相关论文: Markov-Lipschitz Deep Learning

We present a multimodal deep learning (MDL) framework for predicting physical properties of a 10-dimensional acrylic polymer composite material by merging physical attributes and chemical data. Our MDL model comprises four modules,…

Deep metric learning (DML) aims to learn a discriminative high-dimensional embedding space for downstream tasks like classification, clustering, and retrieval. Prior literature predominantly focuses on pair-based and proxy-based methods to…

Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

The task of building footprint segmentation has been well-studied in the context of remote sensing (RS) as it provides valuable information in many aspects, however, difficulties brought by the nature of RS images such as variations in the…

Deep Learning (DL) aims at learning the \emph{meaningful representations}. A meaningful representation refers to the one that gives rise to significant performance improvement of associated Machine Learning (ML) tasks by replacing the raw…

Combinatorial and topological structures, such as graphs, simplicial complexes, and cell complexes, form the foundation of geometric and topological deep learning (GDL and TDL) architectures. These models aggregate signals over such…

This survey is written in summer, 2016. The purpose of this survey is to briefly introduce nonlinear dimensionality reduction (NLDR) in data reduction. The first two NLDR were respectively published in Science in 2000 in which they solve…

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…

Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation.…

Protein engineering is experiencing a paradigmatic shift through the integration of geometric deep learning into computational design workflows. While traditional strategies, such as rational design and directed evolution, have enabled…

We propose Coordinate-based Internal Learning (CoIL) as a new deep-learning (DL) methodology for the continuous representation of measurements. Unlike traditional DL methods that learn a mapping from the measurements to the desired image,…

We are interested to explore the limit in using deep learning (DL) to study the electromagnetic response for complex and random metasurfaces, without any specific applications in mind. For simplicity, we focus on a simple pure reflection…

Deep learning (DL) is the state-of-the-art methodology in various medical image segmentation tasks. However, it requires relatively large amounts of manually labeled training data, which may be infeasible to generate in some applications.…

A data-driven framework is developed to represent chaotic dynamics on an inertial manifold (IM), and applied to solutions of the Kuramoto-Sivashinsky equation. A hybrid method combining linear and nonlinear (neural-network) dimension…

Magnetotelluric deep learning (DL) inversion methods based on joint data-driven and physics-driven have become a hot topic in recent years. When mapping observation data (or forward modeling data) to the resistivity model using neural…

This article provides an expository account of training dynamics in the Deep Linear Network (DLN) from the perspective of the geometric theory of dynamical systems. Rigorous results by several authors are unified into a thermodynamic…

Visual deep learning (VDL) systems have shown significant success in real-world applications like image recognition, object detection, and autonomous driving. To evaluate the reliability of VDL, a mainstream approach is software testing,…

Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…

Recent studies show that deep learning (DL) based MRI reconstruction outperforms conventional methods, such as parallel imaging and compressed sensing (CS), in multiple applications. Unlike CS that is typically implemented with…