Related papers: Embedding Inequalities for Barron-type Spaces

Attributes act as intermediate representations that enable parameter sharing between classes, a must when training data is scarce. We propose to view attribute-based image classification as a label-embedding problem: each class is embedded…

We investigate the approximation of functions $f$ on a bounded domain $\Omega\subset \mathbb{R}^d$ by the outputs of single-hidden-layer ReLU neural networks of width $n$. This form of nonlinear $n$-term dictionary approximation has been…

Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using…

Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be…

In this paper, we present a method of embedding physics data manifolds with metric structure into lower dimensional spaces with simpler metrics, such as Euclidean and Hyperbolic spaces. We then demonstrate that it can be a powerful step in…

Bounding volumes are an established concept in computer graphics and vision tasks but have seen little change since their early inception. In this work, we study the use of neural networks as bounding volumes. Our key observation is that…

interpretable, and well understood models that are routinely employed even though, as is revealed through prior and posterior predictive checks, these can poorly characterise the spatial heterogeneity in the underlying process of interest.…

Embeddings are a basic initial feature extraction step in many machine learning models, particularly in natural language processing. An embedding attempts to map data tokens to a low-dimensional space where similar tokens are mapped to…

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was…

We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…

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…

Statistical neurodynamics studies macroscopic behaviors of randomly connected neural networks. We consider a deep layered feedforward network where input signals are processed layer by layer. The manifold of input signals is embedded in a…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

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…

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…

We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the…

An oblivious subspace embedding is a random $m\times n$ matrix $\Pi$ such that, for any $d$-dimensional subspace, with high probability $\Pi$ preserves the norms of all vectors in that subspace within a $1\pm\epsilon$ factor. In this work,…

While most network embedding techniques model the proximity between nodes in a network, recently there has been significant interest in structural embeddings that are based on node equivalences, a notion rooted in sociology: equivalences or…

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…

The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation…