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The recently proposed network model, Operational Neural Networks (ONNs), can generalize the conventional Convolutional Neural Networks (CNNs) that are homogenous only with a linear neuron model. As a heterogenous network model, ONNs are…

While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…

Designing high-performing networks requires optimizing for functionality while respecting physical, geometric, or budget constraints. Yet, mathematical and computational tools to design such systems remain limited, particularly for…

The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…

Neural Combinatorial Optimization aims to learn to solve a class of combinatorial problems through data-driven methods and notably through employing neural networks by learning the underlying distribution of problem instances. While, so far…

The Orienteering Problem with Time Windows (OPTW) is a combinatorial optimization problem where the goal is to maximize the total score collected from different visited locations. The application of neural network models to combinatorial…

Real-world systems are often formulated as constrained optimization problems. Techniques to incorporate constraints into Neural Networks (NN), such as Neural Ordinary Differential Equations (Neural ODEs), have been used. However, these…

In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…

In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…

Recently, machine learning, particularly message-passing graph neural networks (MPNNs), has gained traction in enhancing exact optimization algorithms. For example, MPNNs speed up solving mixed-integer optimization problems by imitating…

This study investigates perturbation strategies inspired by adversarial attack principles from deep learning, designed to control synchronization dynamics through strategically crafted weak perturbations. We propose a gradient-based…

We propose to formulate MRI image reconstruction as an optimization problem and model the optimization trajectory as a dynamic process using ordinary differential equations (ODEs). We model the dynamics in ODE with a neural network and…

Machine learning (ML) approaches are increasingly being used to accelerate combinatorial optimization (CO) problems. We investigate the Set Cover Problem (SCP) and propose Graph-SCP, a graph neural network method that augments existing…

Decomposing DRAM address mappings into component-level functions is critical for understanding memory behavior and enabling precise RowHammer attacks, yet existing reverse-engineering methods fall short. We introduce novel timing-based…

A knot is a circle embedded in the space. Projecting a knot on a plane, we obtain a diagram which is known as the knot diagram. The vertices of the diagram, where the curved lines are crossed, can be considered as sites occupied by…

In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…

Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep…

The Nearest-Better Network (NBN) is a powerful method to visualize sampled data for continuous optimization problems while preserving multiple landscape features. However, the calculation of NBN is very time-consuming, and the extension of…

The Kuramoto model is a classical mathematical model in the field of non-linear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's…

Optical neural networks (ONNs), or optical neuromorphic hardware accelerators, have the potential to dramatically enhance the computing power and energy efficiency of mainstream electronic processors, due to their ultralarge bandwidths of…