Related papers: Geometric Integration for Neural Control Variates

Graph Neural Networks (GNNs) have become a dominant approach to learning graph representations, primarily because of their message-passing mechanisms. However, GNNs typically adopt a fixed aggregator function such as Mean, Max, or Sum…

In financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of…

Multilayer perceptron (MLP) is a class of networks composed of multiple layers of perceptrons, and it is essentially a mathematical function. Based on MLP, we develop a new numerical method to find the extrema of functionals. As…

This paper investigates a class of algorithms for numerical integration of a function in d dimensions over a compact domain by Monte Carlo methods. We construct a histogram approximation to the function using a partition of the integration…

Operator learning is a rapidly growing field that aims to approximate nonlinear operators related to partial differential equations (PDEs) using neural operators. These rely on discretization of input and output functions and are, usually,…

Recent studies have underscored the capabilities of natural imaging foundation models to serve as powerful feature extractors, even in a zero-shot setting for medical imaging data. Most commonly, a shallow multi-layer perceptron (MLP) is…

For many complex simulation tasks spanning areas such as healthcare, engineering, and finance, Monte Carlo (MC) methods are invaluable due to their unbiased estimates and precise error quantification. Nevertheless, Monte Carlo simulations…

Monte Carlo criticality simulations are widely used in nuclear safety demonstrations, as they offer an arbitrarily precise estimation of global and local tallies while making very few assumptions. However, since the inception of such…

In this paper, we described and developed a framework for Multilayer Perceptron (MLP) to work on low level image processing, where MLP will be used to perform image super-resolution. Meanwhile, MLP are trained with different types of images…

In this work, we propose a balanced multi-component and multi-layer neural network (MMNN) structure to accurately and efficiently approximate functions with complex features, in terms of both degrees of freedom and computational cost. The…

Monte Carlo (MC) sampling is a popular method for estimating the statistics (e.g. expectation and variance) of a random variable. Its slow convergence has led to the emergence of advanced techniques to reduce the variance of the MC…

Sampling-based controllers, such as Model Predictive Path Integral (MPPI) methods, offer substantial flexibility but often suffer from high variance and low sample efficiency. To address these challenges, we introduce a hybrid…

Many machine learning problems involve Monte Carlo gradient estimators. As a prominent example, we focus on Monte Carlo variational inference (MCVI) in this paper. The performance of MCVI crucially depends on the variance of its stochastic…

Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…

This paper introduces the Modular Neural Computer (MNC), a memory-augmented neural architecture for exact algorithmic computation on variable-length inputs. The model combines an external associative memory of scalar cells, explicit read…

Artificial Neural Networks(ANN) has been phenomenally successful on various pattern recognition tasks. However, the design of neural networks rely heavily on the experience and intuitions of individual developers. In this article, the…

Monte Carlo integration is typically interpreted as an estimator of the expected value using stochastic samples. There exists an alternative interpretation in calculus where Monte Carlo integration can be seen as estimating a…

From the perspective of expressive power, this work compares multi-layer Graph Neural Networks (GNNs) with a simplified alternative that we call Graph-Augmented Multi-Layer Perceptrons (GA-MLPs), which first augments node features with…

Machine learning models are commonly applied to human brain imaging datasets in an effort to associate function or structure with behaviour, health, or other individual phenotypes. Such models often rely on low-dimensional maps generated by…

Graph neural networks (GNNs) are a well-regarded tool for learned control of networked dynamical systems due to their ability to be deployed in a distributed manner. However, current distributed GNN architectures assume that all nodes in…