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Alessio Gravina

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9 papers

2 author rows

ICML Conference 2025 Conference Paper

Graph Adaptive Autoregressive Moving Average Models

Moshe Eliasof
Alessio Gravina
Andrea Ceni
Claudio Gallicchio
Davide Bacciu
Carola Schönlieb

Graph State Space Models (SSMs) have recently been introduced to enhance Graph Neural Networks (GNNs) in modeling long-range interactions. Despite their success, existing methods either compromise on permutation equivariance or limit their focus to pairwise interactions rather than sequences. Building on the connection between Autoregressive Moving Average (ARMA) and SSM, in this paper, we introduce GRAMA, a Graph Adaptive method based on a learnable ARMA framework that addresses these limitations. By transforming from static to sequential graph data, GRAMA leverages the strengths of the ARMA framework, while preserving permutation equivariance. Moreover, GRAMA incorporates a selective attention mechanism for dynamic learning of ARMA coefficients, enabling efficient and flexible long-range information propagation. We also establish theoretical connections between GRAMA and Selective SSMs, providing insights into its ability to capture long-range dependencies. Experiments on 26 synthetic and real-world datasets demonstrate that GRAMA consistently outperforms backbone models and performs competitively with state-of-the-art methods.

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AAAI Conference 2025 Conference Paper

On Oversquashing in Graph Neural Networks Through the Lens of Dynamical Systems

Alessio Gravina
Moshe Eliasof
Claudio Gallicchio
Davide Bacciu
Carola-Bibiane Schönlieb

A common problem in Message-Passing Neural Networks is oversquashing -- the limited ability to facilitate effective information flow between distant nodes. Oversquashing is attributed to the exponential decay in information transmission as node distances increase. This paper introduces a novel perspective to address oversquashing, leveraging dynamical systems properties of global and local non-dissipativity, that enable the maintenance of a constant information flow rate. We present SWAN, a uniquely parameterized GNN model with antisymmetry both in space and weight domains, as a means to obtain non-dissipativity. Our theoretical analysis asserts that by implementing these properties, SWAN offers an enhanced ability to transmit information over extended distances. Empirical evaluations on synthetic and real-world benchmarks that emphasize long-range interactions validate the theoretical understanding of SWAN, and its ability to mitigate oversquashing.

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NeurIPS Conference 2025 Conference Paper

On Vanishing Gradients, Over-Smoothing, and Over-Squashing in GNNs: Bridging Recurrent and Graph Learning

Alvaro Arroyo
Alessio Gravina
Benjamin Gutteridge
Federico Barbero
Claudio Gallicchio
Xiaowen Dong
Michael Bronstein
Pierre Vandergheynst

Graph Neural Networks (GNNs) are models that leverage the graph structure to transmit information between nodes, typically through the message-passing operation. While widely successful, this approach is well-known to suffer from representational collapse as the number of layers increases and insensitivity to the information contained at distant and poorly connected nodes. In this paper, we present a unified view of on the appearance of these issues through the lens of vanishing gradients, using ideas from linear control theory for our analysis. We propose an interpretation of GNNs as recurrent models and empirically demonstrate that a simple state-space formulation of an GNN effectively alleviates these issues at no extra trainable parameter cost. Further, we show theoretically and empirically that (i) Traditional GNNs are by design prone to extreme gradient vanishing even after few layers; (ii) Feature collapse is directly related to the mechanism causing vanishing gradients; (iii) Long-range modeling is most easily achieved by a combination of graph rewiring and vanishing gradient mitigation. We believe our work will help bridge the gap between the recurrent and graph neural network literature and will unlock the design of new deep and performant GNNs.

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ICLR Conference 2025 Conference Paper

Port-Hamiltonian Architectural Bias for Long-Range Propagation in Deep Graph Networks

Simon Heilig
Alessio Gravina
Alessandro Trenta
Claudio Gallicchio
Davide Bacciu

The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce port-Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.

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NeurIPS Conference 2025 Conference Paper

Return of ChebNet: Understanding and Improving an Overlooked GNN on Long Range Tasks

Ali Hariri
Alvaro Arroyo
Alessio Gravina
Moshe Eliasof
Carola-Bibiane Schönlieb
Davide Bacciu
Xiaowen Dong
Kamyar Azizzadenesheli

ChebNet, one of the earliest spectral GNNs, has largely been overshadowed by Message Passing Neural Networks (MPNNs), which gained popularity for their simplicity and effectiveness in capturing local graph structure. Despite their success, MPNNs are limited in their ability to capture long-range dependencies between nodes. This has led researchers to adapt MPNNs through rewiring or make use of Graph Transformers, which compromise the computational efficiency that characterized early spatial message passing architectures, and typically disregard the graph structure. Almost a decade after its original introduction, we revisit ChebNet to shed light on its ability to model distant node interactions. We find that out-of-box, ChebNet already shows competitive advantages relative to classical MPNNs and GTs on long-range benchmarks, while maintaining good scalability properties for high-order polynomials. However, we uncover that this polynomial expansion leads ChebNet to an unstable regime during training. To address this limitation, we cast ChebNet as a stable and non-dissipative dynamical system, which we coin Stable-ChebNet. Our Stable-ChebNet model allows for stable information propagation, and has controllable dynamics which do not require the use of eigendecompositions, positional encodings, or graph rewiring. Across several benchmarks, Stable-ChebNet achieves near state-of-the-art performance.

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NeurIPS Conference 2025 Conference Paper

SONAR: Long-Range Graph Propagation Through Information Waves

Alessandro Trenta
Alessio Gravina
Davide Bacciu

Capturing effective long-range information propagation remains a fundamental yet challenging problem in graph representation learning. Motivated by this, we introduce SONAR, a novel GNN architecture inspired by the dynamics of wave propagation in continuous media. SONAR models information flow on graphs as oscillations governed by the wave equation, allowing it to maintain effective propagation dynamics over long distances. By integrating adaptive edge resistances and state-dependent external forces, our method balances conservative and non-conservative behaviors, improving the ability to learn more complex dynamics. We provide a rigorous theoretical analysis of SONAR's energy conservation and information propagation properties, demonstrating its capacity to address the long-range propagation problem. Extensive experiments on synthetic and real-world benchmarks confirm that SONAR achieves state-of-the-art performance, particularly on tasks requiring long-range information exchange.

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ICML Conference 2024 Conference Paper

Long Range Propagation on Continuous-Time Dynamic Graphs

Alessio Gravina
Giulio Lovisotto
Claudio Gallicchio
Davide Bacciu
Claas Grohnfeldt

Learning Continuous-Time Dynamic Graphs (C-TDGs) requires accurately modeling spatio-temporal information on streams of irregularly sampled events. While many methods have been proposed recently, we find that most message passing-, recurrent- or self-attention-based methods perform poorly on long-range tasks. These tasks require correlating information that occurred "far" away from the current event, either spatially (higher-order node information) or along the time dimension (events occurred in the past). To address long-range dependencies, we introduce Continuous-Time Graph Anti-Symmetric Network (CTAN). Grounded within the ordinary differential equations framework, our method is designed for efficient propagation of information. In this paper, we show how CTAN’s (i) long-range modeling capabilities are substantiated by theoretical findings and how (ii) its empirical performance on synthetic long-range benchmarks and real-world benchmarks is superior to other methods. Our results motivate CTAN’s ability to propagate long-range information in C-TDGs as well as the inclusion of long-range tasks as part of temporal graph models evaluation.

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IJCAI Conference 2024 Conference Paper

Temporal Graph ODEs for Irregularly-Sampled Time Series

Alessio Gravina
Daniele Zambon
Davide Bacciu
Cesare Alippi

Modern graph representation learning works mostly under the assumption of dealing with regularly sampled temporal graph snapshots, which is far from realistic, e. g. , social networks and physical systems are characterized by continuous dynamics and sporadic observations. To address this limitation, we introduce the Temporal Graph Ordinary Differential Equation (TG-ODE) framework, which learns both the temporal and spatial dynamics from graph streams where the intervals between observations are not regularly spaced. We empirically validate the proposed approach on several graph benchmarks, showing that TG-ODE can achieve state-of-the-art performance in irregular graph stream tasks.

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ICLR Conference 2023 Conference Paper

Anti-Symmetric DGN: a stable architecture for Deep Graph Networks

Alessio Gravina
Davide Bacciu
Claudio Gallicchio

Deep Graph Networks (DGNs) currently dominate the research landscape of learning from graphs, due to their efficiency and ability to implement an adaptive message-passing scheme between the nodes. However, DGNs are typically limited in their ability to propagate and preserve long-term dependencies between nodes, i.e., they suffer from the over-squashing phenomena. As a result, we can expect them to under-perform, since different problems require to capture interactions at different (and possibly large) radii in order to be effectively solved. In this work, we present Anti-Symmetric Deep Graph Networks (A-DGNs), a framework for stable and non-dissipative DGN design, conceived through the lens of ordinary differential equations. We give theoretical proof that our method is stable and non-dissipative, leading to two key results: long-range information between nodes is preserved, and no gradient vanishing or explosion occurs in training. We empirically validate the proposed approach on several graph benchmarks, showing that A-DGN yields to improved performance and enables to learn effectively even when dozens of layers are used.

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