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.
Absil, Robert Mahony, and Rodolphe Sepulchre.Optimization Algorithms on Matrix Manifolds
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Intrinsic Muon provides closed-form linear maximization oracles on multiple Riemannian matrix manifolds for unitarily invariant norms, with convergence rates depending only on manifold dimension or rank.
Alignment in deep networks is governed by flag varieties, with subspace intersection dimension as the unique reparameterization-invariant observable, explaining regularization and activation effects from first principles.
citing papers explorer
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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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Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds
Intrinsic Muon provides closed-form linear maximization oracles on multiple Riemannian matrix manifolds for unitarily invariant norms, with convergence rates depending only on manifold dimension or rank.
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Flag Varieties: A Geometric Framework for Deep Network Alignment
Alignment in deep networks is governed by flag varieties, with subspace intersection dimension as the unique reparameterization-invariant observable, explaining regularization and activation effects from first principles.