Related papers: Mathematical Introduction to Deep Learning: Method…
These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…
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…
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom…
Deep learning (DL) is transforming industry as decision-making processes are being automated by deep neural networks (DNNs) trained on real-world data. Driven partly by rapidly-expanding literature on DNN approximation theory showing they…
In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…
In recent years, China, the United States and other countries, Google and other high-tech companies have increased investment in artificial intelligence. Deep learning is one of the current artificial intelligence research's key areas. This…
Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain…
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…
This survey provides an in-depth and explanatory review of the approximation properties of deep neural networks, with a focus on feed-forward and residual architectures. The primary objective is to examine how effectively neural networks…
Deep Learning optimization involves minimizing a high-dimensional loss function in the weight space which is often perceived as difficult due to its inherent difficulties such as saddle points, local minima, ill-conditioning of the Hessian…
Much of the present-day Artificial Intelligence (AI) utilizes artificial neural networks, which are sophisticated computational models designed to recognize patterns and solve complex problems by learning from data. However, a major…
Edge computing and artificial intelligence (AI), especially deep learning for nowadays, are gradually intersecting to build a novel system, called edge intelligence. However, the development of edge intelligence systems encounters some…
In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…
In this paper, we examine how deep learning can be utilized to investigate neural health and the difficulties in interpreting neurological analyses within algorithmic models. The key contribution of this paper is the investigation of the…
Artificial Neuronal Networks are models widely used for many scientific tasks. One of the well-known field of application is the approximation of high-dimensional problems via Deep Learning. In the present paper we investigate the Deep…
Deep learning based on artificial neural networks is a powerful machine learning method that, in the last few years, has been successfully used to realize tasks, e.g., image classification, speech recognition, translation of languages,…
Deep learning is pervasive in our daily life, including self-driving cars, virtual assistants, social network services, healthcare services, face recognition, etc. However, deep neural networks demand substantial compute resources during…
Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…
Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…
In this study, we explore the integration of Neural Networks, a powerful class of functions known for their exceptional approximation capabilities. Our primary emphasis is on the integration of multi-layer Neural Networks, a challenging…