Related papers: FC2T2: The Fast Continuous Convolutional Taylor Tr…

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…

We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…

Transposed Convolutions (TCONV) enable the up-scaling mechanism within generative Artificial Intelligence (AI) models. However, the predominant Input-Oriented Mapping (IOM) method for implementing TCONV has complex output mapping,…

Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in error correction coding. Hence, reducing the computational complexities of DFTs is of great significance, especially for long DFTs as increasingly longer…

This paper presents a comprehensive exploration of Fast Fourier Transform (FFT) and linear convolution implementations, integrating both conventional methods and novel approaches leveraging the Bit Slicing Multiplier (BSM) technique. The…

At the CMS experiment, a growing reliance on the fast Monte Carlo application (FastSim) will accompany the high luminosity and detector granularity expected in Phase 2. The FastSim chain is roughly 10 times faster than the application based…

Retrieving object phase from the optical fringe pattern is a critical task in quantitative phase imaging and often requires appropriate image preprocessing (background and noise minimization), especially when retrieving phase from the…

Most existing methods for depth estimation from a focal stack of images employ convolutional neural networks (CNNs) using 2D or 3D convolutions over a fixed set of images. However, their effectiveness is constrained by the local properties…

Deep learning provides a new avenue for image restoration, which demands a delicate balance between fine-grained details and high-level contextualized information during recovering the latent clear image. In practice, however, existing…

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…

Continual learning aims to alleviate catastrophic forgetting when handling consecutive tasks under non-stationary distributions. Gradient-based meta-learning algorithms have shown the capability to implicitly solve the transfer-interference…

Function regression/approximation is a fundamental application of machine learning. Neural networks (NNs) can be easily trained for function regression using a sufficient number of neurons and epochs. The forward-forward learning algorithm…

Convolutions are one of the most relevant operations in artificial intelligence (AI) systems. High computational complexity scaling poses significant challenges, especially in fast-responding network-edge AI applications. Fortunately, the…

Despite its success in image synthesis, we observe that diffusion probabilistic models (DPMs) often lack contextual reasoning ability to learn the relations among object parts in an image, leading to a slow learning process. To solve this…

Feature Transformation (FT) crafts new features from original ones via mathematical operations to enhance dataset expressiveness for downstream models. However, existing FT methods exhibit critical limitations: discrete search struggles…

This paper studies the problem of sampling vector and tensor signals, which is the process of choosing sites in vectors and tensors to place sensors for better recovery. A small core tensor and multiple factor matrices can be used to…

Computer vision is difficult, partly because the desired mathematical function connecting input and output data is often complex, fuzzy and thus hard to learn. Coarse-to-fine (C2F) learning is a promising direction, but it remains unclear…

The technologically-relevant task of feature extraction from data performed in deep-learning systems is routinely accomplished as repeated fast Fourier transforms (FFT) electronically in prevalent domain-specific architectures such as in…

Similarity analysis using neural networks has emerged as a powerful technique for understanding and categorizing complex patterns in various domains. By leveraging the latent representations learned by neural networks, data objects such as…

Within the world of machine learning there exists a wide range of different methods with respective advantages and applications. This paper seeks to present and discuss one such method, namely Convolutional Neural Networks (CNNs). CNNs are…