GNNs preserved under embeddings, injective homomorphisms, and homomorphisms are exactly characterized by existential graded modal logic, its existential-positive fragment, and existential-positive modal logic, with matching GNN architectures existing for each.
Graded modal logic and counting bisimulation
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Craig interpolants for hybrid modal logics are computable in 4-EXPTIME when they exist, while uniform interpolant existence is undecidable.
Logic-based Weisfeiler-Leman variants enable graph-to-table conversion for classification that matches GNN and graph transformer accuracy while running 5-20x faster without GPUs.
SAGE is a self-evolving agentic graph-memory engine that dynamically constructs and refines structured memory graphs via writer-reader feedback, yielding performance gains on multi-hop QA, open-domain retrieval, and long-term agent benchmarks.
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Structural Preservation and the Logical Expressiveness of Graph Neural Networks
GNNs preserved under embeddings, injective homomorphisms, and homomorphisms are exactly characterized by existential graded modal logic, its existential-positive fragment, and existential-positive modal logic, with matching GNN architectures existing for each.
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Graph Learning via Logic-Based Weisfeiler-Leman Variants and Tabularization
Logic-based Weisfeiler-Leman variants enable graph-to-table conversion for classification that matches GNN and graph transformer accuracy while running 5-20x faster without GPUs.
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SAGE: A Self-Evolving Agentic Graph-Memory Engine for Structure-Aware Associative Memory
SAGE is a self-evolving agentic graph-memory engine that dynamically constructs and refines structured memory graphs via writer-reader feedback, yielding performance gains on multi-hop QA, open-domain retrieval, and long-term agent benchmarks.