Related papers: Standalone Neural ODEs with Sensitivity Analysis

Classical neural ODEs trained with explicit methods are intrinsically limited by stability, crippling their efficiency and robustness for stiff learning problems that are common in graph learning and scientific machine learning. We present…

Training deep neural network is a high dimensional and a highly non-convex optimization problem. Stochastic gradient descent (SGD) algorithm and it's variations are the current state-of-the-art solvers for this task. However, due to…

Large Eddy Simulations (LES) are becoming increasingly viable due to the growth in computational power the last few decades, and subgrid stress modelling plays a large role in the accuracy of LES. A new class of neural network models, S4…

Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…

Deep neural networks (DNNs) have achieved superior performance in various prediction tasks, but can be very vulnerable to adversarial examples or perturbations. Therefore, it is crucial to measure the sensitivity of DNNs to various forms of…

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known…

We propose a novel variant of SGD customized for training network architectures that support anytime behavior: such networks produce a series of increasingly accurate outputs over time. Efficient architectural designs for these networks…

Uncertainty quantification is a fundamental yet unsolved problem for deep learning. The Bayesian framework provides a principled way of uncertainty estimation but is often not scalable to modern deep neural nets (DNNs) that have a large…

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be highly non-convex. To understand the success of SGD for…

Spiking neural networks (SNNs) have gained prominence for their potential in neuromorphic computing and energy-efficient artificial intelligence, yet optimizing them remains a formidable challenge for gradient-based methods due to their…

Understanding the behavior of stochastic gradient methods is a central problem in modern machine learning. Recent work has highlighted diagonal linear networks as a simplified yet expressive setting for analyzing the optimization and…

We propose SDORE, a Semi-supervised Deep Sobolev Regressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm…

To better understand and improve the behavior of neural networks, a recent line of works bridged the connection between ordinary differential equations (ODEs) and deep neural networks (DNNs). The connections are made in two folds: (1) View…

In this paper, we propose Neumann Series Neural Operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential…

Pixel-wise prediction with deep neural network has become an effective paradigm for salient object detection (SOD) and achieved remarkable performance. However, very few SOD models are robust against adversarial attacks which are visually…

Deep neural networks (DNNs) must cater to a variety of users with different performance needs and budgets, leading to the costly practice of training, storing, and maintaining numerous user/task-specific models. There are solutions in the…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…

Mixed-signal neuromorphic processors provide extremely low-power operation for edge inference workloads, taking advantage of sparse asynchronous computation within Spiking Neural Networks (SNNs). However, deploying robust applications to…