The paper introduces a general theoretical framework for fibrations on graphs labeled by a commutative monoid, extending the classic theory of graph fibrations to weighted and algebraically labeled graphs. It also accommodates approximate fibrations and demonstrates how this framework can be used to compress arbitrary neural networks, including CNNs, providing a solid theoretical basis for recent findings on fibration symmetries in geometric deep learning.
arXiv:2608.25598v2 Announce Type: replace Abstract: The purpose of this paper is to provide a general, comprehensive, theoretical framework that allows one to deal with fibrations on graphs labelled...
Artificial neural networks generate local symmetries called fibrations and coverings during learning, and these covering symmetries are stable attractors of stochastic gradient descent. The study shows that such symmetries appear across diverse architectures—multilayer, convolutional, recurrent, and transformer networks—and can be exploited for drastic model compression, reducing networks to 17% of their original size without performance loss. Controlled breaking of covering symmetry further improves continual learning, achieving state‑of‑the‑art results.
Positional encodings (PEs) enhance the power of graph neural networks (GNNs), both theoretically and empirically. Two of the most popular families of PEs - spectral (e.
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:2608. 01160v1 Announce Type: new Abstract: Topological neural networks (TNNs) enable leveraging high-order structures on graphs (e.
arXiv:2606. 07728v1 Announce Type: new Abstract: It is well established that ReLU networks define continuous piecewise-linear functions, and that their linear regions are polyhedra in the input space.
arXiv:2410. 00722v3 Announce Type: replace Abstract: We study convolutional neural networks with monomial activation functions.
arXiv:2412. 19419v2 Announce Type: replace-cross Abstract: Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges.
arXiv:2602.15239v3 Announce Type: replace Abstract: Transformers have achieved remarkable success across domains, motivating the rise of Graph Transformers (GTs) as attention-based architectures for...
The paper investigates Graph Transformers (GTs) that use Graph Neural Network (GNN)-based positional encodings. By analyzing GTs through manifold limit models, the authors establish a theoretical link between GTs and Manifold Neural Networks (MNNs), showing that GTs inherit transferability guarantees from their positional encodings. Experiments on standard graph benchmarks confirm that GTs scale comparably to GNNs, and a real‑world shortest‑path estimation task demonstrates their practical efficiency on large terrains.
arXiv:2505.11298v2 Announce Type: replace Abstract: Graph Neural Networks (GNNs) are powerful tools for learning on structured data, yet the relationship between their expressivity and predictive per...
Posted by Ameya Velingker, Research Scientist, Google Research, and Balaji Venkatachalam, Software Engineer, Google Graphs , in which objects and their relations are represented as nodes (or vertices) and edges (or links) between pairs of nodes, are ubiquitous in computing and machine learning (ML). For example, social networks, road networks, and molecular structure and interactions are all domains in which underlying datasets have a natural graph structure.