Related papers: Hybrid Iterative Neural Low-Regularity Integrator …

Whole slide image (WSI) analysis has become increasingly important in the medical imaging community, enabling automated and objective diagnosis, prognosis, and therapeutic-response prediction. However, in clinical practice, the…

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…

Spiking neural networks (SNNs) have received widespread attention as an ultra-low power computing paradigm. Recent studies have shown that SNNs suffer from severe overfitting, which limits their generalization performance. In this paper, we…

Reinforcement Learning (RL) for training Large Language Models is notoriously unstable. While recent studies attribute this to "training inference mismatch stemming" from inconsistent hybrid engines, standard remedies, such as Importance…

The Hirschfeld-Gebelein-R\'enyi (HGR) correlation coefficient is an extension of Pearson's correlation that is not limited to linear correlations, with potential applications in algorithmic fairness, scientific analysis, and causal…

Meta-learning that uses implicit gradient have provided an exciting alternative to standard techniques which depend on the trajectory of the inner loop training. Implicit meta-learning (IML), however, require computing $2^{nd}$ order…

Deep learning has demonstrated strong potential for MRI reconstruction. However, conventional supervised learning requires high-quality, high-SNR references for network training, which are often difficult or impossible to obtain in…

In this paper, we propose a learning-to-optimize (L2O) framework to accelerate solving parametric mixed-integer quadratic programming (MIQP) problems, with a particular focus on mixed-integer model predictive control (MI-MPC) applications.…

Training neural networks (NNs) using combinatorial optimization solvers has gained attention in recent years. In low-data settings, state-of-the-art mixed integer linear programming solvers can train exactly a NN, avoiding intensive…

We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…

Discovering a suitable neural network architecture for modeling complex dynamical systems poses a formidable challenge, often involving extensive trial and error and navigation through a high-dimensional hyper-parameter space. In this…

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…

Contemporary Low-Light Image Enhancement (LLIE) techniques have made notable advancements in preserving image details and enhancing contrast, achieving commendable results on specific datasets. Nevertheless, these approaches encounter…

This paper introduces a deep learning method for solving an elliptic hemivariational inequality (HVI). In this method, an expectation minimization problem is first formulated based on the variational principle of underlying HVI, which is…

We develop resonance-based low-regularity numerical integrators for stochastic Schr"odinger equations with additive $Q$-Wiener noise, covering both the linear equation with rough potential and the cubic nonlinear case. For the linear…

We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from…

Sampling the parameter space of artificial neural networks according to a Boltzmann distribution provides insight into the geometry of low-loss solutions and offers an alternative to conventional loss minimization for training. However,…

We present a new filtered low-regularity Fourier integrator for the cubic nonlinear Schr\"odinger equation based on recent time discretization and filtering techniques. For this new scheme, we perform a rigorous error analysis and establish…

Class-incremental learning (CIL) with Vision Transformers (ViTs) faces a major computational bottleneck during the classifier reconstruction phase, where most existing methods rely on costly iterative stochastic gradient descent (SGD). We…