Hypergraph neural networks obey a strict expressivity hierarchy indexed by hypertree width, creating a Width Wall that no fixed-depth model, hidden dimension, or training procedure can cross for wider patterns.
Limits of dense graph sequences.Journal of Combinatorial Theory, Series B, 96(6):933–957
3 Pith papers cite this work. Polarity classification is still indexing.
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Random sampling maps (with-replacement, binning, species) induce metrics that give uniform any-dimensional generalization and sketching rates for continuous functions on sequences, graphs and tensors.
A Jacobi diffusion on graphon space is discretized into a graph-level generative process that matches the continuous process's first moment exactly and second moment up to a closed-form gap, enabling out-of-scale graph generation.
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The WidthWall: A Strict Expressivity Hierarchy for Hypergraph Neural Networks
Hypergraph neural networks obey a strict expressivity hierarchy indexed by hypertree width, creating a Width Wall that no fixed-depth model, hidden dimension, or training procedure can cross for wider patterns.
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Any-Dimensional Learning by Sampling
Random sampling maps (with-replacement, binning, species) induce metrics that give uniform any-dimensional generalization and sketching rates for continuous functions on sequences, graphs and tensors.
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DiPhon: Diffusion on Graphons for Scalable Graph Generation
A Jacobi diffusion on graphon space is discretized into a graph-level generative process that matches the continuous process's first moment exactly and second moment up to a closed-form gap, enabling out-of-scale graph generation.