Related papers: Convolution theorems for the free metaplectic tran…

We introduce the Latent Fourier Transform (LatentFT), a framework that provides novel frequency-domain controls for generative music models. LatentFT combines a diffusion autoencoder with a latent-space Fourier transform to separate musical…

Convolutional Neural Networks (CNNs) have become the state-of-the-art in supervised learning vision tasks. Their convolutional filters are of paramount importance for they allow to learn patterns while disregarding their locations in input…

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…

Convolutional neural networks (CNNs) have achieved state-of-the-art results on many visual recognition tasks. However, current CNN models still exhibit a poor ability to be invariant to spatial transformations of images. Intuitively, with…

The study of neural networks from the perspective of Fourier features has garnered significant attention. While existing analytical research suggests that neural networks tend to learn low-frequency features, a clear attribution method for…

This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…

Convolution is an integral operation that defines how the shape of one function is modified by another function. This powerful concept forms the basis of hierarchical feature learning in deep neural networks. Although performing convolution…

We construct a phenomenological conformal field theory (CFT) model of the three-dimensional Hawking-Page transition. We find that free fermion CFT models on the boundary torus give a description of the three-dimensional Hawking-Page…

Image matching that finding robust and accurate correspondences across images is a challenging task under extreme conditions. Capturing local and global features simultaneously is an important way to mitigate such an issue but recent…

In the paper it is shown that there exist infinite classes of fast DFT algorithms having multiplicative complexity lower than O(NlogN), i.e. smaller than their arithmetical complexity. The derivation starts with nesting of Discrete Fourier…

Finding semantic correspondences is a challenging problem. With the breakthrough of CNNs stronger features are available for tasks like classification but not specifically for the requirements of semantic matching. In the following we…

Following the traditional paradigm of convolutional neural networks (CNNs), modern CNNs manage to keep pace with more recent, for example transformer-based, models by not only increasing model depth and width but also the kernel size. This…

In parallel with the success of CNNs to solve vision problems, there is a growing interest in developing methodologies to understand and visualize the internal representations of these networks. How the responses of a trained CNN encode the…

The conventional Cohen's distribution can't meet the requirement of additive noises jamming signals high-performance denoising under the condition of low signal-to-noise ratio, it is necessary to integrate the metaplectic transform for…

Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…

Expanding the receptive field to capture large-scale context is key to obtaining good performance in dense prediction tasks, such as human pose estimation. While many state-of-the-art fully-convolutional architectures enlarge the receptive…

We introduce the notion of a conditionally free product and conditionally free convolution. We describe this convolution both from a combinatorial point of view, by showing its connection with the lattice of non-crossing partitions, and…

In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…

In this paper, we propose a new convolutional layer called Depthwise-STFT Separable layer that can serve as an alternative to the standard depthwise separable convolutional layer. The construction of the proposed layer is inspired by the…

This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between…