Related papers: Invariant polynomials and machine learning

Near-term noisy intermediate-scale quantum circuits can efficiently implement implicit probabilistic models in discrete spaces, supporting distributions that are practically infeasible to sample from using classical means. One of the…

Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…

While recent progress has spawned very powerful machine learning systems, those agents remain extremely specialized and fail to transfer the knowledge they gain to similar yet unseen tasks. In this paper, we study a simple reinforcement…

In this paper, the class of random irregular block-hierarchical networks is defined and algorithms for generation and calculation of network properties are described. The algorithms presented for this class of networks are more efficient…

We propose an alternative approach to neural network training using the monotone vector field, an idea inspired by the seminal work of Juditsky and Nemirovski [Juditsky & Nemirovsky, 2019] developed originally to solve parameter estimation…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…

Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds for a single triangular set in terms of intrinsic data of the…

We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints. We focus on problems with a great number of local minima which are hard to obtain by local…

This work introduces a latent space method to calculate the demagnetization reversal process of multigrain permanent magnets. The algorithm consists of two deep learning models based on neural networks. The embedded Stoner-Wohlfarth method…

We propose two new strategies based on Machine Learning techniques to handle polyhedral grid refinement, to be possibly employed within an adaptive framework. The first one employs the k-means clustering algorithm to partition the points of…

The intention of this note is two-fold. First, we study integer optimization problems in standard form defined by $A \in\mathbb{Z}^{m\times{}n}$ and present an algorithm to solve such problems in polynomial-time provided that both the…

Reduced-rank decompositions provide descriptions of the variation among the elements of a matrix or array. In such decompositions, the elements of an array are expressed as products of low-dimensional latent factors. This article presents a…

The advancement of deep learning has led to the development of neural decoders for low latency communications. However, neural decoders can be very complex which can lead to increased computation and latency. We consider iterative pruning…

The performance of machine learning models can be impacted by changes in data over time. A promising approach to address this challenge is invariant learning, with a particular focus on a method known as invariant risk minimization (IRM).…

The rising computational and energy demands of deep learning, particularly in large-scale architectures such as foundation models and large language models (LLMs), pose significant challenges to sustainability. Traditional gradient-based…

We study in-context learning for nonparametric regression with $\alpha$-H\"older smooth regression functions, for some $\alpha>0$. We prove that, with $n$ in-context examples and $d$-dimensional regression covariates, a pretrained…

Deep neural networks have dramatically advanced the state of the art for many areas of machine learning. Recently they have been shown to have a remarkable ability to generate highly complex visual artifacts such as images and text rather…

Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…

Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…