Gaussian Sheaf Neural Networks derive a sheaf Laplacian for Gaussian node features on graphs to preserve their geometric structure during message passing.
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Renyi differential privacy for manifold-valued data is characterized via dimension-free Harnack inequalities and governed by Ricci curvature, with heat diffusion and Langevin mechanisms plus application to private Frechet mean estimation.
An efficient algorithm recovers phylogenetic trees from Θ(n) noisy quartets under random classification noise, matching the information-theoretic lower bound and achieving near-optimal quartet distance.
A Bayesian hyperbolic latent space model with inferable temperature parameter outperforms fixed-temperature and Euclidean models in network reconstruction by better capturing tree-like topologies.
Triplet constraints realizable in D-dimensional Euclidean space cannot be preserved above 50% accuracy by any embedding of dimension at most cD for constant c<1, with UGC-hardness preventing better polynomial-time solutions in any dimension.
citing papers explorer
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Gaussian Sheaf Neural Networks
Gaussian Sheaf Neural Networks derive a sheaf Laplacian for Gaussian node features on graphs to preserve their geometric structure during message passing.
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Geometric Renyi Differential Privacy: Ricci Curvature Characterized by Heat Diffusion Mechanisms
Renyi differential privacy for manifold-valued data is characterized via dimension-free Harnack inequalities and governed by Ricci curvature, with heat diffusion and Langevin mechanisms plus application to private Frechet mean estimation.
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Optimal Phylogenetic Reconstruction from Sampled Quartets
An efficient algorithm recovers phylogenetic trees from Θ(n) noisy quartets under random classification noise, matching the information-theoretic lower bound and achieving near-optimal quartet distance.
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Hyperbolic Latent Space Models for Network Embedding: Model Specification and Bayesian Inference
A Bayesian hyperbolic latent space model with inferable temperature parameter outperforms fixed-temperature and Euclidean models in network reconstruction by better capturing tree-like topologies.
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Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch
Triplet constraints realizable in D-dimensional Euclidean space cannot be preserved above 50% accuracy by any embedding of dimension at most cD for constant c<1, with UGC-hardness preventing better polynomial-time solutions in any dimension.