arXiv subjects

Qianyu Chen

Publications and source records attributed to Qianyu Chen.

29 records · Page 2Linked to original sources

arXiv2024

CoCoCo: Improving Text-Guided Video Inpainting for Better Consistency, Controllability and Compatibility

Recent advancements in video generation have been remarkable, yet many existing methods struggle with issues of consistency and poor text-video alignment. Moreover, the field lacks effective techniques for text-guided video inpainting, a stark contrast to the well-explored domain of text-guided image inpainting. To this end, this paper proposes a novel text-guided video inpainting model that achieves better consistency, controllability and compatibility. Specifically, we introduce a simple but efficient motion capture module to preserve motion consistency, and design an instance-aware region selection instead of a random region selection to obtain better textual controllability, and utilize a novel strategy to inject some personalized models into our CoCoCo model and thus obtain better model compatibility. Extensive experiments show that our model can generate high-quality video clips. Meanwhile, our model shows better motion consistency, textual controllability and model compatibility. More details are shown in [cococozibojia.github.io](cococozibojia.github.io).

cs.CV↗

arXiv2024

V-filtrations and minimal exponents for locally complete intersection singularities

We define and study a notion of minimal exponent for a locally complete intersection subscheme $Z$ of a smooth complex algebraic variety $X$, extending the invariant defined by Saito in the case of hypersurfaces. Our definition is in terms of the Kashiwara-Malgrange $V$-filtration associated to $Z$. We show that the minimal exponent describes how far the Hodge filtration and order filtration agree on the local cohomology $H^r_Z({\mathcal O}_X)$, where $r$ is the codimension of $Z$ in $X$. We also study its relation to the Bernstein-Sato polynomial of $Z$. Our main result describes the minimal exponent of a higher codimension subscheme in terms of the invariant associated to a suitable hypersurface; this allows proving the main properties of this invariant by reduction to the codimension $1$ case. A key ingredient for our main result is a description of the Kashiwara-Malgrange $V$-filtration associated to any ideal $(f_1,\ldots,f_r)$ in terms of the microlocal $V$-filtration associated to the hypersurface defined by $\sum_{i=1}^rf_iy_i$.

math.AG↗

arXiv2024

Prediction of vaccination coverage level in the heterogeneous mixing population

Heterogeneity of population is a key factor in modeling the transmission of disease among the population and has huge impact on the outcome of the transmission. In order to investigate the decision making process in the heterogeneous mixing population regarding whether to be vaccinated or not, we propose the modeling framework which includes the epidemic models and the game theoretical analysis. We consider two sources of heterogeneity in this paper: the different activity levels and the different relative vaccination costs. It is interesting to observe that, if both sources of heterogeneity are considered, there exist a finite number of Nash equilibria (evolutionary stable strategies (ESS)) of the vaccination game. While if only the difference of activity levels is considered, there are infinitely many Nash equilibira. For the latter case, the initial condition of the decision making process becomes highly sensitive. In the application of public health management, the inclusion of population heterogeneity significantly complicates the prediction of the overall vaccine coverage level.

q-bio.PE↗

arXiv2024

Inversion of Adjunction for the minimal exponent

We prove that the minimal exponent for local complete intersections satisfies an Inversion-of-Adjunction property. As a result, we also obtain the Inversion of Adjunction for higher Du Bois and higher rational singularities for local complete intersections.

math.AG↗

arXiv2024

An introduction to $V$-filtrations

We give an introduction to the theory of $V$-filtrations of Malgrange and Kashiwara. After discussing the basic properties of this construction (in the case of a smooth hypersurface and, later, in the general case), we describe the connection with the theory of $b$-functions. As an example, we treat the case of weighted homogeneous isolated singularities. We discuss the compatibility of $V$-filtrations with proper push-forward and duality and the connection with nearby and vanishing cycles via the Riemann-Hilbert correspondence. We end by describing some invariants of singularities via the $V$-filtration.

math.AG↗

arXiv2023

Limits of Hodge structures via holonomic D-modules

We construct the limiting mixed Hodge structure of a degeneration of compact Kähler manifolds over the unit disk with a possibly non-reduced simple normal crossing singular central fiber via holonomic $\mathscr D$-modules, generalizing some results of Steenbrink. Our limiting mixed Hodge structure does not carry a $\mathbb Q$-structure; instead, we use sesquilinear pairings on $\mathscr D$-modules as a replacement. The limiting mixed Hodge structure can be computed by the cohomology of the cyclic coverings of certain intersections of components of the central fiber. Additionally, we prove the local invariant cycle theorem in this setting.

math.AG↗

arXiv2023

Verdier specialization and restrictions of Hodge modules

We give an explicit formula to express the cohomological pullback functors of Hodge modules under closed immersions of smooth varieties using Verdier specializations and $V$-filtrations of Kashiwara and Malgrange. This was locally obtained by the first two authors assuming the existence of global defining functions. We also give a quite simplified proof of the theorem reducing to the monodromical case via the Verdier specialization and using induction on codimension.

math.AG↗

arXiv2023

The minimal exponent and $k$-rationality for local complete intersections

We show that if $Z$ is a local complete intersection subvariety of a smooth complex variety $X$, of pure codimension $r$, then $Z$ has $k$-rational singularities if and only if $\widetildeα(Z)>k+r$, where $\widetildeα(Z)$ is the minimal exponent of $Z$. We also characterize this condition in terms of the Hodge filtration on the intersection cohomology Hodge module of $Z$. Furthermore, we show that if $Z$ has $k$-rational singularities, then the Hodge filtration on the local cohomology sheaf $\mathcal{H}^r_Z(\mathcal{O}_X)$ is generated at level $\dim(X)-\lceil \widetildeα(Z)\rceil-1$ and, assuming that $k\geq 1$ and $Z$ is singular, of dimension $d$, that $\mathcal{H}^k(\underlineΩ_Z^{d-k})\neq 0$. All these results have been known for hypersurfaces in smooth varieties.

math.AG↗

arXiv2023

On $V$-filtration, Hodge filtration and Fourier transform

For $i : Z \to X$ a closed immersion of smooth varieties, we study how the $V$-filtration along $Z$ and the Hodge filtration on a mixed Hodge module $M$ on $X$ interact with each other. We also give a formula for the functors $i^*$, $i^!$ in terms of this $V$-filtration. As applications, we obtain results on the Hodge filtration of monodromic mixed Hodge modules and we give a Hodge theoretic proof of Skoda's theorem on multiplier ideals. Finally, we use the results to study the Fourier-Laplace transform of a monodromic mixed Hodge module.

math.AG↗

arXiv2022

PEVL: Position-enhanced Pre-training and Prompt Tuning for Vision-language Models

Vision-language pre-training (VLP) has shown impressive performance on a wide range of cross-modal tasks, where VLP models without reliance on object detectors are becoming the mainstream due to their superior computation efficiency and competitive performance. However, the removal of object detectors also deprives the capability of VLP models in explicit object modeling, which is essential to various position-sensitive vision-language (VL) tasks, such as referring expression comprehension and visual commonsense reasoning. To address the challenge, we introduce PEVL that enhances the pre-training and prompt tuning of VLP models with explicit object position modeling. Specifically, PEVL reformulates discretized object positions and language in a unified language modeling framework, which facilitates explicit VL alignment during pre-training, and also enables flexible prompt tuning for various downstream tasks. We show that PEVL enables state-of-the-art performance of detector-free VLP models on position-sensitive tasks such as referring expression comprehension and phrase grounding, and also improves the performance on position-insensitive tasks with grounded inputs. We make the data and code for this paper publicly available at https://github.com/thunlp/PEVL.

cs.CV↗

arXiv2022

Fine-Grained Scene Graph Generation with Data Transfer

Scene graph generation (SGG) is designed to extract (subject, predicate, object) triplets in images. Recent works have made a steady progress on SGG, and provide useful tools for high-level vision and language understanding. However, due to the data distribution problems including long-tail distribution and semantic ambiguity, the predictions of current SGG models tend to collapse to several frequent but uninformative predicates (e.g., on, at), which limits practical application of these models in downstream tasks. To deal with the problems above, we propose a novel Internal and External Data Transfer (IETrans) method, which can be applied in a plug-and-play fashion and expanded to large SGG with 1,807 predicate classes. Our IETrans tries to relieve the data distribution problem by automatically creating an enhanced dataset that provides more sufficient and coherent annotations for all predicates. By training on the enhanced dataset, a Neural Motif model doubles the macro performance while maintaining competitive micro performance. The code and data are publicly available at https://github.com/waxnkw/IETrans-SGG.pytorch.

cs.CV↗