Dimitrios Kelesis

Dimitrios Kelesis, Dimitris Fotakis, Georgios Paliouras

In this work, we generalize the ideas of Kaiming initialization to Graph Neural Networks (GNNs) and propose a new scheme (G-Init) that reduces oversmoothing, leading to very good results in node and graph classification tasks. GNNs are commonly initialized using methods designed for other types of Neural Networks, overlooking the underlying graph topology. We analyze theoretically the variance of signals flowing forward and gradients flowing backward in the class of convolutional GNNs. We then simplify our analysis to the case of the GCN and propose a new initialization method. Our results indicate that the new method (G-Init) reduces oversmoothing in deep GNNs, facilitating their effective use. Experimental validation supports our theoretical findings, demonstrating the advantages of deep networks in scenarios with no feature information for unlabeled nodes (i.e., ``cold start'' scenario).

Dimitrios Kelesis, Dimitris Fotakis, Georgios Paliouras

In this paper, we study the factors that contribute to the effect of oversmoothing in deep Graph Neural Networks (GNNs). Specifically, our analysis is based on a new metric (Mean Average Squared Distance - $MASED$) to quantify the extent of oversmoothing. We derive layer-wise bounds on $MASED$, which aggregate to yield global upper and lower distance bounds. Based on this quantification of oversmoothing, we further analyze the importance of two different properties of the model; namely the norms of the generated node embeddings, along with the largest and smallest singular values of the weight matrices. Building on the insights drawn from the theoretical analysis, we show that oversmoothing increases as the number of trainable weight matrices and the number of adjacency matrices increases. We also use the derived layer-wise bounds on $MASED$ to form a proposal for decoupling the number of hops (i.e., adjacency depth) from the number of weight matrices. In particular, we introduce G-Reg, a regularization scheme that increases the bounds, and demonstrate through extensive experiments that by doing so node classification accuracy increases, achieving robustness at large depths. We further show that by reducing oversmoothing in deep networks, we can achieve better results in some tasks than using shallow ones. Specifically, we experiment with a ``cold start" scenario, i.e., when there is no feature information for the unlabeled nodes. Finally, we show empirically the trade-off between receptive field size (i.e., number of weight matrices) and performance, using the $MASED$ bounds. This is achieved by distributing adjacency hops across a small number of trainable layers, avoiding the extremes of under- or over-parameterization of the GNN.

Dimitrios Kelesis, Dimitris Fotakis, Georgios Paliouras

In this work we investigate an observation made by Kipf \& Welling, who suggested that untrained GCNs can generate meaningful node embeddings. In particular, we investigate the effect of training only a single layer of a GCN, while keeping the rest of the layers frozen. We propose a basis on which the effect of the untrained layers and their contribution to the generation of embeddings can be predicted. Moreover, we show that network width influences the dissimilarity of node embeddings produced after the initial node features pass through the untrained part of the model. Additionally, we establish a connection between partially trained GCNs and oversmoothing, showing that they are capable of reducing it. We verify our theoretical results experimentally and show the benefits of using deep networks that resist oversmoothing, in a ``cold start'' scenario, where there is a lack of feature information for unlabeled nodes.

Andreas Kontogiannis, Dimitrios Kelesis, Vasilis Pollatos et al.

A focused crawler aims at discovering as many web pages and web sites relevant to a target topic as possible, while avoiding irrelevant ones. Reinforcement Learning (RL) has been a promising direction for optimizing focused crawling, because RL can naturally optimize the long-term profit of discovering relevant web locations within the context of a reward. In this paper, we propose TRES, a novel RL-empowered framework for focused crawling that aims at maximizing both the number of relevant web pages (aka \textit{harvest rate}) and the number of relevant web sites (\textit{domains}). We model the focused crawling problem as a novel Markov Decision Process (MDP), which the RL agent aims to solve by determining an optimal crawling strategy. To overcome the computational infeasibility of exhaustively searching for the best action at each time step, we propose Tree-Frontier, a provably efficient tree-based sampling algorithm that adaptively discretizes the large state and action spaces and evaluates only a few representative actions. Experimentally, utilizing online real-world data, we show that TRES significantly outperforms and Pareto-dominates state-of-the-art methods in terms of harvest rate and the number of retrieved relevant domains, while it provably reduces by orders of magnitude the number of URLs needed to be evaluated at each crawling step.