Graph neural networks (GNNs) have emerged as a powerful framework for a wide range of node-level graph learning tasks. However, their performance typically depends on random or minimally informed initial feature representations, where poor initialization can lead to slower convergence and increased training instability. In this paper, we address this limitation by leveraging a statistically grounded one-hot graph encoder embedding (GEE) as a high-quality, structure-aware initialization for node features. Integrating GEE into standard GNNs yields the GEE-powered GNN (GG) framework. Across extensive simulations and real-world benchmarks, GG provides consistent and substantial performance gains in both unsupervised and supervised settings. For node classification, we further introduce GG-C, which concatenates the outputs of GG and GEE and outperforms competing methods, achieving roughly 10-50% accuracy improvements across most datasets. These results demonstrate the importance of principled, structure-aware initialization for improving the efficiency, stability, and overall performance of graph neural network architecture, enabling models to better exploit graph topology from the outset.

Large language models (LLMs) are capable of producing high quality information at unprecedented rates.As these models continue to entrench themselves in society, the content they produce will become increasingly pervasive in databases that are, in turn, incorporated into the pre-training data, fine-tuning data, retrieval data, etc. of other language models.In this paper we formalize the idea of a communication network of LLMs and introduce a method for representing the perspective of individual models within a collection of LLMs.Given these tools we systematically study information diffusion in the communication network of LLMs in various simulated settings.

Learning to rank – producing a ranked list of items specific to a query and with respect to a set of supervisory items – is a problem of general interest. The setting we consider is one in which no analytic description of what constitutes a good ranking is available. Instead, we have a collection of representations and supervisory information consisting of a (target item, interesting items set) pair. We demonstrate analytically, in simulation, and in real data examples that learning to rank via combining representations using an integer linear program is effective when the supervision is as light as “these few items are similar to your item of interest.” While this nomination task is quite general, for specificity we present our methodology from the perspective of vertex nomination in graphs. The methodology described herein is model agnostic.

The problem of finding the vertex correspondence between two noisy graphs with different number of vertices where the smaller graph is still large has many applications in social networks, neuroscience, and computer vision. We propose a solution to this problem via a graph matching matched filter: centering and padding the smaller adjacency matrix and applying graph matching methods to align it to the larger network. The centering and padding schemes can be incorporated into any algorithm that matches using adjacency matrices. Under a statistical model for correlated pairs of graphs, which yields a noisy copy of the small graph within the larger graph, the resulting optimization problem can be guaranteed to recover the true vertex correspondence between the networks. However, there are currently no efficient algorithms for solving this problem. To illustrate the possibilities and challenges of such problems, we use an algorithm that can exploit a partially known correspondence and show via varied simulations and applications to Drosophila and human connectomes that this approach can achieve good performance.

We consider the problem of detecting a noisy induced multiplex template network in a larger multiplex background network. Our approach, which extends the framework of [14] to the multiplex setting, leverages a multiplex analogue of the classical graph matching problem to use the template as a matched filter for efficiently searching the background for candidate template matches. The effectiveness of our approach is demonstrated both theoretically and empirically, with particular attention paid to the potential benefits of considering multiple channels.