Related papers: MixFunn: A Neural Network for Differential Equatio…

In this paper, we introduce a novel deep learning framework, termed Purine. In Purine, a deep network is expressed as a bipartite graph (bi-graph), which is composed of interconnected operators and data tensors. With the bi-graph…

We present a Fourier neural network (FNN) that can be mapped directly to the Fourier decomposition. The choice of activation and loss function yields results that replicate a Fourier series expansion closely while preserving a…

In traditional software programs, it is easy to trace program logic from variables back to input, apply assertion statements to block erroneous behavior, and compose programs together. Although deep learning programs have demonstrated…

In this paper, we propose a novel design, called MixNN, for protecting deep learning model structure and parameters. The layers in a deep learning model of MixNN are fully decentralized. It hides communication address, layer parameters and…

Convolutional Neural Networks (CNNs) have achieved remarkable success across a wide range of machine learning tasks by leveraging hierarchical feature learning through deep architectures. However, the large number of layers and millions of…

Deep neural networks are highly expressive models that have recently achieved state of the art performance on speech and visual recognition tasks. While their expressiveness is the reason they succeed, it also causes them to learn…

Despite a lack of theoretical understanding, deep neural networks have achieved unparalleled performance in a wide range of applications. On the other hand, shallow representation learning with component analysis is associated with rich…

Predicting multiple real-world tasks in a single model often requires a particularly diverse feature space. Multimodal (MM) models aim to extract the synergistic predictive potential of multiple data types to create a shared feature space…

Image decomposition aims to analyze an image into elementary components, which is essential for numerous downstream tasks and also by nature provides certain interpretability to the analysis. Deep learning can be powerful for such tasks,…

Diffractive neural network (DNN), which can perform machine learning tasks based on the light propagation and diffraction, has recently emerged as a promising optical computing paradigm due to its high parallel processing speed and low…

Deploying deep learning models on mobile devices draws more and more attention recently. However, designing an efficient inference engine on devices is under the great challenges of model compatibility, device diversity, and resource…

The layered structure of deep neural networks hinders the use of numerous analysis tools and thus the development of its interpretability. Inspired by the success of functional brain networks, we propose a novel framework for…

Structured neuron encapsulation introduces a modular framework that enables more effective aggregation and specialization of information within deep learning architectures. A model modified through this framework demonstrated improved…

Physics-informed neural networks (PINNs) have been widely applied in different fields due to their effectiveness in solving partial differential equations (PDEs). However, the accuracy and efficiency of PINNs need to be considerably…

In this paper we use deep feedforward artificial neural networks to approximate solutions to partial differential equations in complex geometries. We show how to modify the backpropagation algorithm to compute the partial derivatives of the…

Fully connected multilayer perceptrons are used for obtaining numerical solutions of partial differential equations in various dimensions. Independent variables are fed into the input layer, and the output is considered as solution's value.…

Physics-Informed Neural Networks (PINNs) have advanced the data-driven solution of differential equations (DEs) in dynamic physical systems, yet challenges remain in explainability, scalability, and architectural complexity. This paper…

With the advent of deep learning, progressively larger neural networks have been designed to solve complex tasks. We take advantage of these capacity-rich models to lower the cost of inference by exploiting computation in superposition. To…

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions…