Related papers: Optimal Matrix-Mimetic Tensor Algebras via Variabl…

Feature transformation aims to reconstruct an effective representation space by mathematically refining the existing features. It serves as a pivotal approach to combat the curse of dimensionality, enhance model generalization, mitigate…

Data scientists seeking a good supervised learning model on a new dataset have many choices to make: they must preprocess the data, select features, possibly reduce the dimension, select an estimation algorithm, and choose hyperparameters…

The embedding layers transforming input words into real vectors are the key components of deep neural networks used in natural language processing. However, when the vocabulary is large, the corresponding weight matrices can be enormous,…

We consider the problem of solving mixed random linear equations with $k$ components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels…

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…

One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a…

Super-symmetric tensors - a higher-order extension of scatter matrices - are becoming increasingly popular in machine learning and computer vision for modelling data statistics, co-occurrences, or even as visual descriptors. However, the…

This paper presents an algorithm for multiobjective optimization that blends together a number of heuristics. A population of agents combines heuristics that aim at exploring the search space both globally and in a neighborhood of each…

We propose and experimentally demonstrate an innovative stock index prediction method using a weighted optical reservoir computing system. We construct fundamental market data combined with macroeconomic data and technical indicators to…

The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The…

An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…

We consider the hashing mechanism for constructing binary embeddings, that involves pseudo-random projections followed by nonlinear (sign function) mappings. The pseudo-random projection is described by a matrix, where not all entries are…

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…

Random linear mappings are widely used in modern signal processing, compressed sensing and machine learning. These mappings may be used to embed the data into a significantly lower dimension while at the same time preserving useful…

Linear representation hypothesis posits that high-level concepts are encoded as linear directions in the representation spaces of LLMs. Park et al. (2024) formalize this notion by unifying multiple interpretations of linear representation,…

Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…

Identification of the optimal quantum metrological protocols in realistic many particle quantum models is in general a challenge that cannot be efficiently addressed by the state-of-the-art numerical and analytical methods. Here we provide…