Related papers: Gauge invariant input to neural network for path o…

Gating mechanisms are widely used in neural network models, where they allow gradients to backpropagate more easily through depth or time. However, their saturation property introduces problems of its own. For example, in recurrent models…

We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph…

We propose neural control variates (NCV) for unbiased variance reduction in parametric Monte Carlo integration. So far, the core challenge of applying the method of control variates has been finding a good approximation of the integrand…

A method of path integral construction without gauge fixing in the holomorphic representation is proposed for finite-dimensional gauge models. This path integral determines a manifestly gauge-invariant kernel of the evolution operator.

The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing…

Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…

Graph Neural Networks (GNNs) have greatly advanced the semi-supervised node classification task on graphs. The majority of existing GNNs are trained in an end-to-end manner that can be viewed as tackling a bi-level optimization problem.…

Early efforts to understand complexity in field theory have primarily employed a geometric approach based on the concept of circuit complexity in quantum information theory. In a parallel vein, it has been proposed that certain deformations…

We propose a novel graph visualization method leveraging random walk-based embeddings to replace costly graph-theoretical distance computations. Using word2vec-inspired embeddings, our approach captures both structural and semantic…

We introduce a novel architecture for graph networks which is equivariant to any transformation in the coordinate embeddings that preserves the distance between neighbouring nodes. In particular, it is equivariant to the Euclidean and…

The path optimization method with machine learning is applied to the one-dimensional massive lattice Thirring model, which has the sign problem caused by the fermion determinant. This study aims to investigate how the path optimization…

We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to…

Recent advances in Graph Neural Networks (GNNs) have explored the potential of random noise as an input feature to enhance expressivity across diverse tasks. However, naively incorporating noise can degrade performance, while architectures…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

Given a road network modelled as a planar straight-line graph $G=(V,E)$ with $|V|=n$, let $(u,v)\in V\times V$, the shortest path (distance) between $u,v$ is denoted as $\delta_G(u,v)$. Let $\delta(G)=\max_{(u,v)}\delta_G(u,v)$, for…

Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…

The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…

Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…

Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this…

In this paper, the problem of finding optimal success probabilities of static linear optics quantum gates is linked to the theory of convex optimization. It is shown that by exploiting this link, upper bounds for the success probability of…