相关论文: Riemannian Batch Normalization: A Gyro Approach

GANS are powerful generative models that are able to model the manifold of natural images. We leverage this property to perform manifold regularization by approximating the Laplacian norm using a Monte Carlo approximation that is easily…

The deep linear network (DLN) is a model for implicit regularization in gradient based optimization of overparametrized learning architectures. Training the DLN corresponds to a Riemannian gradient flow, where the Riemannian metric is…

Geometric representation learning in preserving the intrinsic geometric and topological properties for discrete non-Euclidean data is crucial in scientific applications. Previous research generally mapped non-Euclidean discrete data into…

Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…

Despite the recent success of Bayesian optimization (BO) in a variety of applications where sample efficiency is imperative, its performance may be seriously compromised in settings characterized by high-dimensional parameter spaces. A…

We present a theoretical analysis of Gaussian-binary restricted Boltzmann machines (GRBMs) from the perspective of density models. The key aspect of this analysis is to show that GRBMs can be formulated as a constrained mixture of…

In geotechnical engineering, constitutive models are central to capturing soil behavior across diverse drainage conditions, stress paths,and loading histories. While data driven deep learning (DL) approaches have shown promise as…

Restricted Boltzmann Machines (RBMs) are widely used probabilistic undirected graphical models with visible and latent nodes, playing an important role in statistics and machine learning. The task of structure learning for RBMs involves…

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…

Hyperbolic deep learning leverages the metric properties of hyperbolic spaces to develop efficient and informative embeddings of hierarchical data. Here, we focus on the solvable group structure of hyperbolic spaces, which follows naturally…

Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize…

Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from…

Generative Adversarial Networks are powerful generative models that are able to model the manifold of natural images. We leverage this property to perform manifold regularization by approximating a variant of the Laplacian norm using a…

In Artificial Intelligence (AI) and computational science, learning the mappings between functions (called operators) defined on complex computational domains is a common theoretical challenge. Recently, Neural Operator emerged as a…

Recently, combinations of generative and Bayesian machine learning have been introduced in particle physics for both fast detector simulation and inference tasks. These neural networks aim to quantify the uncertainty on the generated…

Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…

This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…

This review deals with Restricted Boltzmann Machine (RBM) under the light of statistical physics. The RBM is a classical family of Machine learning (ML) models which played a central role in the development of deep learning. Viewing it as a…

Graph representation learning has been widely studied and demonstrated effectiveness in various graph tasks. Most existing works embed graph data in the Euclidean space, while recent works extend the embedding models to hyperbolic or…

Deep generative models based on Generative Adversarial Networks (GANs) have demonstrated impressive sample quality but in order to work they require a careful choice of architecture, parameter initialization, and selection of…