Related papers: A Gradient Estimator for Time-Varying Electrical N…

In this work, we provide a non-asymptotic convergence analysis of projected gradient descent for physics-informed neural networks for the Poisson equation. Under suitable assumptions, we show that the optimization error can be bounded by…

In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

We report a learning rule for neural networks that computes how much each neuron should contribute to minimize a giving cost function via the estimation of its target value. By theoretical analysis, we show that this learning rule contains…

The existence of global weak solutions to a partial-differential-algebraic system is proved. The system consists of the drift-diffusion equations for the electron, hole, and oxide vacancy densities in a memristor device, the Poisson…

There is a growing attention given to utilizing Lagrangian and Hamiltonian mechanics with network training in order to incorporate physics into the network. Most commonly, conservative systems are modeled, in which there are no frictional…

With the increasing scale and dynamics of data, distributed online optimization has become essential for real-time decision-making in various applications. However, existing algorithms often rely on bounded gradient assumptions and overlook…

Particle-based approximate Bayesian inference approaches such as Stein Variational Gradient Descent (SVGD) combine the flexibility and convergence guarantees of sampling methods with the computational benefits of variational inference. In…

Pathophysiolpgical modelling of brain systems from microscale to macroscale remains difficult in group comparisons partly because of the infeasibility of modelling the interactions of thousands of neurons at the scales involved. Here, to…

How much can you say about the gradient of a neural network without computing a loss or knowing the label? This may sound like a strange question: surely the answer is "very little." However, in this paper, we show that gradients are more…

Saliency methods interpret the prediction of a neural network by showing the importance of input elements for that prediction. A popular family of saliency methods utilize gradient information. In this work, we empirically show that two…

We investigate a distributed optimization problem over a cooperative multi-agent time-varying network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…

Much of studies on neural computation are based on network models of static neurons that produce analog output, despite the fact that information processing in the brain is predominantly carried out by dynamic neurons that produce discrete…

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation…

We propose a general framework for computing Retarded Green's Functions (RGFs) on quantum computers by recasting their evaluation as a problem of circuit differentiation. Our proposal is based on real-time evolution and specifically…

The discrete gradient structure and the positive definiteness of discrete fractional integrals or derivatives are fundamental to the numerical stability in long-time simulation of nonlinear integro-differential models. We build up a…

Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to…

The Propagation-Separation approach is an iterative procedure for pointwise estimation of local constant and local polynomial functions. The estimator is defined as a weighted mean of the observations with data-driven weights. Within…

Our proposed framework attempts to break the trade-off between performance and explainability by introducing an explainable-by-design convolutional neural network (CNN) based on the lateral inhibition mechanism. The ExplaiNet model consists…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…