Quantification of the number of variables needed to locally explain complex
data is often the first step to better understanding it. Existing techniques
from intrinsic dimension estimation leverage statistical models to glean this
information from samples within a neighborhood. However, existing methods often
rely on well-picked hyperparameters and ample data as manifold dimension and
curvature increases. Leveraging insight into the fixed point of the score
matching objective as the score map is regularized by its Dirichlet energy, we
show that it is possible to retrieve the topological dimension of the manifold
learned by the score map. We then introduce a novel method to measure the
learned manifold's topological dimension (i.e., local intrinsic dimension)
using adversarial attacks, thereby generating useful interpretations of the
learned manifold.

利用对得分映射的固定点 insight，通过利用对应的狄利克雷能量进行正则化将其前提条件确认为对潜在 manifold 学习的拓扑维度进行回归是可能的，然后引入了一种使用对抗性攻击来测量学习的 manifold 的拓扑维度的新方法，从而产生对学习的 manifold 的有用解释。

用对抗方法估计拓扑维度的谐波评分图

Adversarial Estimation of Topological Dimension with Harmonic Score Maps

This work studies the problem of few-shot object counting, which counts the
number of exemplar objects (i.e., described by one or several support images)
occurring in the query image. The major challenge lies in that the target
objects can be densely packed in the query image, making it hard to recognize
every single one. To tackle the obstacle, we propose a novel learning block,
equipped with a similarity comparison module and a feature enhancement module.
Concretely, given a support image and a query image, we first derive a score
map by comparing their projected features at every spatial position. The score
maps regarding all support images are collected together and normalized across
both the exemplar dimension and the spatial dimensions, producing a reliable
similarity map. We then enhance the query feature with the support features by
employing the developed point-wise similarities as the weighting coefficients.
Such a design encourages the model to inspect the query image by focusing more
on the regions akin to the support images, leading to much clearer boundaries
between different objects. Extensive experiments on various benchmarks and
training setups suggest that we surpass the state-of-the-art methods by a
sufficiently large margin. For instance, on a recent large-scale FSC-147
dataset, we surpass the state-of-the-art method by improving the mean absolute
error from 22.08 to 14.32 (35%$\uparrow$). Code has been released in
this https URL

本文提出了一种针对少样本目标计数的新型学习模块，其中包括相似性比较模块和特征增强模块，通过得分图，利用支持图像和查询图像来增强查询特征，大大提高了目标计数的精度和效率，成果优于现有最先进技术

相似性感知特征增强的小样本目标计数

Few-shot Object Counting with Similarity-Aware Feature Enhancement

Face detection is challenging as faces in images could be present at
arbitrary locations and in different scales. We propose a three-stage cascade
structure based on fully convolutional neural networks (FCNs). It first
proposes the approximate locations where the faces may be, then aims to find
the accurate location by zooming on to the faces. Each level of the FCN cascade
is a multi-scale fully-convolutional network, which generates scores at
different locations and in different scales. A score map is generated after
each FCN stage. Probable regions of face are selected and fed to the next
stage. The number of proposals is decreased after each level, and the areas of
regions are decreased to more precisely fit the face. Compared to passing
proposals directly between stages, passing probable regions can decrease the
number of proposals and reduce the cases where first stage doesn't propose good
bounding boxes. We show that by using FCN and score map, the FCN cascade face
detector can achieve strong performance on public datasets.

本研究提出一种基于全卷积神经网络的三级级联结构，采用多尺度全卷积网络生成得分图，使用可能区域而非建议直接连接下一级级联，通过使用得分图可以在公共数据集上获得强大的人脸检测性能。