In computer vision, keypoint detection is a fundamental task, with
applications spanning from robotics to image retrieval; however, existing
learning-based methods suffer from scale dependency and lack flexibility. This
paper introduces a novel approach that leverages Morse theory and persistent
homology, powerful tools rooted in algebraic topology. We propose a novel loss
function based on the recent introduction of a notion of subgradient in
persistent homology, paving the way toward topological learning. Our detector,
MorseDet, is the first topology-based learning model for feature detection,
which achieves competitive performance in keypoint repeatability and introduces
a principled and theoretically robust approach to the problem.

介绍了一种基于 Morse 理论和持续同调的新颖方法，该方法在计算机视觉中应用于特征检测，具有竞争性的关键点可重复性和理论上鲁棒性的方法。

使用可微持久同调的无标度图像关键点

Scale-Free Image Keypoints Using Differentiable Persistent Homology

Masked graph autoencoders have emerged as a powerful graph self-supervised
learning method that has yet to be fully explored. In this paper, we unveil
that the existing discrete edge masking and binary link reconstruction
strategies are insufficient to learn topologically informative representations,
from the perspective of message propagation on graph neural networks. These
limitations include blocking message flows, vulnerability to over-smoothness,
and suboptimal neighborhood discriminability. Inspired by these understandings,
we explore non-discrete edge masks, which are sampled from a continuous and
dispersive probability distribution instead of the discrete Bernoulli
distribution. These masks restrict the amount of output messages for each edge,
referred to as "bandwidths". We propose a novel, informative, and effective
topological masked graph autoencoder using bandwidth masking and a layer-wise
bandwidth prediction objective. We demonstrate its powerful graph topological
learning ability both theoretically and empirically. Our proposed framework
outperforms representative baselines in both self-supervised link prediction
(improving the discrete edge reconstructors by at most 20%) and node
classification on numerous datasets, solely with a structure-learning pretext.
Our implementation is available at this https URL

使用带宽掩蔽和逐层带宽预测目标，我们提出了一种新颖且有效的拓扑掩蔽图自编码器，理论上和经验上证明了其强大的图拓扑学习能力，通过自我监督的链接预测和节点分类，在各种数据集上优于代表性的基准模型。

具有非离散带宽的掩盖图自编码器

Masked Graph Autoencoder with Non-discrete Bandwidths

The understanding of toxicity is of paramount importance to human health and
environmental protection. Quantitative toxicity analysis has become a new
standard in the field. This work introduces element specific persistent
homology (ESPH), an algebraic topology approach, for quantitative toxicity
prediction. ESPH retains crucial chemical information during the topological
abstraction of geometric complexity and provides a representation of small
molecules that cannot be obtained by any other method. To investigate the
representability and predictive power of ESPH for small molecules, ancillary
descriptors have also been developed based on physical models. Topological and
physical descriptors are paired with advanced machine learning algorithms, such
as deep neural network (DNN), random forest (RF) and gradient boosting decision
tree (GBDT), to facilitate their applications to quantitative toxicity
predictions. A topology based multi-task strategy is proposed to take the
advantage of the availability of large data sets while dealing with small data
sets. Four benchmark toxicity data sets that involve quantitative measurements
are used to validate the proposed approaches. Extensive numerical studies
indicate that the proposed topological learning methods are able to outperform
the state-of-the-art methods in the literature for quantitative toxicity
analysis. Our online server for computing element-specific topological
descriptors (ESTDs) is available at this http URL

本研究基于持久同调和机器学习算法，提出了一种新的拓扑学方法 —— 元素特异性持久同调（ESPH），可用于小分子的毒性定量预测，并可优于现有方法。同时提出了一种基于拓扑学的多任务策略，并开发了计算带有元素特异性拓扑描述符（ESTDs）的在线服务器。