Related papers: Finding geodesics on graphs using reinforcement le…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Understanding how neural networks learn remains one of the central challenges in machine learning research. From random at the start of training, the weights of a neural network evolve in such a way as to be able to perform a variety of…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
For minimally rigid graphs, the same edge-length data can admit multiple realizations (up to translations and rotations). Finding graphs with exceptionally many realizations is an extremal problem in rigidity theory, but exhaustive search…
We develop a model for a random walker with long-range hops on general graphs. This random multi-hopper jumps from a node to any other node in the graph with a probability that decays as a function of the shortest-path distance between the…
Many learning tasks require observing a sequence of images and making a decision. In a transportation problem of designing and planning for shipping boxes between nodes, we show how to treat the network of nodes and the flows between them…
Recently reinforcement learning (RL) has emerged as a promising approach for quadrupedal locomotion, which can save the manual effort in conventional approaches such as designing skill-specific controllers. However, due to the complex…
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of…
Graph Neural Networks (GNNs) have achieved remarkable success across diverse tasks on graph-structured data, primarily through the use of learned weights in message passing layers. In this paper, we demonstrate that random weights can be…
Graphs (networks) are ubiquitous and allow us to model entities (nodes) and the dependencies (edges) between them. Learning a useful feature representation from graph data lies at the heart and success of many machine learning tasks such as…
We propose a new probabilistic ant-based heuristic (ANTH-LS) for the longest simple cycle problem. This NP-hard problem has numerous real-world applications in complex networks, including efficient construction of graph layouts, analysis of…
Predicting links in complex networks has been one of the essential topics within the realm of data mining and science discovery over the past few years. This problem remains an attempt to identify future, deleted, and redundant links using…
Controlling a biped robot to walk stably is a challenging task considering its nonlinearity and hybrid dynamics. Reinforcement learning can address these issues by directly mapping the observed states to optimal actions that maximize the…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
A mobile agent, starting from a node $s$ of a simple undirected connected graph $G=(V,E)$, has to explore all nodes and edges of $G$ using the minimum number of edge traversals. To do so, the agent uses a deterministic algorithm that allows…
Landing probabilities (LP) of random walks (RW) over graphs encode rich information regarding graph topology. Generalized PageRanks (GPR), which represent weighted sums of LPs of RWs, utilize the discriminative power of LP features to…
In this paper, we propose a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node. By utilizing the spectral graph theory, we provide an exact formula for mean first-passage time…
Given a directed graph of nodes and edges connecting them, a common problem is to find the shortest path between any two nodes. Here we show that the shortest path distances can be found by a simple matrix inversion: If the edges are given…
The main purpose of this thesis is to study the interplay between geometric properties of infinite graphs and analytic and probabilistic objects such as transition operators, harmonic functions and random walks on these graphs. For a…
A few of ant robots are dropped to a labirynth, formed by a square lattice with a small number of nodes removed. Ants move according to a deterministic algorithm designed to explore all corridors. Each ant remembers the shape of corridors…