Related papers: Solving Sudoku using oscillatory neural networks
Sudoku is a puzzle well-known to the scientific community with simple rules of completion, which may require a com-plex line of reasoning. This paper addresses the problem of partitioning the Sudoku image into a 1-D array, recognizing…
Programmable optical neural networks (ONNs) can offer high-throughput and energy-efficient solutions for accelerating artificial intelligence (AI) computing. However, existing ONN architectures, typically based on cascaded unitary…
Combinatorial optimization is considered a promising class of problems in which quantum computers can show significant advantages. However, problems of practical relevance typically have more variables than current or foreseeable quantum…
We demonstrate the utility of machine learning algorithms for the design of Oscillatory Neural Networks (ONNs). After constructing a circuit model of the oscillators in a machine-learning-enabled simulator and performing Backpropagation…
Data-driven approaches have been proven effective in solving combinatorial optimization problems over graphs such as the traveling salesman problems and the vehicle routing problem. The rationale behind such methods is that the input…
The increasing amount of data to be processed on edge devices, such as cameras, has motivated Artificial Intelligence (AI) integration at the edge. Typical image processing methods performed at the edge, such as feature extraction or edge…
This article describes how to solve Sudoku puzzles using Quadratic Unconstrained Binary Optimization (QUBO). To this end, a QUBO instance with 729 variables is constructed, encoding a Sudoku grid with all constraints in place, which is then…
We propose the Kuramoto Graph Neural Network (KuramotoGNN), a novel class of continuous-depth graph neural networks (GNNs) that employs the Kuramoto model to mitigate the over-smoothing phenomenon, in which node features in GNNs become…
Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…
This paper proposes a novel inverse kinematics (IK) solver of articulated robotic systems for path planning. IK is a traditional but essential problem for robot manipulation. Recently, data-driven methods have been proposed to quickly solve…
The current study uses a novel method of multilevel neurons and high order synchronization effects described by a family of special metrics, for pattern recognition in an oscillatory neural network (ONN). The output oscillator (neuron) of…
In the ongoing quest for hybridizing discrete reasoning with neural nets, there is an increasing interest in neural architectures that can learn how to solve discrete reasoning or optimization problems from natural inputs, a task that Large…
Optical neural network (ONN) is emerging as an attractive proposal for machine-learning applications, enabling high-speed computation with low-energy consumption. However, there are several challenges in applying ONN for industrial…
Sudoku puzzles are now popular among people in many countries across the world with simple constraints that no repeated digits in each row, each column, or each block. In this paper, we demonstrate that the Sudoku configuration provides us…
Computing with coupled oscillators or oscillatory neural networks (ONNs) has recently attracted a lot of interest due to their potential for massive parallelism and energy-efficient computing. However, to date, ONNs have primarily been…
We propose and evaluate a quantum-inspired algorithm for solving Quadratic Unconstrained Binary Optimization (QUBO) problems, which are mathematically equivalent to finding ground states of Ising spin-glass Hamiltonians. The algorithm…
Neural Ordinary Differential Equations (Neural ODEs) represent continuous-time dynamics with neural networks, offering advancements for modeling and control tasks. However, training Neural ODEs requires solving differential equations at…
We provide a simple linear time transformation from a directed or undirected graph with labeled edges to an unlabeled digraph, such that paths in the input graph in which no two consecutive edges have the same label correspond to paths in…
This work examines the problem to describe an efficient algorithm for obtaining $n^2 \times n^2$ Sudoku matrices. For this purpose, we define the concepts of $n\times n$ $\Pi_n$-matrix and disjoint $\Pi_n$-matrices. The article, using the…
Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are…