Related papers: HANN: Homotopy auxiliary neural network for solvin…
Automated mathematical reasoning is a challenging problem that requires an agent to learn algebraic patterns that contain long-range dependencies. Two particular tasks that test this type of reasoning are (1) mathematical equation…
In this study, we introduce HOBOTAN, a new solver designed for Higher Order Binary Optimization (HOBO). HOBOTAN supports both CPU and GPU, with the GPU version developed based on PyTorch, offering a fast and scalable system. This solver…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
A coupled spintronic oscillator array has been considered attractive for neuromorphic computing applications. Experimental reports have shown the nano-constriction geometry to be a relatively easier-to-fabricate platform for implementing…
Hypergraph matching has recently become a popular approach for solving correspondence problems in computer vision as it allows to integrate higher-order geometric information. Hypergraph matching can be formulated as a third-order…
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a special class of polynomial systems. The root number bound of…
Graph Neural Networks (GNNs) struggle to balance heterophily and homophily in representation learning, a challenge further amplified in self-supervised settings. We propose H$^3$GNNs, an end-to-end self-supervised learning framework that…
Solutions to differential equations are of significant scientific and engineering relevance. Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving differential equations, but they lack a theoretical…
This paper extends and explains the Multiple Additive Neural Networks (MANN) methodology, an enhancement to the traditional Gradient Boosting framework, utilizing nearly shallow neural networks instead of decision trees as base learners.…
Artificial hydrocarbon networks (AHN) is a novel supervised learning method inspired on the structure and the inner chemical mechanisms of organic compounds. As any other cutting-edge algorithm, there are two challenges to be faced:…
This paper is to introduce a type of full multigrid method for the nonlinear eigenvalue problem. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary…
This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…
We present a homotopic approach to solving challenging, optimization-based motion planning problems. The approach uses Homotopy Optimization, which, unlike standard continuation methods for solving homotopy problems, solves a sequence of…
This work considers the trade-off between accuracy and test-time computational cost of deep neural networks (DNNs) via \emph{anytime} predictions from auxiliary predictions. Specifically, we optimize auxiliary losses jointly in an…
$ \ell_1 $-regularized linear inverse problems are frequently used in signal processing, image analysis, and statistics. The correct choice of the regularization parameter $ t \in \mathbb{R}_{\geq 0} $ is a delicate issue. Instead of…
The incompressible magnetohydrodynamic (MHD) equations are fundamental in many scientific and engineering applications. However, their strong nonlinearity and dual divergence-free constraints make them highly challenging for conventional…
We present the first generative adversarial network (GAN) for natural image matting. Our novel generator network is trained to predict visually appealing alphas with the addition of the adversarial loss from the discriminator that is…
The increasing spread of artificial neural networks does not stop at ultralow-power edge devices. However, these very often have high computational demand and require specialized hardware accelerators to ensure the design meets power and…
Recently, lightweight methods for single image super-resolution (SISR) have gained significant popularity and achieved impressive performance due to limited hardware resources. These methods demonstrate that adopting residual feature…
By a numerical continuation method called a diagonal homotopy we can compute the intersection of two positive dimensional solution sets of polynomial systems. This paper proposes to use this diagonal homotopy as the key step in a procedure…