Related papers: Tensor Random Projection for Low Memory Dimension …
Visual Place Recognition (VPR) localizes a query image by matching it against a database of geo-tagged reference images, making it essential for navigation and mapping in robotics. Although Vision Transformer (ViT) solutions deliver high…
Recursive projection aggregation (RPA) decoding as introduced in [1] is a novel decoding algorithm which performs close to the maximum likelihood decoder for short-length Reed-Muller codes. Recently, an extension to RPA decoding, called…
Advancing loss function design is pivotal for optimizing neural network training and performance. This work introduces Random Linear Projections (RLP) loss, a novel approach that enhances training efficiency by leveraging geometric…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
Large language model (LLM) training is often bottlenecked by memory constraints and stochastic gradient noise in extremely high-dimensional parameter spaces. Motivated by empirical evidence that many LLM gradient matrices are effectively…
Random projection is widely used as a method of dimension reduction. In recent years, its combination with standard techniques of regression and classification has been explored. Here we examine its use with principal component analysis…
Since higher-order tensors are naturally suitable for representing multi-dimensional data in real-world, e.g., color images and videos, low-rank tensor representation has become one of the emerging areas in machine learning and computer…
Tensor networks developed in the context of condensed matter physics try to approximate order-$N$ tensors with a reduced number of degrees of freedom that is only polynomial in $N$ and arranged as a network of partially contracted smaller…
We introduce Random Projection Flows (RPFs), a principled framework for injective normalizing flows that leverages tools from random matrix theory and the geometry of random projections. RPFs employ random semi-orthogonal matrices, drawn…
Dimensionality reduction (DR) techniques map high-dimensional data into lower-dimensional spaces. Yet, current DR techniques are not designed to explore semantic structure that is not directly available in the form of variables or class…
Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…
Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors…
Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
Our objective is to efficiently design a robust projection matrix $\Phi$ for the Compressive Sensing (CS) systems when applied to the signals that are not exactly sparse. The optimal projection matrix is obtained by mainly minimizing the…
With appropriately chosen sampling probabilities, sampling-based random projection can be used to implement large-scale statistical methods, substantially reducing computational cost while maintaining low statistical error. However,…
Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of…