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...
arXiv:2608.22334v1 Announce Type: new
Abstract: Near a smooth data manifold, one tangent space summarizes local geometry. At a branch point, the corresponding first-order object is instead a measure...
By Ziqi Zhao, Qingjian Ni
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.
arXiv:2609.36252v1 Announce Type: new
Abstract: Closed-form recourse moves a rejected user along the unit gradient $\hat g$ of the classifier score $f$ by the promised distance $d_p=|f(x)|/\|\nabla f...
By Hazar Yueksel (Google)
arXiv:2607. 04113v1 Announce Type: new Abstract: Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $\sigma_{\min}$, at which the score is stiff and the flow develops a boundary layer.
By Shiheng Zhang
Diffusion and flow-matching samplers integrate a learned probability-flow ODE from a large noise scale down to a small terminal floor $σ_{\min}$, at which the score is stiff and the flow develops a boundary layer. We treat $σ_{\min}$ as a singular-perturbation parameter and determine which fixed-step samplers are asymptotic-preserving (AP), that is, stable and uniformly accurate as $σ_{\min}\to0$, casting the criteria as an a posteriori audit: residual functionals with $σ_{\min}$-uniform coefficients, computable on a pretrained checkpoint without ground-truth scores or exact trajectories.