arXiv subjects

Zhehao Xu

Publications and source records attributed to Zhehao Xu.

6 recordsLinked to original sources

arXiv2026

Computational and Statistical Guarantees of the \textit{c}-Rectified flow

Recently, rectified flow has emerged as a fundamental framework for large-scale image generation, powering state-of-the-art systems such as FLUX.1 and Stable Diffusion 3. Despite its remarkable empirical success, the computational and statistical guarantees of iterative rectified flow have remained largely unexplored. We address this problem by studying \textit{c}-rectified flow, a cost-aware class of rectified flow that projects velocity fields onto a gradient class while preserving endpoint marginals. The ordinary rectified flow can fail to recover the optimal transport coupling: in a Gaussian case study, the iteration converges to the optimal coupling if and only if the source and target covariance matrices commute. In contrast, under suitable compactness and uniform-integrability assumptions, iterative \textit{c}-rectified flow always converges to the optimal transport coupling. We further establish quantitative one-step contraction and exponential convergence guarantees under projection-stability assumptions for both quadratic and strongly convex displacement costs. Finally, under a H\"older ball assumption, we develop new minimax-optimal score estimation rates and show that, when combined with iterative \textit{c}-rectified flow, they yield a rate-optimal estimator of the optimal transport for the dimension $d \ge 3$ and a nearly parametric rate for $d=1,2$.

stat.ML↗

arXiv2026

Free-Boundary Quasiconformal Maps via a Least-squares Operator in Diffeomorphism Optimization

Free-boundary diffeomorphism optimization, an important and widely occurring task in geometric modeling, computer graphics, and biological imaging, requires simultaneously determining a planar target domain and a locally bijective map with well-controlled distortion. We formulate this task through the least-squares quasiconformal (LSQC) operator and establish key structural properties of the LSQC minimizer, including well-posedness under mild conditions, invariance under similarity transformations, and resolution-independent behavior with stability under mesh refinement. We further analyze the sensitivity of the LSQC solution with respect to the Beltrami coefficient, establishing stability and differentiability properties that enable gradient-based optimization over the space of Beltrami coefficients. To make this differentiable formulation practical at scale and to facilitate the optimization process, we introduce the Spectral Beltrami Network (SBN), a multiscale mesh-spectral surrogate that approximates the LSQC solution operator in a single differentiable forward pass. This yields SBN-Opt, an optimization framework that searches over admissible Beltrami coefficients and pinning conditions to solve free-boundary diffeomorphism objectives with explicit distortion control. Extensive experiments on equiareal parameterization and inconsistent surface registration demonstrate consistent improvements over traditional numerical algorithms.

cs.LG↗

arXiv2026

Two-chart Beltrami Optimization for Distortion-Controlled Spherical Bijection with Application to Brain Surface Registration

Many genus-0 surface mapping tasks such as landmark alignment, feature matching, and image-driven registration, can be reduced (via an initial spherical conformal map) to optimizing a spherical self-homeomorphism with controlled distortion. However, existing works lack efficient mechanisms to control the geometric distortion of the resulting mapping. To resolve this issue, we formulate this as a Beltrami-space optimization problem, where the angle distortion is encoded explicitly by the Beltrami differential and bijectivity can be enforced through the constraint $\|μ\|_{\infty}<1$. To make this practical on the sphere, we introduce the Spherical Beltrami Differential (SBD), a two-chart representation of quasiconformal self-maps of the unit sphere $\mathbb{S}^2$, together with cross-chart consistency conditions that yield a globally bijective spherical deformation (up to conformal automorphisms). Building on the Spectral Beltrami Network, we develop BOOST, a differentiable optimization framework that updates two Beltrami fields to minimize task-driven losses while regularizing distortion and enforcing consistency along the seam. Experiments on large-deformation landmark matching and intensity-based spherical registration demonstrate improved task performance meanwhile maintaining controlled distortion and robust bijective behavior. We also apply the method to cortical surface registration by aligning sulcal landmarks and matching cortical sulcal depth, achieving comparative or better registration performance without sacrificing geometric validity.

cs.GR↗

arXiv2025

Optical coherence and hyperfine structure of the 7F0-5D0 transition in EuCaWO4

Rare-earth ions doped in crystals with low nuclear-spin densities are highly promising candidates for quantum technology applications. In this study, we investigated the spectroscopic properties of the 7F0 - 5 D0 optical and the hyperfine transitions of Eu3+ ions in a CaWO4 crystal, where the nuclear spin arises solely from the 183W isotope, with a natural abundance of 14%. At a temperature of 3 K, we experimentally identified four distinct crystal field environments for Eu3+ ions in a 0.1 at.% Eu3+ doped CaWO4 crystal. The optical coherence properties of Eu3+ ions in these environments were characterized. Additionally, we resolved the hyperfine structures in the 7F0 ground state and 5D0 excited state, and determined the 7F0 ground state lifetimes using spectral hole-burning techniques. These findings highlight the significant potential of Eu3+:CaWO4 for optical quantum memory applications.

cond-mat.mtrl-sci↗

arXiv2024

From optimal score matching to optimal sampling

The recent, impressive advances in algorithmic generation of high-fidelity image, audio, and video are largely due to great successes in score-based diffusion models. A key implementing step is score matching, that is, the estimation of the score function of the forward diffusion process from training data. As shown in earlier literature, the total variation distance between the law of a sample generated from the trained diffusion model and the ground truth distribution can be controlled by the score matching risk. Despite the widespread use of score-based diffusion models, basic theoretical questions concerning exact optimal statistical rates for score estimation and its application to density estimation remain open. We establish the sharp minimax rate of score estimation for smooth, compactly supported densities. Formally, given $n$ i.i.d. samples from an unknown $α$-Hölder density $f$ supported on $[-1, 1]$, we prove the minimax rate of estimating the score function of the diffused distribution $f * \mathcal{N}(0, t)$ with respect to the score matching loss is $\frac{1}{nt^2} \wedge \frac{1}{nt^{3/2}} \wedge (t^{α-1} + n^{-2(α-1)/(2α+1)})$ for all $α> 0$ and $t \ge 0$. As a consequence, it is shown the law $\hat{f}$ of a sample generated from the diffusion model achieves the sharp minimax rate $\bE(\dTV(\hat{f}, f)^2) \lesssim n^{-2α/(2α+1)}$ for all $α> 0$ without any extraneous logarithmic terms which are prevalent in the literature, and without the need for early stopping which has been required for all existing procedures to the best of our knowledge.

stat.ML↗

arXiv2024

Line identification of extreme ultraviolet spectra from aluminum ions in EAST Tokamak plasmas

Extreme ultraviolet (EUV) spectra emitted from aluminum in the 5-340 A wavelength range were observed in Experimental Advanced Superconducting Tokamak (EAST) discharges. Several spectral lines from aluminum ions with different degrees of ionization were successfully observed with sufficient spectral intensities and resolutions using three fast-time-response EUV spectrometers. The line identification uses three independent state-of-art computational codes for the atomic structure calculations, which provide the wavelengths and radiative transition probabilities rate coefficients. These programs are HULLAC (Hebrew University - Lawrence Livermore Atomic Code), AUTOSTRUCTURE, and FAC (Flexible Atomic Code). Using three different codes allows us to resolve some ambiguities in identifying certain spectral lines and assess the validity of the theoretical predictions.

physics.plasm-ph↗