Related papers: AERK: Aligned Entropic Reproducing Kernels through…

Quantum and classical machine learning have been naturally connected through kernel methods, which have also served as proof-of-concept for quantum advantage. Quantum embeddings encode classical data into quantum feature states, enabling…

Kernel functions are vital ingredients of several machine learning algorithms, but often incur significant memory and computational costs. We introduce an approach to kernel approximation in machine learning algorithms suitable for…

Given a graph $\mathcal{G}$, the spanning centrality (SC) of an edge $e$ measures the importance of $e$ for $\mathcal{G}$ to be connected. In practice, SC has seen extensive applications in computational biology, electrical networks, and…

Recently, quantum neural networks or quantum-classical neural networks (qcNN) have been actively studied, as a possible alternative to the conventional classical neural network (cNN), but their practical and theoretically-guaranteed…

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any…

The Neural Tangent Kernel (NTK) has recently attracted intense study, as it describes the evolution of an over-parameterized Neural Network (NN) trained by gradient descent. However, it is now well-known that gradient descent is not always…

We address the correspondence search problem among multiple graphs with complex properties while considering the matching consistency. We describe each pair of graphs by combining multiple attributes, then jointly match them in a unified…

The rapid development of Internet technology has given rise to a vast amount of graph-structured data. Graph Neural Networks (GNNs), as an effective method for various graph mining tasks, incurs substantial computational resource costs when…

We revisit a simple model class for machine learning on graphs, where a random walk on a graph produces a machine-readable record, and this record is processed by a deep neural network to directly make vertex-level or graph-level…

Using the spectral distribution associated with the adjacency matrix of graphs, we introduce a new method of calculation of amplitudes of continuous-time quantum walk on some rather important graphs, such as line, cycle graph $C_n$,…

For a graph representation of a dataset, a straightforward normality measure for a sample can be its graph degree. Considering a weighted graph, degree of a sample is the sum of the corresponding row's values in a similarity matrix. The…

Random walk neural networks (RWNNs) have emerged as a promising approach for graph representation learning, leveraging recent advances in sequence models to process random walks. However, under realistic sampling constraints, RWNNs often…

We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form…

For graph classification tasks, many traditional kernel methods focus on measuring the similarity between graphs. These methods have achieved great success on resolving graph isomorphism problems. However, in some classification problems,…

The (standard) average mixing matrix of a continuous-time quantum walk is computed by taking the expected value of the mixing matrices of the walk under the uniform sampling distribution on the real line. In this paper we consider…

Many deep learning tasks have to deal with graphs (e.g., protein structures, social networks, source code abstract syntax trees). Due to the importance of these tasks, people turned to Graph Neural Networks (GNNs) as the de facto method for…

Multi-kernel learning (MKL) has been widely used in function approximation tasks. The key problem of MKL is to combine kernels in a prescribed dictionary. Inclusion of irrelevant kernels in the dictionary can deteriorate accuracy of MKL,…

How can we approximate sparse graphs and sequences of sparse graphs (with unbounded average degree)? We consider convergence in the first $k$ moments of the graph spectrum (equivalent to the numbers of closed $k$-walks) appropriately…

In estimating the complexity of objects, in particular of graphs, it is common practice to rely on graph- and information-theoretic measures. Here, using integer sequences with properties such as Borel normality, we explain how these…

The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We…