SIGIL unifies several existing regimes in graph foundation model design under a single framework that maps any attributed graph to a unified representation space of fixed dimension.
Abstract
A central obstacle in building graph foundation models is the input heterogeneity in terms of feature space dimensionality, semantics, and structure. Such heterogeneity limits the capability of graph neural networks to generalize to new graphs with unseen feature spaces. We address the transferability challenge with SIGIL, a framework that maps any attributed graph to a unified representation space of fixed dimension. Given a graph, SIGIL lifts it to a structural interaction graph, where nodes are the input feature dimensions and weighted, typed edges encode feature alignment across multiple orders of the graph's connectivity. A relational message-passing network embeds each feature dimension into a shared space, transforming the original node features, of arbitrary dimensionality, into representations transferable to any downstream graph. By construction, SIGIL is equivariant to permutations of nodes, feature dimensions, and labels. Additionally, when the input features are one-hot indicators of discrete relations, SIGIL recovers and strictly generalizes existing foundation models for knowledge graph reasoning. A single SIGIL model, pretrained on one graph, delivers strong fully-inductive link prediction. Also, SIGIL can be used to implement existing knowledge graph foundation models. As such, SIGIL unifies several existing regimes in graph foundation model design under a single framework
Graph neural networks are commonly described through family-specific equations whose notation obscures shared computations and structural differences. We introduce a common layer equation that represents covered architectures through seven components: an update domain, channel set, propagation bank, per-channel message maps, channel-fusion operator, ego/residual map, and update map. The central factorization separates where information moves, encoded by the propagation bank, from what moves, encoded by the message maps. Function-valued fillings extend the same equation across local message passing, attention, spectral filtering, global communication, relation-specific channels, higher-order domains, and geometric messages. We make this unification explicit and checkable through worked reductions of canonical layers and component assignments spanning seven nonexclusive architectural families. A fixed slot discipline assigns operations by computational role and defines the framework's coverage boundary. The decomposition also yields component-level theoretical insights: under endpoint-local messages and node-local updates, operator support bounds one-layer dependencies, and one-layer global mixing requires a full effective operator row under the stated hypotheses. The resulting framework organizes more than 200 architectures in a common design space, enables component-wise comparison and generation of structurally consistent architectures, and connects propagation choices to oversmoothing, oversquashing, heterophily, and expressivity. It further exposes the empirical inverse problem of mapping measurable graph and task properties to validated component choices.
S. Navuluru, Siddhartha Shankar Das, B. Ni et al.· 0 citations
DIAL, a message-passing layer that gives nodes access to graph structure through the diagonal of graph-derived operators, is introduced, which uses randomized probing to provide nodes with learnable, permutation equivariant access to diagonal entries.
Saku Peltonen, H. Bilgi, Kubilay Atasu· 0 citations
Graph Neural Networks (GNNs) are popular deep learning models designed to process graph-structured data through recursive neighborhood aggregations in the message passing process. When applied to semi-supervised node classification, the message-passing enables GNNs to understand short-range spatial interactions, but also causes them to suffer from over-smoothing and over-squashing. These challenges hinder model expressiveness and prevent the use of deeper models to capture long-range node interactions (LRIs) within the graph. Popular solutions for LRIs detection are either too expensive to process large graphs due to high time complexity or fail to generalize across diverse graph structures. To address these limitations, we propose a mechanism called information flow control, which leverages a novel connectivity measure, called information flow score, to address over-smoothing and over-squashing with linear computational overhead, supported by theoretical evidence. Building on this mechanism, we introduce DeltaGNN, to the best of our knowledge among the first scalable (featuring linear computational and memory complexity overhead) and generalizable (capable of effectively handling graphs with diverse homophily, density, and topology) architectures for long-range and short-range interaction detection. We benchmark our model across 10 real-world datasets, including graphs with varying sizes, topologies, densities, and homophilic ratios, showing superior performance with limited computational complexity.
Kevin Mancini, Islem Rekik· IEEE Transactions on Pattern...· 2 citations
A graph foundation model generalizes across graph domains by mapping every input into one shared representation before any task reasoning. We call this map the alignment layer, the component that separates a graph foundation model from a graph neural network, and we show it is a distinct attack surface that prior work has not studied. We attack it at inference time, with no access to training, on six public models spanning spectral tokenizers, text embedding spaces, and a discrete codebook. A directed representation-space perturbation collapses every model, but at a budget comparable to the representation norm a plain graph network also needs, with one exception: OpenGraph, whose spectral tokenizer collapses at a fifth of that budget, an alignment-specific fragility a plain network does not share and which a same-representation control traces to the tokenizer rather than the decoder. A realizable input-space attack that edits edges, features, or text removes at least half the correct predictions on three of the six models at peak. How much of this fragility an input-access attacker realizes tracks how directly the decoder reads the representation, and not the clean accuracy a task leaves; we measure this carrier gain structurally from the decoder's local Lipschitz sensitivity, and report clean-accuracy headroom as a within-model ordering heuristic that does not survive on realizable attacks.
This work proposes a novel Adaptive Dual-level Collaborative GNN associated with an adaptive dual-level collaborative mechanism, and shows that the ADC-GNN can inject the learned high-level information back into the node level, forming a closed-loop, bidirectional optimization process.
A diffusion-enhanced inductive link prediction framework that combines Graph Diffusion Convolution (GDC), structural node descriptors, and neighborhood aggregation from GraphSAGE is proposed that achieves higher accuracy than the other models on the benchmark datasets.