Related papers: SigMA: Path Signatures and Multi-head Attention fo…
Rough path theory is focused on capturing and making precise the interactions between highly oscillatory and non-linear systems. It draws on the analysis of LC Young and the geometric algebra of KT Chen. The concepts and the uniform…
Benchmarking the performance of complex systems such as rail networks, renewable generation assets and national economies is central to transport planning, regulation and macroeconomic analysis. Classical frontier methods, notably Data…
Recurrent neural networks and Transformers have recently dominated most applications in hyperspectral (HS) imaging, owing to their capability to capture long-range dependencies from spectrum sequences. However, despite the success of these…
Stochastic integration w.r.t. fractional Brownian motion (fBm) has raised strong interest in recent years, motivated in particular by applications in finance and Internet traffic modelling. Since fBm is not a semi-martingale, stochastic…
Medical image analysis using deep learning is often challenged by limited labeled data and high annotation costs. Fine-tuning the entire network in label-limited scenarios can lead to overfitting and suboptimal performance. Recently, prompt…
Although softmax attention drives state-of-the-art performance for sequence models, its quadratic complexity limits scalability, motivating linear alternatives such as state space models (SSMs). While these alternatives improve efficiency,…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
Attention Mechanism is a widely used method for improving the performance of convolutional neural networks (CNNs) on computer vision tasks. Despite its pervasiveness, we have a poor understanding of what its effectiveness stems from. It is…
We study pathwise approximation of scalar stochastic differential equations at a single point. We provide the exact rate of convergence of the minimal errors that can be achieved by arbitrary numerical methods that are based (in a…
The $d$-dimensional fractional Brownian motion (FBM for short) $B_t=((B_t^{(1)},...,B_t^{(d)}),t\in\mathbb{R})$ with Hurst exponent $\alpha$, $\alpha\in(0,1)$, is a $d$-dimensional centered, self-similar Gaussian process with covariance…
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…
While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This…
Deep neural networks (DNNs) are increasingly used to solve partial differential equations (PDEs) that naturally arise while modeling a wide range of systems and physical phenomena. However, the accuracy of such DNNs decreases as the PDE…
In this paper, we present a new method, Transductive Multi-Head Few-Shot learning (TMHFS), to address the Cross-Domain Few-Shot Learning (CD-FSL) challenge. The TMHFS method extends the Meta-Confidence Transduction (MCT) and Dense…
Machine Learning algorithms based on Brain-inspired Hyperdimensional(HD) computing imitate cognition by exploiting statistical properties of high-dimensional vector spaces. It is a promising solution for achieving high energy efficiency in…
Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…
To support mechanism online learning and facilitate digital twin development for biomanufacturing processes, this paper develops an efficient Bayesian inference approach for partially observed enzymatic stochastic reaction network (SRN), a…
Spatial transcriptomics (ST) technologies enable gene expression profiling with spatial resolution, offering unprecedented insights into tissue organization and disease heterogeneity. However, current analysis methods often struggle with…
The self-attention mechanism has emerged as a critical component for improving the performance of various backbone neural networks. However, current mainstream approaches individually incorporate newly designed self-attention modules (SAMs)…
Early detection and accurate diagnosis are essential to improving patient outcomes. The use of convolutional neural networks (CNNs) for tumor detection has shown promise, but existing models often suffer from overparameterization, which…