prediction, time series classification. The $\psi$-weak dependence structure considered is quite large and covers other conditions such as mixing, association,$\ldots$ Firstly, the approximation of smooth functions by deep neural networks with a broad class of activation functions is considered. We derive the required depth, width and sparsity of a deep neural network to approximate any H\"{o}lder smooth function, defined on any compact set $\mx$. Secondly, we establish a bound of the excess risk for the learning of weakly dependent observations by deep neural networks. When the target function is sufficiently smooth, this bound is close to the usual $\mathcal{O}(n^{-1/2})$.