Related papers: Neural Lattice Reduction: A Self-Supervised Geomet…
Lattice reduction algorithms, such as the LLL algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in MIMO communications. In this paper we introduce a new kind of lattice…
We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure. Our approach develops within a recently introduced framework…
In many optimization problems in wireless communications, the expressions of objective function or constraints are hard or even impossible to derive, which makes the solutions difficult to find. In this paper, we propose a model-free…
In this paper, we propose a machine learning (ML) method to learn how to solve a generic constrained continuous optimization problem. To the best of our knowledge, the generic methods that learn to optimize, focus on unconstrained…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This work presents a novel lattice-based methodology for incorporating multidimensional constraints into continuous decision variables within a genetic algorithm (GA) framework. The proposed approach consolidates established transcription…
We propose a recursive lattice reduction framework for finding short non-zero vectors or dense sublattices of a lattice. The framework works by recursively searching for dense sublattices of dense sublattices (or their duals) with…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
Training a classifier under non-convex constraints has gotten increasing attention in the machine learning community thanks to its wide range of applications such as algorithmic fairness and class-imbalanced classification. However, several…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
Convolutions encode equivariance symmetries into neural networks leading to better generalisation performance. However, symmetries provide fixed hard constraints on the functions a network can represent, need to be specified in advance, and…
Overparameterization refers to the important phenomenon where the width of a neural network is chosen such that learning algorithms can provably attain zero loss in nonconvex training. The existing theory establishes such global convergence…
Since the invention of the famous LLL algorithm, lattice reduction has been an extremely useful tool in computational number theory. By construction, the LLL algorithm deals with lattices living in a vector space endowed with a positive…
Learning the optimized solution as a function of environmental parameters is effective in solving numerical optimization in real time for time-sensitive applications. Existing works of learning to optimize train deep neural networks (DNN)…
Over the past years, there has been significant interest in understanding the implicit bias of gradient descent optimization and its connection to the generalization properties of overparametrized neural networks. Several works observed…
We introduce a novel stochastic regularization technique for deep neural networks, which decomposes a layer into multiple branches with different parameters and merges stochastically sampled combinations of the outputs from the branches…
Deep neural networks trained using a softmax layer at the top and the cross-entropy loss are ubiquitous tools for image classification. Yet, this does not naturally enforce intra-class similarity nor inter-class margin of the learned deep…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
Deep learning methods have been shown to be effective in representing ground-state wave functions of quantum many-body systems. Existing methods use convolutional neural networks (CNNs) for square lattices due to their image-like…