arXiv Statistics ML
Recovering Weighted Tangent Geometry from a Single-Scale Score Field
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Matched Queries for Curvature and Density at Branching Junctions
arXiv:2609. 01319v1 Announce Type: cross Abstract: At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center.
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Matched Queries for Curvature and Density at Branching Junctions
At a junction, a score field can reveal weighted tangent rays, yet these first-order quantities do not determine how individual branches bend or how their densities change away from the center. Recove...
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EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale
EGGROLL replaces dense Gaussian perturbations in evolution strategies with low‑rank Gaussian products, enabling practical optimization of large language models while maintaining exactness on quadratic objectives. The paper analyzes the mean update field, error bounds, and shows that rank‑one perturbations add only a small variance penalty compared to dense ES. A new leave‑one‑out estimator, LOO‑ROLL, further reduces estimator MSE and improves post‑training performance on transformer blocks and GSM8K accuracy.
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EGGROLL, Unrolled: Understanding and Improving Low-Rank Evolution Strategies at Scale
EGGROLL makes evolution strategies (ES) practical for LLMs by replacing dense Gaussian weight perturbations with low-rank Gaussian products, often of rank one. This choice is computationally attractiv...
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TAP Accuracy Below the Fluctuation Scale and Universal Posterior Geometry in Spherical Linear Models
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The Precision Wall: An Optimizer-Dependent Boundary for Optimization under Power-Law Measurement Spectra
In low-rank matrix sensing of a rank-$D$ factor $U^\ast \in \mathbb{R}^{V \times D}$, replacing isotropic Gaussian designs with power-law measurement covariance $Σ= \mathrm{diag}(j^{-s})_{j=1}^V$ leaves the Burer--Monteiro landscape free of spurious local minima, yet division-normalised first-order optimizers stall above a critical exponent $s^\ast$. We trace this failure to a numerical precision wall.