Related papers: Uniform Brackets, Containers, and Combinatorial Ma…

We study the problems of testing and learning high-dimensional discrete convex sets. The simplest high-dimensional discrete domain where convexity is a non-trivial property is the ternary hypercube, $\{-1,0,1\}^n$. The goal of this work is…

Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…

Combining the properties of monovariate internal functions as proposed in Kolmogorov superimposition theorem, in tandem with the bounds wielded by the multivariate formulation of Chebyshev inequality, a hybrid model is presented, that…

This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…

We consider a group of computation units trying to cooperatively solve a distributed optimization problem with shared linear equality and inequality constraints. Assuming that the computation units are communicating over a network whose…

Embedding techniques have become essential components of large databases in the deep learning era. By encoding discrete entities, such as words, items, or graph nodes, into continuous vector spaces, embeddings facilitate more efficient…

Motivated by multi-task and meta-learning approaches, we consider the problem of learning structure shared by tasks or users, such as shared low-rank representations or clustered structures. While all previous works focus on well-specified…

Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar…

In this paper we establish a general framework in which the verification of support theorems for generalized convex functions acting between an algebraic structure and an ordered algebraic structure is still possible. As for the domain…

Attempts of learning from hierarchical taxonomies in computer vision have been mostly focusing on image classification. Though ways of best harvesting learning improvements from hierarchies in classification are far from being solved, there…

This survey article is devoted to general results in combinatorial enumeration. The first part surveys results on growth of hereditary properties of combinatorial structures. These include permutations, ordered and unordered graphs and…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems. In those methods a deep neural network is used as a solution generator which is then trained by…

In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane…

Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…

We show that discrete synaptic weights can be efficiently used for learning in large scale neural systems, and lead to unanticipated computational performance. We focus on the representative case of learning random patterns with binary…

We characterize conditions under which collections of distributions on $\{0,1\}^\mathbb{N}$ admit uniform estimation of their mean. Prior work from Vapnik and Chervonenkis (1971) has focused on uniform convergence using the empirical mean…

Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…

A unified and versatile LiDAR segmentation model with strong robustness and generalizability is desirable for safe autonomous driving perception. This work presents M3Net, a one-of-a-kind framework for fulfilling multi-task, multi-dataset,…

In this paper, we study the convergence of the spectral embeddings obtained from the leading eigenvectors of certain similarity matrices to their population counterparts. We opt to study this convergence in a uniform (instead of average)…