Related papers: Exploring the Manifold of Neural Networks Using Di…

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 neural networks implement a sequence of layer-by-layer operations that are each relatively easy to understand, but the resulting overall computation is generally difficult to understand. We consider a simple hypothesis for interpreting…

We present a new nonlinear dimensionality reduction method, MAPLE, that enhances UMAP by improving manifold modeling. MAPLE employs a self-supervised learning approach to more efficiently encode low-dimensional manifold geometry. Central to…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Neural networks can be thought of as applying a transformation to an input dataset. The way in which they change the topology of such a dataset often holds practical significance for many tasks, particularly those demanding non-homeomorphic…

Current theoretical and empirical research in neural networks suggests that complex datasets require large network architectures for thorough classification, yet the precise nature of this relationship remains unclear. This paper tackles…

Understanding the reasons for the success of deep neural networks trained using stochastic gradient-based methods is a key open problem for the nascent theory of deep learning. The types of data where these networks are most successful,…

The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…

Neuroevolution is an alternative to gradient-based optimisation that has the potential to avoid local minima and allows parallelisation. The main limiting factor is that usually it does not scale well with parameter space dimensionality.…

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…

Deep neural networks (DNNs) have shown much empirical success in solving perceptual tasks across various cognitive modalities. While they are only loosely inspired by the biological brain, recent studies report considerable similarities…

We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…

We propose a manifold matching approach to generative models which includes a distribution generator (or data generator) and a metric generator. In our framework, we view the real data set as some manifold embedded in a high-dimensional…

As a pivotal branch of machine learning, manifold learning uncovers the intrinsic low-dimensional structure within complex nonlinear manifolds in high-dimensional space for visualization, classification, clustering, and gaining key…

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…

Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

Understanding how neural systems efficiently process information through distributed representations is a fundamental challenge at the interface of neuroscience and machine learning. Recent approaches analyze the statistical and geometrical…