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
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.
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.
By Guoqing Zhang, Zhaixin Chen
The paper investigates how hard‑ReLU training behaves when perturbations have a finite radius. It shows that the usual infinitesimal sensitivities are insufficient to predict the response at a chosen radius, and it characterizes the intermediate regime where the perturbation radius scales with the gradient‑descent step. The authors derive crossing indices, a uniform endpoint expansion for separated transverse events, and provide explicit remainder terms in contractive affine regions to certify finite candidate comparisons, supported by experiments on nonlinear networks.
By Xiaoyang Li, Runni Zhou, Xinghao Yan