Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
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A finite sheaf-theoretic framework ranks obstruction measures to identify when an AI agent's theory must deform within its language or extend to a new one, validated on a controlled transition benchmark.
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
Introduces geometric-sensitivity and active-set-instability signals to adaptively allocate measurements for kernel SVMs under Bernoulli noise, with theory and synthetic/quantum-kernel experiments showing improved margin and support-vector recovery.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
citing papers explorer
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Scale-Calibrated Median-of-Means for Robust Distributed Principal Component Analysis
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
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Sheaf-Theoretic Transport and Obstruction for Detecting Scientific Theory Shift in AI Agents
A finite sheaf-theoretic framework ranks obstruction measures to identify when an AI agent's theory must deform within its language or extend to a new one, validated on a controlled transition benchmark.
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Intrinsic effective sample size for manifold-valued Markov chain Monte Carlo via kernel discrepancy
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
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Profile Likelihood Inference for Anisotropic Hyperbolic Wrapped Normal Models on Hyperbolic Space
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
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Adaptive Measurement Allocation for Learning Kernelized SVMs Under Noisy Observations
Introduces geometric-sensitivity and active-set-instability signals to adaptively allocate measurements for kernel SVMs under Bernoulli noise, with theory and synthetic/quantum-kernel experiments showing improved margin and support-vector recovery.
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Scale selection for geometric medians on product manifolds
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
- Kernel Affine Hull Machines as Compute-Efficient Encoders for Frozen Semantic Spaces