Related papers: Fixed Integral Neural Networks

In this paper, we propose a constrained linear data-feature mapping model as an interpretable mathematical model for image classification using convolutional neural network (CNN) such as the ResNet. From this viewpoint, we establish the…

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of…

Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…

There exist many problem domains where the interpretability of neural network models is essential for deployment. Here we introduce a recurrent architecture composed of input-switched affine transformations - in other words an RNN without…

Graph neural networks (GNNs) are the predominant approach for graph-based machine learning. While neural networks have shown great performance at learning useful representations, they are often criticized for their limited high-level…

The explainable artificial intelligence is used to analyze the stochastic Fredholm integral equations (SFIEs) and stochastic deep neural networks (SDNNs). The neural operator-based stochastic fixed point framework is used to develop SDNNs.…

We present a novel approach to hard-constrain Neumann boundary conditions in physics-informed neural networks (PINNs) using Fourier feature embeddings. Neumann boundary conditions are used to described critical processes in various…

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Implicit Neural Representations (INRs) are powerful to parameterize continuous signals in computer vision. However, almost all INRs methods are limited to low-level tasks, e.g., image/video compression, super-resolution, and image…

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…

Radiation heat transfer in a graded-index medium often suffers accuracy problems due to the gradual changes in the refractive index. The finite element method, meshfree, and other numerical methods often struggle to maintain accuracy when…

Deep neural networks (DNNs) have transformed fields such as computer vision and natural language processing by employing architectures aligned with domain-specific structural patterns. In algorithmic trading, however, there remains a lack…

Deep neural networks have seen enormous success in various real-world applications. Beyond their predictions as point estimates, increasing attention has been focused on quantifying the uncertainty of their predictions. In this review, we…

Deep learning refers to the shining branch of machine learning that is based on learning levels of representations. Convolutional Neural Networks (CNN) is one kind of deep neural network. It can study concurrently. In this article, we gave…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend…

Functional near-infrared spectroscopy (fNIRS) is a non-invasive technique for monitoring brain activity. To better understand the brain, researchers often use deep learning to address the classification challenges of fNIRS data. Our study…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

Deep learning has arguably achieved tremendous success in recent years. In simple words, deep learning uses the composition of many nonlinear functions to model the complex dependency between input features and labels. While neural networks…