Related papers: Heaven & Hell: One-Step Hub Consensus
We study Heaven-Hell dynamics, a model for network consensus. A known result establishes an exact one-step convergence threshold for systems with a single uniform hub: the per-node inbound hub weight W suffices if and only if W >= maxrest,…
We study a graph-theoretic approach to the $\mathcal{H}_{\infty}$ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system $\mathcal{H}_{\infty}$ norm of the…
Interactions in many real-world phenomena can be explained by a strong hierarchical structure. Typically, this structure or ranking is not known; instead we only have observed outcomes of the interactions, and the goal is to infer the…
In this paper, we formulate and investigate a generalized consensus algorithm which makes an attempt to unify distributed averaging and maximizing algorithms considered in the literature. Each node iteratively updates its state as a…
We study adaptive aggregation for heterogeneous local SGD in convex finite-sum optimization, allowing heterogeneous local horizons, minibatch sizes, gradient noise, and participation. We introduce HEW-Local SGD, a corrected local-SGD method…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
We consider models of evolving networks $\{\mathcal{G}_n:n\geq 0\}$ modulated by two parameters: an attachment function $f:\mathbb{N}_0\to\mathbb{R}_+$ and a (possibly random) attachment sequence $\{m_i:i\geq 1\}$. Starting with a single…
Trophic coherence, a measure of a graph's hierarchical organisation, has been shown to be linked to a graph's structural and dynamical aspects such as cyclicity, stability and normality. Trophic levels of vertices can reveal their…
Consider a point-to-point message-passing network. We are interested in the asynchronous crash-tolerant consensus problem in incomplete networks. We study the feasibility and efficiency of approximate consensus under different restrictions…
We consider the following natural generalization of Binary Search: in a given undirected, positively weighted graph, one vertex is a target. The algorithm's task is to identify the target by adaptively querying vertices. In response to…
This work considers a point-to-point network of n nodes connected by directed links, and proves tight necessary and sufficient conditions on the underlying communication graphs for achieving consensus among these nodes under crash faults.…
This letter examines the controllability of consensus dynamics on matrix-weighed networks from a graph-theoretic perspective. Unlike the scalar-weighted networks, the rank of weight matrix introduces additional intricacies into…
This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…
Hierarchical SGD (H-SGD) has emerged as a new distributed SGD algorithm for multi-level communication networks. In H-SGD, before each global aggregation, workers send their updated local models to local servers for aggregations. Despite…
We present a new method to accelerate the HITS algorithm by exploiting hyperlink structure of the web graph. The proposed algorithm extends the idea of authority and hub scores from HITS by introducing two diagonal matrices which contain…
Distributed consensus algorithm over networks of quantum systems has been the focus of recent studies in the context of quantum computing and distributed control. Most of the progress in this category have been on the convergence conditions…
We consider the problem of learning a high-dimensional graphical model in which certain hub nodes are highly-connected to many other nodes. Many authors have studied the use of an l1 penalty in order to learn a sparse graph in…
We introduce the concept of control centrality to quantify the ability of a single node to control a directed weighted network. We calculate the distribution of control centrality for several real networks and find that it is mainly…
Neural networks achieve strong empirical performance, but robustness concerns still hinder deployment in safety-critical applications. Formal verification provides robustness guarantees, but current methods face a scalability-completeness…
Link prediction is a fundamental task in graph learning, inherently shaped by the topology of the graph. While traditional heuristics are grounded in graph topology, they encounter challenges in generalizing across diverse graphs. Recent…