A finite causal set from Poisson sprinkling cannot faithfully embed into two macroscopically distinct spacetimes; the two geometries are forced to agree up to an explicitly bounded approximate isometry that vanishes in the high-density limit.
Karcher, Riemannian center of mass and mollifier smoothing, Comm
8 Pith papers cite this work, alongside 1,003 external citations. Polarity classification is still indexing.
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Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
SLoD detects emergent scale boundaries in knowledge graphs by applying spectral heat diffusion to Poincare embeddings, recovering planted hierarchies in synthetic data and aligning with taxonomic depths in WordNet without resolution-parameter tuning.
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
Introduces intrinsic barycentric projection via conditional Fréchet means as the optimal deterministic map under squared geodesic loss for OT couplings on Riemannian manifolds, plus a tangential log-exp projection with Euclidean exactness and Monge compatibility.
An intrinsic spherical kernel ridge regression framework is introduced for non-linear responses on spheres, reducing infinite-dimensional estimation to finite via the representer theorem with convergence rates shown.
DoRA-RBAC experiments on LLaMA-3.1-8B and Mistral-7B across QA benchmarks show geometry-aware merging offers no advantage over Euclidean averaging, indicating adapter interference stems from nonlinear representation interactions rather than parameter-space geometry.
A multimodal registration pipeline models splints as rigid mandible transformations to quantify TMJ configuration changes via error propagation and surface metrics.
citing papers explorer
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On the Uniqueness of Embeddings of Causal Sets
A finite causal set from Poisson sprinkling cannot faithfully embed into two macroscopically distinct spacetimes; the two geometries are forced to agree up to an explicitly bounded approximate isometry that vanishes in the high-density limit.
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Fast Computation of Free-Support Wasserstein Medians
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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Semantic Level of Detail for Knowledge Graphs: Discovering Abstraction Boundaries via Spectral Heat Diffusion
SLoD detects emergent scale boundaries in knowledge graphs by applying spectral heat diffusion to Poincare embeddings, recovering planted hierarchies in synthetic data and aligning with taxonomic depths in WordNet without resolution-parameter tuning.
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Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
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Barycentric Projections of Optimal Transport Plans on Riemannian Manifolds
Introduces intrinsic barycentric projection via conditional Fréchet means as the optimal deterministic map under squared geodesic loss for OT couplings on Riemannian manifolds, plus a tangential log-exp projection with Euclidean exactness and Monge compatibility.
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Infinite-Dimensional Spherical Kernel ridge Regression
An intrinsic spherical kernel ridge regression framework is introduced for non-linear responses on spheres, reducing infinite-dimensional estimation to finite via the representer theorem with convergence rates shown.
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PermDoRA -- Understanding Adapter Interference in Language Models: Limits of Parameter-Space Geometry
DoRA-RBAC experiments on LLaMA-3.1-8B and Mistral-7B across QA benchmarks show geometry-aware merging offers no advantage over Euclidean averaging, indicating adapter interference stems from nonlinear representation interactions rather than parameter-space geometry.
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Assessment of the quantitative impact of occlusal positioning splints on temporomandibular joint conditions
A multimodal registration pipeline models splints as rigid mandible transformations to quantify TMJ configuration changes via error propagation and surface metrics.