相关论文: FAN: Fourier Analysis Networks

As function approximators, deep neural networks have served as an effective tool to represent various signal types. Recent approaches utilize multi-layer perceptrons (MLPs) to learn a nonlinear mapping from a coordinate to its corresponding…

The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…

This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…

We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) -- DNNs often fit target functions from low to high frequencies -- on…

Deep neural networks can struggle to learn continually in the face of non-stationarity. This phenomenon is known as loss of plasticity. In this paper, we identify underlying principles that lead to plastic algorithms. In particular, we…

Fourier Analysis Network (FAN) was recently proposed as a simple way to improve neural network performance by replacing part of Rectified Linear Unit (ReLU) activations with sine and cosine functions. Although several studies have reported…

Modern deep neural networks suffer from performance degradation when evaluated on testing data under different distributions from training data. Domain generalization aims at tackling this problem by learning transferable knowledge from…

Machine learning applied to computer vision and signal processing is achieving results comparable to the human brain on specific tasks due to the great improvements brought by the deep neural networks (DNN). The majority of state-of-the-art…

A neural network is essentially a high-dimensional complex mapping model by adjusting network weights for feature fitting. However, the spectral bias in network training leads to unbearable training epochs for fitting the high-frequency…

This study presents a novel time series prediction model, FPN-fusion, designed with linear computational complexity, demonstrating superior predictive performance compared to DLiner without increasing parameter count or computational…

The enormous energy demand of artificial intelligence is driving the development of alternative hardware for deep learning. Physical neural networks try to exploit physical systems to perform machine learning more efficiently. In…

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…

Non-stationarity is a fundamental challenge in multivariate long-term time series forecasting, often manifested as rapid changes in amplitude and phase. These variations lead to severe distribution shifts and consequently degrade predictive…

Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both to accelerate…

Optimal Power Flow (OPF) is a fundamental problem in power systems. It is computationally challenging and a recent line of research has proposed the use of Deep Neural Networks (DNNs) to find OPF approximations at vastly reduced runtimes…

Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic…

Time series forecasting has important applications in financial analysis, weather forecasting, and traffic management. However, existing deep learning models are limited in processing non-stationary time series data because they cannot…

It is challenging to reduce the complexity of neural networks while maintaining their generalization ability and robustness, especially for practical applications. Conventional solutions for this problem incorporate quantum-inspired neural…

Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…

Function plays an important role in mathematics and many science branches. As the fast development of computer technology, more and more study on computational function analysis, e.g., Fast Fourier Transform, Wavelet Transform, Curve…