We analyze the Wasserstein distance ($W$-distance) between two probability
distributions associated with two multidimensional jump-diffusion processes.
Specifically, we analyze a temporally decoupled squared $W_2$-distance, which
provides both upper and lower bounds associated with the discrepancies in the
drift, diffusion, and jump amplitude functions between the two jump-diffusion
processes. Then, we propose a temporally decoupled squared $W_2$-distance
method for efficiently reconstructing unknown jump-diffusion processes from
data using parameterized neural networks. We further show its performance can
be enhanced by utilizing prior information on the drift function of the
jump-diffusion process. The effectiveness of our proposed reconstruction method
is demonstrated across several examples and applications.

通过分析两个多维跳扩散过程的概率分布之间的 Wasserstein 距离（W - 距离），我们提出了一种时间解耦的平方 W_2 - 距离方法，该方法提供了与两个跳扩散过程的漂移、扩散和跳跃幅度函数之间的差异相关的上下界。然后，我们利用参数化神经网络从数据中高效重建未知的跳扩散过程，并展示了通过利用跳扩散过程的漂移函数的先验信息可以提高其性能。我们还通过几个示例和应用程序演示了我们提出的重建方法的有效性。

使用参数化神经网络重建跳跃扩散过程的高效瓦辛斯坦距离方法

An efficient Wasserstein-distance approach for reconstructing  jump-diffusion processes using parameterized neural networks

This paper presents a novel reconstruction method that leverages Diffusion
Models to protect machine learning classifiers against adversarial attacks, all
without requiring any modifications to the classifiers themselves. The
susceptibility of machine learning models to minor input perturbations renders
them vulnerable to adversarial attacks. While diffusion-based methods are
typically disregarded for adversarial defense due to their slow reverse
process, this paper demonstrates that our proposed method offers robustness
against adversarial threats while preserving clean accuracy, speed, and
plug-and-play compatibility. Code at:
this https URL

这篇论文提出了一种新的重建方法，利用扩散模型来保护机器学习分类器免受对抗攻击，而无需对分类器本身进行任何修改。

DiffDefense: 通过扩散模型抵御对抗性攻击

DiffDefense: Defending against Adversarial Attacks via Diffusion Models

Animating an object in 3D often requires an articulated structure, e.g. a
kinematic chain or skeleton of the manipulated object with proper skinning
weights, to obtain smooth movements and surface deformations. However, existing
models that allow direct pose manipulations are either limited to specific
object categories or built with specialized equipment. To reduce the work
needed for creating animatable 3D models, we propose a novel reconstruction
method that learns an animatable kinematic chain for any articulated object.
Our method operates on monocular videos without prior knowledge of the object's
shape or underlying structure. Our approach is on par with state-of-the-art 3D
surface reconstruction methods on various articulated object categories while
enabling direct pose manipulations by re-posing the learned kinematic chain.

提出一种新的重建方法，可以学习任何物品的动画运动学链，不需要事先了解物品的形状或基础结构，能够实现直接姿势操纵，并在各种复杂的关节对象类型上获得与最先进的三维表面重建方法相当的表现。

从单目视频中构建类别不可知和可动画的三维模型：CAMM

CAMM: Building Category-Agnostic and Animatable 3D Models from Monocular  Videos

We present a strong lensing modeling technique based on versatile basis sets
for the lens and source planes. Our method uses high performance Monte Carlo
algorithms, allows for an adaptive build up of complexity and bridges the gap
between parametric and pixel based reconstruction methods. We apply our method
to a HST image of the strong lens system RXJ1131-1231 and show that our method
finds a reliable solution and is able to detect substructure in the lens and
source planes simultaneously. Using mock data we show that our method is
sensitive to sub-clumps with masses four orders of magnitude smaller than the
main lens, which corresponds to about $10^8 M_{\odot}$, without prior knowledge
on the position and mass of the sub-clump. The modelling approach is flexible
and maximises automation to facilitate the analysis of the large number of
strong lensing systems expected in upcoming wide field surveys. The resulting
search for dark sub-clumps in these systems, without mass-to-light priors,
offers promise for probing physics beyond the standard model in the dark matter
sector.

本文提出基于万能基组的强透镜建模方法，使用高性能蒙特卡罗算法，桥接参数化与像素化重建方法的差距，可发现镜中和源面的亚结构，跨度范围宽，为大规模强透镜天体观测提供了新方法。