Related papers: Machine Learning Holographic Mapping by Neural Net…

Graph neural networks (GNNs) provide powerful insights for brain neuroimaging technology from the view of graphical networks. However, most existing GNN-based models assume that the neuroimaging-produced brain connectome network is a…

There is some tension between two well-known ideas in holography. On the one hand, subregion duality asserts that the reduced density matrix associated with a limited region of the boundary theory is dual to a correspondingly limited region…

This paper aims to establish a framework for extreme learning machines (ELMs) on general hypercomplex algebras. Hypercomplex neural networks are machine learning models that feature higher-dimension numbers as parameters, inputs, and…

Coordinated inference problems are being introduced as a basis for a neural network representation of the locality problem in the holographic bulk. It is argued that a type of problem originating in the "prisoners and hats" dilemma involves…

Many real-world data can be represented as heterogeneous graphs with different types of nodes and connections. Heterogeneous graph neural network model aims to embed nodes or subgraphs into low-dimensional vector space for various…

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding…

We present a "holographic" reconstruction of bulk spacetime geometry using correlation functions of a massless field living at the "future boundary" of the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic in the…

Reconstruction of tomographic images from boundary measurements requires flexibility with respect to target domains. For instance, when the system equations are modeled by partial differential equations the reconstruction is usually done on…

Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…

We propose a neural parameterization of convex sets by learning sublinear (positively homogeneous and convex) functions. Our networks implicitly represent both the support and gauge functions of a convex body. We prove a universal…

Euclidean Distance Matrix (EDM), which consists of pairwise squared Euclidean distances of a given point configuration, finds many applications in modern machine learning. This paper considers the setting where only a set of anchor nodes is…

Due to the over-parameterization nature, neural networks are a powerful tool for nonlinear function approximation. In order to achieve good generalization on unseen data, a suitable inductive bias is of great importance for neural networks.…

Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However,…

In this paper we propose a conceptual framework for higher-order artificial neural networks. The idea of higher-order networks arises naturally when a model is required to learn some group of transformations, every element of which is…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Geometric deep learning has recently gained significant attention in the computer vision community for its ability to capture meaningful representations of data lying in a non-Euclidean space. To this end, we propose E2E-GNet, an end-to-end…

Gauging is a general procedure for mapping a quantum many-body system with a global symmetry to one with a local gauge symmetry. We consider a generalized gauging map that does not enforce gauge symmetry at all lattice sites, and show that…

A probabilistic model for random hypergraphs is introduced to represent unary, binary and higher order interactions among objects in real-world problems. This model is an extension of the Latent Class Analysis model, which captures…

The geometerization of the renormalization group flow triggered by the $T\bar{T}$ deformation of large $c$ conformal field theories in two dimensions is presented. This entails the construction of the off shell Einstein-Hilbert action in…

We present here a new approach for using the intelligence aspects of artificial intelligence for knowledge discovery rather than device optimization in electromagnetic (EM) nanostructures. This approach uses training data obtained through…