Dmitry Eremeev

Dmitry Eremeev, Salem Said, Viacheslav Borovitskiy

Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels that respect the natural geometry of the space of matchings. To this end, we first provide a complete characterization of stationary kernels, i.e. kernels that respect the inherent symmetries of this space. Because the class of stationary kernels is too broad, we specifically focus on the heat and Matérn kernel families, adding an appropriate inductive bias of smoothness to stationarity. While these families successfully extend widely popular Euclidean kernels to matchings, evaluating them naively incurs a prohibitive super-exponential computational cost. To overcome this difficulty, we introduce and analyze a novel, sub-exponential algorithm leveraging zonal polynomials for efficient kernel evaluation. Finally, motivated by the known bijective correspondence between matchings and phylogenetic trees-a crucial data modality in biology-we explore whether our framework can be seamlessly transferred to the space of trees, establishing novel negative results and identifying a significant open problem.

Oleg Platonov, Gleb Bazhenov, Dmitry Eremeev et al.

Due to the wide use of graph-structured data in different fields of industry and science, the development of Graph Foundation Models (GFMs) has recently attracted a lot of attention. While many different types of models are called GFMs, particular interest has been paid to GFMs designed for node property prediction tasks, which is one of the most popular settings in Graph ML with lots of real-world applications from fraud detection in financial and social networks to recommendation systems for e-commerce and user-generated content platforms. While a number of GFMs for this task have been recently proposed, the field has not converged to a unified evaluation setting, and different works evaluate their models in widely different ways, preventing reliable comparison of GFMs with each other and with other types of models. In this work, we conduct a fair and rigorous reevaluation of 9 recent GFMs for node property prediction, comparing them to strong Graph Neural Network (GNN) baselines. We find that, among these GFMs, only the most recent ones based on the Prior-data Fitted Networks paradigm outperform well-tuned GNNs in predictive performance, although at a higher inference cost.

Dmitry Eremeev, Gleb Bazhenov, Oleg Platonov et al.

While foundation models have revolutionized such fields as natural language processing and computer vision, their potential in graph machine learning remains largely unexplored. One of the key challenges in designing graph foundation models (GFMs) is handling diverse node features that can vary across different graph datasets. While many works on GFMs have focused exclusively on text-attributed graphs, the problem of handling arbitrary features of other types in GFMs has not been fully addressed. However, this problem is not unique to the graph domain, as it also arises in the field of machine learning for tabular data. In this work, motivated by the recent success of tabular foundation models (TFMs) like TabPFNv2 or LimiX, we propose G2T-FM, a simple framework for turning tabular foundation models into graph foundation models. Specifically, G2T-FM augments the original node features with neighborhood feature aggregation, adds structural embeddings, and then applies a TFM to the constructed node representations. Even in a fully in-context regime, our model achieves strong results, significantly outperforming publicly available GFMs and performing competitively with, and often better than, well-tuned GNNs trained from scratch. Moreover, after finetuning, G2T-FM surpasses well-tuned GNN baselines. In particular, when combined with LimiX, G2T-FM often outperforms the best GNN by a significant margin. In summary, our paper reveals the potential of a previously overlooked direction of utilizing tabular foundation models for graph machine learning tasks.

Dmitry Eremeev, Oleg Platonov, Gleb Bazhenov et al.

Foundation models pretrained on large-scale datasets have transformed such fields as natural language processing and computer vision, but their application to graph data remains limited. Recently emerged graph foundation models, such as G2T-FM, utilize tabular foundation models for graph tasks and were shown to significantly outperform prior attempts to create GFMs. However, these models primarily rely on hand-crafted graph features, limiting their ability to learn complex graph-specific patterns. In this work, we propose GraphPFN: a prior-data fitted network for node-level prediction. First, we design a prior distribution of synthetic attributed graphs. For graph structure generation, we use a novel combination of multiple stochastic block models and a preferential attachment process. We then apply graph-aware structured causal models to generate node attributes and targets. This procedure allows us to efficiently generate a wide range of realistic graph datasets. Then, we augment the tabular foundation model LimiX with attention-based graph neighborhood aggregation layers and train it on synthetic graphs sampled from our prior, allowing the model to capture graph structural dependencies not present in tabular data. On diverse real-world graph datasets with up to 50,000 nodes, GraphPFN shows strong in-context learning performance and achieves state-of-the-art results after finetuning, outperforming both G2T-FM and task-specific GNNs trained from scratch on most datasets. More broadly, our work demonstrates that pretraining on synthetic graphs from a well-designed prior distribution is an effective strategy for building graph foundation models.