arXiv Machine Learning
M-Fibration Theory with Applications to Weighted Graphs
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arXiv Machine Learning
Aug 27
M-Fibration Theory with Applications to Neural Network Compression
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.
Google AI Blog
Jan 23, 2024
Exphormer: Scaling transformers for graph-structured data
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.
arXiv AI
Aug 19
Graph Surgery and the Do-Operator: A Precise Correspondence for Acyclic Structural Causal Models
The paper establishes a precise mathematical link between graph surgery and the do‑operator in deterministic acyclic structural causal models. It shows that deleting arrows in a graph corresponds exactly to replacing the associated mechanisms with constants, proving that “Graph(F^\iota)=Surg(Graph(F),T_\iota)”. The authors further characterize when this equality holds for the full graph, define the intervened model, and demonstrate how sequential interventions combine, concluding that an outcome depends only on interventions at its actual dependency ancestors.
arXiv Machine Learning
Oct 9
Graphons of Line Graphs
The paper studies graphons—limits of graph sequences—by transforming sparse finite graphs into their line graphs. It identifies a property called the square‑degree property that ensures sparse graphs produce dense line graphs, allowing dense‑graph limit results to apply. Examples include star graphs and superlinear preferential attachment graphs, whose line graphs yield non‑zero graphons, while dense graphs such as Erdős–Rényi produce sparse line graphs and the zero graphon.
arXiv Machine Learning
Jul 2
Characterizing and Identifying Separable Graphical Models
arXiv:2607. 01057v1 Announce Type: cross Abstract: We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms.
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).