This paper presents the geometric aspect of the autoencoder framework, which,
despite its importance, has been relatively less recognized. Given a set of
high-dimensional data points that approximately lie on some lower-dimensional
manifold, an autoencoder learns the \textit{manifold} and its
\textit{coordinate chart}, simultaneously. This geometric perspective naturally
raises inquiries like "Does a finite set of data points correspond to a single
manifold?" or "Is there only one coordinate chart that can represent the
manifold?". The responses to these questions are negative, implying that there
are multiple solution autoencoders given a dataset. Consequently, they
sometimes produce incorrect manifolds with severely distorted latent space
representations. In this paper, we introduce recent geometric approaches that
address these issues.

这篇论文介绍了自编码器框架的几何方面，强调了它的重要性，同时提出了一些解决这些问题的几何方法。

自动编码器的几何视角

A Geometric Perspective on Autoencoders

While many phenomena in physics and engineering are formally
high-dimensional, their long-time dynamics often live on a lower-dimensional
manifold. The present work introduces an autoencoder framework that combines
implicit regularization with internal linear layers and $L_2$ regularization
(weight decay) to automatically estimate the underlying dimensionality of a
data set, produce an orthogonal manifold coordinate system, and provide the
mapping functions between the ambient space and manifold space, allowing for
out-of-sample projections. We validate our framework's ability to estimate the
manifold dimension for a series of datasets from dynamical systems of varying
complexities and compare to other state-of-the-art estimators. We analyze the
training dynamics of the network to glean insight into the mechanism of
low-rank learning and find that collectively each of the implicit regularizing
layers compound the low-rank representation and even self-correct during
training. Analysis of gradient descent dynamics for this architecture in the
linear case reveals the role of the internal linear layers in leading to faster
decay of a "collective weight variable" incorporating all layers, and the role
of weight decay in breaking degeneracies and thus driving convergence along
directions in which no decay would occur in its absence. We show that this
framework can be naturally extended for applications of state-space modeling
and forecasting by generating a data-driven dynamic model of a spatiotemporally
chaotic partial differential equation using only the manifold coordinates.
Finally, we demonstrate that our framework is robust to hyperparameter choices.

本文介绍了一个自编码器框架，结合隐式正则化和内部线性层，自动估计数据集的底层维度，生成正交流形坐标系，并提供周围空间和流形空间之间的映射函数，为拓展样本作出一定的贡献，展示了该框架在各种数据集中对流形维度的能够自动估计，分析了该架构的梯度下降动态，以及扩展到状态空间建模和预测的应用，并证明了该框架对超参数选择的鲁棒性。

用于发现复杂动力系统数据中 Manifold 的维度和坐标的自编码器

Autoencoders for discovering manifold dimension and coordinates in data  from complex dynamical systems

Gait, the walking pattern of individuals, is one of the most important
biometrics modalities. Most of the existing gait recognition methods take
silhouettes or articulated body models as the gait features. These methods
suffer from degraded recognition performance when handling confounding
variables, such as clothing, carrying and view angle. To remedy this issue, we
propose a novel AutoEncoder framework to explicitly disentangle pose and
appearance features from RGB imagery and the LSTM-based integration of pose
features over time produces the gait feature. In addition, we collect a
Frontal-View Gait (FVG) dataset to focus on gait recognition from frontal-view
walking, which is a challenging problem since it contains minimal gait cues
compared to other views. FVG also includes other important variations, e.g.,
walking speed, carrying, and clothing. With extensive experiments on CASIA-B,
USF and FVG datasets, our method demonstrates superior performance to the state
of the arts quantitatively, the ability of feature disentanglement
qualitatively, and promising computational efficiency.

该研究提出一种基于 AutoEncoder 框架、利用 RGB 成像中的姿态和外貌特征，以及对前方视角步行进行重点研究的 FVG 数据集来辅助鲁棒的步态识别方法，通过在 CASIA-B，USF 和 FVG 数据集上的大量实验证明了该方法具有优秀的识别性能、特征解缠能力和有前途的计算效率。

基于解缠表示学习的步态识别

Gait Recognition via Disentangled Representation Learning

Generative Adversarial Networks (GAN) have received wide attention in the
machine learning field for their potential to learn high-dimensional, complex
real data distribution. Specifically, they do not rely on any assumptions about
the distribution and can generate real-like samples from latent space in a
simple manner. This powerful property leads GAN to be applied to various
applications such as image synthesis, image attribute editing, image
translation, domain adaptation and other academic fields. In this paper, we aim
to discuss the details of GAN for those readers who are familiar with, but do
not comprehend GAN deeply or who wish to view GAN from various perspectives. In
addition, we explain how GAN operates and the fundamental meaning of various
objective functions that have been suggested recently. We then focus on how the
GAN can be combined with an autoencoder framework. Finally, we enumerate the
GAN variants that are applied to various tasks and other fields for those who
are interested in exploiting GAN for their research.

本文主要讨论生成对抗网络的应用和基本操作，介绍了 GAN 如何学习高维度、复杂的真实数据分布，并不需要假设分布，同时讨论了 GAN 加入自动编码器框架、用于图像合成、图像编辑和分布学习等多种变体。