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Ben Finkelshtein

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6 papers

2 author rows

ICML Conference 2025 Conference Paper

Covered Forest: Fine-grained generalization analysis of graph neural networks

Antonis Vasileiou
Ben Finkelshtein
Floris Geerts
Ron Levie
Christopher Morris 0001

The expressive power of message-passing graph neural networks (MPNNs) is reasonably well understood, primarily through combinatorial techniques from graph isomorphism testing. However, MPNNs’ generalization abilities—making meaningful predictions beyond the training set—remain less explored. Current generalization analyses often overlook graph structure, limit the focus to specific aggregation functions, and assume the impractical, hard-to-optimize $0$-$1$ loss function. Here, we extend recent advances in graph similarity theory to assess the influence of graph structure, aggregation, and loss functions on MPNNs’ generalization abilities. Our empirical study supports our theoretical insights, improving our understanding of MPNNs’ generalization properties.

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NeurIPS Conference 2025 Conference Paper

Equivariance Everywhere All At Once: A Recipe for Graph Foundation Models

Ben Finkelshtein
Ismail Ilkan Ceylan
Michael Bronstein
Ron Levie

Graph machine learning architectures are typically tailored to specific tasks on specific datasets, which hinders their broader applicability. This has led to a new quest in graph machine learning: \emph{how to build graph foundation models (GFMs)} capable of generalizing across arbitrary graphs and features? In this work, we present a recipe for designing GFMs for node-level tasks from first principles. The key ingredient underpinning our study is a systematic investigation of the symmetries that a graph foundation model must respect. In a nutshell, we argue that label permutation-equivariance alongside feature permutation-invariance are necessary in addition to the common node permutation-equivariance on each local neighborhood of the graph. To this end, we first characterize the space of linear transformations that are equivariant to permutations of nodes and labels, and invariant to permutations of features. We then prove that the resulting network is a universal approximator on multisets that respect the aforementioned symmetries. Our recipe uses such layers on the multiset of features induced by the local neighborhood of the graph to obtain a class of graph foundation models for node property prediction. We validate our approach through extensive experiments on 29 real-world node classification datasets, demonstrating both strong zero-shot empirical performance and consistent improvement as the number of training graphs increases.

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NeurIPS Conference 2024 Conference Paper

Almost Surely Asymptotically Constant Graph Neural Networks

Sam Adam-Day
Michael Benedikt
İsmail İ. Ceylan
Ben Finkelshtein

We present a new angle on the expressive power of graph neural networks (GNNs) by studying how the predictions of real-valued GNN classifiers, such as those classifying graphs probabilistically, evolve as we apply them on larger graphs drawn from some random graph model. We show that the output converges to a constant function, which upper-bounds what these classifiers can uniformly express. This strong convergence phenomenon applies to a very wide class of GNNs, including state of the art models, with aggregates including mean and the attention-based mechanism of graph transformers. Our results apply to a broad class of random graph models, including sparse and dense variants of the Erdős-Rényi model, the stochastic block model, and the Barabási-Albert model. We empirically validate these findings, observing that the convergence phenomenon appears not only on random graphs but also on some real-world graphs.

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ICML Conference 2024 Conference Paper

Cooperative Graph Neural Networks

Ben Finkelshtein
Xingyue Huang
Michael M. Bronstein
Ismail Ilkan Ceylan

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either listen, broadcast, listen and broadcast, or to isolate. The standard message propagation scheme can then be viewed as a special case of this framework where every node listens and broadcasts to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic and real-world datasets.

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NeurIPS Conference 2024 Conference Paper

Learning on Large Graphs using Intersecting Communities

Ben Finkelshtein
İsmail İ. Ceylan
Michael Bronstein
Ron Levie

Message Passing Neural Networks (MPNNs) are a staple of graph machine learning. MPNNs iteratively update each node’s representation in an input graph by aggregating messages from the node’s neighbors, which necessitates a memory complexity of the order of the number of graph edges. This complexity might quickly become prohibitive for large graphs provided they are not very sparse. In this paper, we propose a novel approach to alleviate this problem by approximating the input graph as an intersecting community graph (ICG) -- a combination of intersecting cliques. The key insight is that the number of communities required to approximate a graph does not depend on the graph size. We develop a new constructive version of the Weak Graph Regularity Lemma to efficiently construct an approximating ICG for any input graph. We then devise an efficient graph learning algorithm operating directly on ICG in linear memory and time with respect to the number of nodes (rather than edges). This offers a new and fundamentally different pipeline for learning on very large non-sparse graphs, whose applicability is demonstrated empirically on node classification tasks and spatio-temporal data processing.

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ICLR Conference 2023 Conference Paper

Strategic Classification with Graph Neural Networks

Itay Eilat
Ben Finkelshtein
Chaim Baskin
Nir Rosenfeld

Strategic classification studies learning in settings where users can modify their features to obtain favorable predictions. Most current works focus on simple classifiers that trigger independent user responses. Here we examine the implications of learning with more elaborate models that break the independence assumption. Motivated by the idea that applications of strategic classification are often social in nature, we focus on graph neural networks, which make use of social relations between users to improve predictions. Using a graph for learning introduces inter-user dependencies in prediction; our key point is that strategic users can exploit these to promote their goals. As we show through analysis and simulation, this can work either against the system---or for it. Based on this, we propose a differentiable framework for strategically-robust learning of graph-based classifiers. Experiments on several real networked datasets demonstrate the utility of our approach.

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