Related papers: Embedding principle of homogeneous neural network …

A map $\varphi:K\to R^2$ of a graph $K$ is approximable by embeddings, if for each $\varepsilon>0$ there is an $\varepsilon$-close to $\varphi$ embedding $f:K\to R^2$. Analogous notions were studied in computer science under the names of…

Neural networks are widely used as a model for classification in a large variety of tasks. Typically, a learnable transformation (i.e. the classifier) is placed at the end of such models returning a value for each class used for…

In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose…

The evolution of a deep neural network trained by the gradient descent can be described by its neural tangent kernel (NTK) as introduced in [20], where it was proven that in the infinite width limit the NTK converges to an explicit limiting…

In this paper, we study the data-dependent convergence and generalization behavior of gradient methods for neural networks with smooth activation. Our first result is a novel bound on the excess risk of deep networks trained by the logistic…

Current Graph Neural Networks (GNN) architectures generally rely on two important components: node features embedding through message passing, and aggregation with a specialized form of pooling. The structural (or topological) information…

We propose a numerical method for solving the multi-marginal Monge problem, which extends the classical Monge formulation to settings involving multiple target distributions. Our approach is based on the Hilbert space embedding of…

Most work on wireless network resource allocation use physical layer performance such as sum rate and outage probability as the figure of merit. These metrics may not reflect the true user QoS in future heterogenous networks (HetNets) with…

Neural Tangent Kernel (NTK) is widely used to analyze overparametrized neural networks due to the famous result by Jacot et al. (2018): in the infinite-width limit, the NTK is deterministic and constant during training. However, this result…

In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the…

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…

Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

A k-page book embedding of a graph G draws the vertices of G on a line and the edges on k half-planes (called pages) bounded by this line, such that no two edges on the same page cross. We study the problem of determining whether G admits a…

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,…

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…

Graph node embedding aims at learning a vector representation for all nodes given a graph. It is a central problem in many machine learning tasks (e.g., node classification, recommendation, community detection). The key problem in graph…

Influence maximization--the problem of identifying a subset of k influential seeds (vertices) in a network--is a classical problem in network science with numerous applications. The problem is NP-hard, but there exist efficient polynomial…

Recent theoretical results show that gradient descent on deep neural networks under exponential loss functions locally maximizes classification margin, which is equivalent to minimizing the norm of the weight matrices under margin…

We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…