arXiv Machine Learning
Aug 4
Differentiable Lifting for Topological Neural Networks
arXiv:2608. 01160v1 Announce Type: new Abstract: Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.
On the Expressive Power of Sparse Geometric MPNNs
arXiv:2407. 02025v5 Announce Type: replace-cross Abstract: Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions.
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arXiv AI
Sep 1
Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
arXiv AI
Aug 25
Which Algorithms Can Graph Neural Networks Learn?
arXiv:2602.13106v2 Announce Type: replace-cross Abstract: In recent years, there has been growing interest in understanding neural architectures' ability to learn to execute discrete algorithms, a li...
arXiv Machine Learning
Sep 2
Why Multi-Layer Message Passing Works: Completeness Theory for Graph Neural Network Interatomic Potentials
arXiv:2609.00528v1 Announce Type: new Abstract: We prove that the Hypergraph Neural Network, an invariant architecture with 3-body message passing, is a universal approximator for potential energy su...
arXiv Machine Learning
Jun 30
Lost in Aggregation: On a Fundamental Expressivity Limit of Message-Passing Graph Neural Networks
arXiv:2603. 14846v3 Announce Type: replace Abstract: We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices).
arXiv Machine Learning
Jun 25
Ramanujan Graph Rewiring with Non Negative Resistance Curvature
arXiv:2606. 21333v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a powerful paradigm for learning on graph-structured data by iteratively propagating and aggregating information across edges.
arXiv Machine Learning
Jun 5
HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations
arXiv:2505. 15405v3 Announce Type: replace Abstract: While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems.
arXiv Machine Learning
Jun 16
Graph Learning Should Move Beyond Restrictive Views of Spectral and Message-Passing GNNs
arXiv:2602. 10031v2 Announce Type: replace Abstract: Graph neural networks (GNNs) are commonly divided into message-passing neural networks (MPNNs) and spectral GNNs, reflecting two largely separate research traditions in machine learning and signal processing.
arXiv Machine Learning
Jul 31
Train Small, Deploy Large: Zero-Shot GNN Transfer Through Geometric Renormalization
arXiv:2607. 27767v1 Announce Type: new Abstract: Graph neural networks (GNNs) can operate on large graphs but become infrastructure-sensitive at the scale of millions of nodes and typically require scalable training techniques for even larger graphs.
arXiv Machine Learning
Aug 10
Hyperbolic Graph Embedders for Link Prediction and Topology Reconstruction
arXiv:2608. 07029v1 Announce Type: new Abstract: Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare.
arXiv Machine Learning
Jun 2
Sheaf Neural Networks on SPD Manifolds: Second-Order Geometric Representation Learning
arXiv:2604. 20308v2 Announce Type: replace Abstract: Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued representations that capture relationships between directions-such as how atomic orientations covary in a molecule.
arXiv AI
Jun 18
Fully Geometric Multi-Hop Reasoning on Knowledge Graphs with Transitive Relations
arXiv:2505. 12369v2 Announce Type: replace Abstract: Multi-hop logical reasoning on knowledge graphs requires faithfully mapping the logical semantics to latent space.