Autoencoding Dynamics: Topological Limitations and Capabilities
Given a "data manifold" $M\subset \mathbb{R}^n$ and "latent space" $\mathbb{R}^\ell$, an autoencoder is a pair of continuous maps consisting of an "encoder" $E\colon \mathbb{R}^n\to \mathbb{R}^\ell$ and "decoder" $D\colon \mathbb{R}^\ell\to \mathbb{R}^n$ such that the "round trip" map $D\circ E$ is as close as possible to the identity map $\mbox{id}_M$ on $M$. We present various topological limitations and capabilites inherent to the search for an autoencoder, and describe capabilities for autoencoding dynamical systems having $M$ as an invariant manifold.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Koopman Autoencoders Learn Neural Representation Dynamics
This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through …
Analysis on the Nonlinear Dynamics of Deep Neural Networks: Topological Entropy and Chaos
The theoretical explanation for deep neural network (DNN) is still an open problem. In this paper DNN is considered as a discrete-time dynamical system due to its layered structure. The complexity provided by the nonline…
General ClassificationVAMAE: Vessel-Aware Masked Autoencoders for OCT Angiography
Optical coherence tomography angiography (OCTA) provides non-invasive visualization of retinal microvasculature, but learning robust representations remains challenging due to sparse vessel structures and strong topologi…
Self-Supervised LearningData-driven model reconstruction for nonlinear wave dynamics
The use of machine learning to predict wave dynamics is a topic of growing interest, but commonly-used deep learning approaches suffer from a lack of interpretability of the trained models. Here we present an interpretab…
Interpretable Machine LearningmodelTopology-Aware Latent Diffusion for 3D Shape Generation
We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves repre…
3D Shape GenerationDiversityNavigate