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Sining Wei

Publications and source records attributed to Sining Wei.

16 recordsLinked to original sources
arXiv2026

Hamiltonian-Type Spectral Functionals for Time-Dependent Perturbed Hodge--de Rham Operators

Let $g_t$ be a smooth family of Riemannian metrics on an oriented manifold of even dimension $n\geq4$, and let $D_t=d+δ_{g_t}+Ψ_t$ on the fixed exterior bundle, with $Ψ_t$ self-adjoint. We evaluate a scalar-weighted residue functional obtained from the operator expression in Hawkins' Hamiltonian action using the coefficient derivative $\partial_tD_t$. The velocity contribution depends only on $\partial_tg_t$. A direct symbol calculation reduces the lapse correction to a divergence and a Dirichlet term; for a nonconstant test function, integration by parts retains a mixed gradient term. For compact manifolds with a warped collar, we specify compatible factorizations of the weighted KKW term and of the commutator correction. Their boundary residues are computed explicitly. The collar-derivative and perturbation contributions cancel in the weighted KKW factorization, and the remaining boundary terms involve normal derivatives of the scalar weights. The closed formula is recovered when the boundary is empty.

math.DG↗
arXiv2026

The Bimetric generalization of Kastler--Kalau--Walze Type Theorems

Let $M^n$ be a closed oriented manifold of even dimension $n=2m\ge2$, equipped with a smooth metric $g_1$ and a Riemannian metric $g_2$. We compute the Wodzicki residue of $D_{g_1}^2D_{g_2}^{-n}$ on the common exterior bundle, where $D_{g_r}=d+δ_{g_r}$. This is the noncommutative integral of $D_{g_1}^2$ relative to the reference operator $D_{g_2}$. Its local density involves the curvatures of the two metrics and the difference of their Levi--Civita connections. Integration by parts gives a closed-manifold formula without explicit derivatives of the connection difference. For compact manifolds with boundary and $n\ge4$, we assume that both metrics are Riemannian and satisfy $g_r=h_r(x_n)^{-1}g^{\partial M}+dx_n^2$ near the boundary, with $h_r(0)=1$. We compute the noncommutative residues of two factorizations involving even and odd powers of $D_{g_2}$. Their interior contributions coincide, whereas their boundary terms are explicit multiples of the integral of $K_{g_1}-K_{g_2}$, with the coefficient for the even factorization twice that for the odd one. Here $K_{g_r}$ is the trace of the second fundamental form with respect to the inward unit normal. The calculation uses a second-order residue formula and direct boundary symbol expansions. When the metrics coincide, the formulas reduce to the Hodge--de Rham Kastler--Kalau--Walze identity.

math.DG↗
arXiv2026

RMSWeb: Reflection, Failure-Mode Mining, and Salvage-DS for Web Agent Reinforcement Learning

Compact web agents can reduce deployment cost, but training them poses challenges in both data collection and post-SFT reinforcement learning (RL). Successful trajectories are expensive to collect and often contain inefficient detours. After supervised fine-tuning (SFT), full trajectory corpora are dominated by routine states; moreover, when group-relative RL is applied to web actions, inadequately designed action-level rewards can yield weak or misleading relative updates, while groups rejected as unsuitable for such updates receive no fallback learning signal. We present RMSWeb, a three-part recipe for Qwen3-VL-Instruct at 8B and 32B. Reflection-conditioned retries increase collection yield and shorten successful trajectories; failure-mode mining concentrates offline RL on critical states exposed by the SFT policy; and Salvage-DS combines an action-semantic polarized reward, contrast-and-competence-gated dynamic sampling, and an action-only anchor for rejected groups. Policies trained with reflection-collected data use up to 19.7% fewer action steps on solved tasks. On WebVoyager, Online-Mind2Web, and WebTailBench, RMSWeb improves over SFT by 2.4-7.0 points at 8B and 1.2-7.7 points at 32B. Our 8B model also achieves the strongest reported Online-Mind2Web result among similarly sized open-weight models in our comparison and a leading reported accuracy-cost trade-off on WebVoyager and WebTailBench, with the caveat that external evaluation protocols differ.

cs.AI↗
arXiv2020

XGLUE: A New Benchmark Dataset for Cross-lingual Pre-training, Understanding and Generation

In this paper, we introduce XGLUE, a new benchmark dataset that can be used to train large-scale cross-lingual pre-trained models using multilingual and bilingual corpora and evaluate their performance across a diverse set of cross-lingual tasks. Comparing to GLUE(Wang et al., 2019), which is labeled in English for natural language understanding tasks only, XGLUE has two main advantages: (1) it provides 11 diversified tasks that cover both natural language understanding and generation scenarios; (2) for each task, it provides labeled data in multiple languages. We extend a recent cross-lingual pre-trained model Unicoder(Huang et al., 2019) to cover both understanding and generation tasks, which is evaluated on XGLUE as a strong baseline. We also evaluate the base versions (12-layer) of Multilingual BERT, XLM and XLM-R for comparison.

cs.CL↗
arXiv2020

Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane

In this paper, we compute sub-Riemannian limits of Gaussian curvature for a Euclidean $C^2$-smooth surface in the affine group and the group of rigid motions of the Minkowski plane away from characteristic points and signed geodesic curvature for Euclidean $C^2$-smooth curves on surfaces. We get Gauss-Bonnet theorems in the affine group and the group of rigid motions of the Minkowski plane.

math.DG↗
arXiv2019

PasteGAN: A Semi-Parametric Method to Generate Image from Scene Graph

Despite some exciting progress on high-quality image generation from structured(scene graphs) or free-form(sentences) descriptions, most of them only guarantee the image-level semantical consistency, i.e. the generated image matching the semantic meaning of the description. They still lack the investigations on synthesizing the images in a more controllable way, like finely manipulating the visual appearance of every object. Therefore, to generate the images with preferred objects and rich interactions, we propose a semi-parametric method, PasteGAN, for generating the image from the scene graph and the image crops, where spatial arrangements of the objects and their pair-wise relationships are defined by the scene graph and the object appearances are determined by the given object crops. To enhance the interactions of the objects in the output, we design a Crop Refining Network and an Object-Image Fuser to embed the objects as well as their relationships into one map. Multiple losses work collaboratively to guarantee the generated images highly respecting the crops and complying with the scene graphs while maintaining excellent image quality. A crop selector is also proposed to pick the most-compatible crops from our external object tank by encoding the interactions around the objects in the scene graph if the crops are not provided. Evaluated on Visual Genome and COCO-Stuff dataset, our proposed method significantly outperforms the SOTA methods on Inception Score, Diversity Score and Fréchet Inception Distance. Extensive experiments also demonstrate our method's ability to generate complex and diverse images with given objects.

cs.CV↗