Related papers: Fourier Series Expansion Based Filter Parametrizat…
Recent advances in vision foundation models have revolutionized geometry reconstruction and semantic understanding. Yet, most of the existing approaches treat these capabilities in isolation, leading to redundant pipelines and compounded…
In this paper we show an alternative way of defining Fourier Series and Transform by using the concept of convolution with exponential signals. This approach has the advantage of simplifying proofs of transforms properties and, in our view,…
Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT),…
Series expansions have been a cornerstone of applied mathematics and engineering for centuries. In this paper, we revisit the Taylor series expansion from a modern Machine Learning perspective. Specifically, we introduce the Fast Continuous…
Deep Learning-based Computer Vision field has recently been trying to explore larger kernels for convolution to effectively scale up Convolutional Neural Networks. Simultaneously, new paradigm of models such as Vision Transformers find it…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
Convolution has been the core ingredient of modern neural networks, triggering the surge of deep learning in vision. In this work, we rethink the inherent principles of standard convolution for vision tasks, specifically spatial-agnostic…
Existing convolutional neural networks widely adopt spatial down-/up-sampling for multi-scale modeling. However, spatial up-sampling operators (\emph{e.g.}, interpolation, transposed convolution, and un-pooling) heavily depend on local…
Recently, 2D convolution has been found unqualified in sound event detection (SED). It enforces translation equivariance on sound events along frequency axis, which is not a shift-invariant dimension. To address this issue, dynamic…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
In object recognition, Fisher vector (FV) representation is one of the state-of-art image representations ways at the expense of dense, high dimensional features and increased computation time. A simplification of FV is attractive, so we…
Computational Fluid Dynamics (CFD) is crucial for automotive design, requiring the analysis of large 3D point clouds to study how vehicle geometry affects pressure fields and drag forces. However, existing deep learning approaches for CFD…
With the rapid development of information technology, "information overload" has become the main theme that plagues people's online life. As an effective tool to help users quickly search for useful information, a personalized…
Fourier extension is an approximation method that alleviates the periodicity requirements of Fourier series and avoids the Gibbs phenomenon when approximating functions. We describe a similar extension approach using regular wavelet bases…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
Deep learning methods are powerful tools but often suffer from expensive computation and limited flexibility. An alternative is to combine light-weight models with deep representations. As successful cases exist in several visual problems,…
Convolutional Neural Networks (CNNs) have achieved state-of-the-art performance in many computer vision tasks over the years. However, this comes at the cost of heavy computation and memory intensive network designs, suggesting potential…
Convolutional neural network (CNN)-based filters have achieved great success in video coding. However, in most previous works, individual models are needed for each quantization parameter (QP) band. This paper presents a generic method to…
Hyperspectral image classification (HSIC) has been significantly advanced by deep learning methods that exploit rich spatial-spectral correlations. However, existing approaches still face fundamental limitations: transformer-based models…
Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…