相关论文: Learning on hexagonal structures and Monge-Amp\`er…

Dense Associative Memory (DAM) models have been attracting renewed attention since they were shown to be robust to adversarial examples and closely related to cutting edge machine learning paradigms, such as the attention mechanism and…

This work develops the global equations of neural networks through stacked piecewise manifolds, fixed-point theory, and boundary-conditioned iteration. Once fixed coordinates and operators are removed, a neural network appears as a…

Human learning is a complex phenomenon requiring flexibility to adapt existing brain function and precision in selecting new neurophysiological activities to drive desired behavior. These two attributes -- flexibility and selection -- must…

We clarify the linear algebra used in the quaternionic pluripotential theory so that proofs of several results there can be greatly simplified. In particular, we characterize and normalize real $2$-forms with respect to the quaternionic…

We consider degenerate Monge-Amp\`ere equations on compact Hessian manifolds. We establish compactness properties of the set of normalized quasi-convex functions and show local and global comparison principles for twisted Monge-Amp\`ere…

Bayesian learning is ubiquitous for implementing classification and regression tasks, however, it is accompanied by computationally intractable limitations when the feature spaces become extremely large. Aiming to solve this problem, we…

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address…

Monge--Amp\`ere equation plays an important part in Analysis. For example, it is instrumental in mass transport problems. On the other hand, the Bellman function technique appeared recently as a way to consider certain Harmonic Analysis…

We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks…

In this paper, we give several new approaches to study interior estimates for a class of fourth order equations of Monge-Amp\`ere type. First, we prove interior estimates for the homogeneous equation in dimension two by using the partial…

In this paper we examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional…

Random graphs are increasingly becoming objects of interest for modeling networks in a wide range of applications. Latent position random graph models posit that each node is associated with a latent position vector, and that these vectors…

We construct rational models for classifying spaces of self-equivalences of bundles over simply connected finite CW-complexes relative to a given simply connected subcomplex. Via work of Berglund-Madsen and Krannich this specializes to…

We study the characteristic probability density distribution of random flat band models by machine learning. The models considered here are constructed on the basis of the molecular-orbital representation, which guarantees the existence of…

Given a cohomology $(1,1)$-class $\{\beta\}$ of compact Hermitian manifold $(X,\omega)$ possessing a bounded potential and fixed a model potential $\phi$, motivated by Darvas-Di Nezza-Lu and Li-Wang-Zhou's work, we show that degenerate…

Manifold learning methods play a prominent role in nonlinear dimensionality reduction and other tasks involving high-dimensional data sets with low intrinsic dimensionality. Many of these methods are graph-based: they associate a vertex…

We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…

A Restricted Boltzmann Machine (RBM) is an unsupervised machine-learning bipartite graphical model that jointly learns a probability distribution over data and extracts their relevant statistical features. As such, RBM were recently…

The use of machine learning in artistic music generation leads to controversial discussions of the quality of art, for which objective quantification is nonsensical. We therefore consider a music-generating algorithm as a counterpart to a…

Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact…