Related papers: SNEkhorn: Dimension Reduction with Symmetric Entro…
In 2013, Cuturi [Cut13] introduced the Sinkhorn algorithm for matrix scaling as a method to compute solutions to regularized optimal transport problems. In this paper, aiming at a better convergence rate for a high accuracy solution, we…
We introduce in this paper a novel strategy for efficiently approximating the Sinkhorn distance between two discrete measures. After identifying neglectable components of the dual solution of the regularized Sinkhorn problem, we propose to…
Graph neural networks have been used for a variety of learning tasks, such as link prediction, node classification, and node clustering. Among them, link prediction is a relatively under-studied graph learning task, with current…
Given a non-negative $n \times m$ real matrix $A$, the {\em matrix scaling} problem is to determine if it is possible to scale the rows and columns so that each row and each column sums to a specified target value for it. This problem…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
Neural networks that are equivariant to rotations, translations, reflections, and permutations on n-dimensional geometric space have shown promise in physical modeling for tasks such as accurately but inexpensively modeling complex…
Recently, a race towards the simplification of deep networks has begun, showing that it is effectively possible to reduce the size of these models with minimal or no performance loss. However, there is a general lack in understanding why…
In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of…
Parallelism has become a central concern in modern decoding frameworks aiming to meet stringent throughput and latency requirements. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed decoding paradigm that tests…
We propose an entropic approximation approach for optimal transportation problems with a supremal cost. We establish $\Gamma$-convergence for suitably chosen parameters for the entropic penalization and that this procedure selects…
Several recent applications of optimal transport (OT) theory to machine learning have relied on regularization, notably entropy and the Sinkhorn algorithm. Because matrix-vector products are pervasive in the Sinkhorn algorithm, several…
The central aim of this paper is to implement Deep Autoencoder and Neighborhood Components Analysis (NCA) dimensionality reduction methods in Matlab and to observe the application of these algorithms on nine unlike datasets from UCI machine…
Deep Metric Learning algorithms aim to learn an efficient embedding space to preserve the similarity relationships among the input data. Whilst these algorithms have achieved significant performance gains across a wide plethora of tasks,…
Deep neural networks (DNNs) have shown their success as high-dimensional function approximators in many applications; however, training DNNs can be challenging in general. DNN training is commonly phrased as a stochastic optimization…
Variational Auto-Encoders (VAEs) have emerged as powerful probabilistic models for generative tasks. However, their convergence properties have not been rigorously proven. The challenge of proving convergence is inherently difficult due to…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for…
Entity Resolution (ER) is a constitutional part for integrating different knowledge graphs in order to identify entities referring to the same real-world object. A promising approach is the use of graph embeddings for ER in order to…
Dimension reduction (DR) algorithms have proven to be extremely useful for gaining insight into large-scale high-dimensional datasets, particularly finding clusters in transcriptomic data. The initial phase of these DR methods often…
Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the…