Hugging Face Trending Papers
On Counting Graphs for Modal Logic with Counting
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arXiv AI
Sep 15
Recurrent GraphNeural NetworkswithSet-BasedAggregation
The paper introduces recurrent Graph Neural Networks (GNNs) that use set-based aggregation and establishes conditions that can be verified directly from the network weights. It proves a two‑directional equivalence between these networks and the Boolean closure of reachability and safety properties, corresponding to the fragment BΣ◦₁ of the modal μ‑calculus. This equivalence allows for verifiable symbolic explanations of networks that satisfy the identified conditions, without relying on counting logic or external halting signals.
arXiv AI
Jun 17
Structural Preservation and the Logical Expressiveness of Graph Neural Networks
arXiv:2606. 17882v1 Announce Type: new Abstract: Bridges between graph neural networks (GNNs) and logical formalisms have been established by fixing architectural choices, such as the types of aggregation, combination, and activation functions.
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
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.
arXiv AI
Sep 4
Complete Identification of Deep ReLU Networks through {\L}ukasiewicz Logic
The paper presents a complete characterization of when two deep ReLU networks realize the same function, showing that this occurs iff one can be transformed into the other using a set of axioms from many‑valued logic. It introduces a symbolic calculus that maps networks to substitution graphs, proves a completeness theorem linking equivalent formulas, and provides an algorithm to reconstruct networks from these graphs. The framework yields a new compositional normal form for MV logic that preserves the algebraic structure of deep ReLU networks.
arXiv AI
Jun 8
Learning to Execute Graph Algorithms Exactly with Graph Neural Networks
arXiv:2601. 23207v2 Announce Type: replace-cross Abstract: Understanding what graph neural networks can learn, especially their ability to learn to execute algorithms, remains a central theoretical challenge.