Related papers: Deep Manifold Transformation for Nonlinear Dimensi…
Deep learning models have proven enormously successful at using multiple layers of representation to learn relevant features of structured data. Encoding physical symmetries into these models can improve performance on difficult tasks, and…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
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…
Existing EEG foundation models mainly treat neural signals as generic time series in Euclidean space, ignoring the intrinsic geometric structure of neural dynamics that constrains brain activity to low-dimensional manifolds. This…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
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…
Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input to these networks lie in a vector space and the operations…
We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…
Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…
Deep neural networks (DNNs) provide useful models of visual representational transformations. We present a method that enables a DNN (student) to learn from the internal representational spaces of a reference model (teacher), which could be…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Despite significant advances in the field of deep learning in applications to various fields, explaining the inner processes of deep learning models remains an important and open question. The purpose of this article is to describe and…
Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists in training composite architectures in an end-to-end…
Deep neural networks (DNNs) are becoming increasingly deeper, wider, and non-linear due to the growing demands on prediction accuracy and analysis quality. When training a DNN model, the intermediate activation data must be saved in the…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
Nonlinear manifold learning from unorganized data points is a very challenging unsupervised learning and data visualization problem with a great variety of applications. In this paper we present a new algorithm for manifold learning and…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
Neural Metamorphosis (NeuMeta) is a recent paradigm for generating neural networks of varying width and depth. Based on Implicit Neural Representation (INR), NeuMeta learns a continuous weight manifold, enabling the direct generation of…
This paper introduces MDP homomorphic networks for deep reinforcement learning. MDP homomorphic networks are neural networks that are equivariant under symmetries in the joint state-action space of an MDP. Current approaches to deep…
Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational…