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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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 SRTD and SRTD-lite to symmetrize topological divergences for neural representations and NTS as a rank-correlation-based metric bounded in [-1,1] for cross-scenario benchmarking.
TopoAlign applies mapper graphs with joint force-directed layout, Bubble Sets, and motif queries to align and visualize representation structures across models.
PRISM supplies a geometric upper bound on LLM variant risk that splits drift into scale, shape, and head axes and doubles as a differentiable regularizer against forgetting.
Stable personality vectors in LLMs function as intrinsic guardrails, with ablation increasing emergent misalignment above 40% and amplification reducing it below 3%, enabling zero-shot transfer from aligned to corrupted models.
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.
Merging any combination of monolingual pre-trained models leads to performance collapse due to interference, indicating that merging flexibility from fine-tuning does not extend to pre-training.
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PRISM: A Geometric Risk Bound that Decomposes Drift into Scale, Shape, and Head
PRISM supplies a geometric upper bound on LLM variant risk that splits drift into scale, shape, and head axes and doubles as a differentiable regularizer against forgetting.