Related papers: Riemannian Geometric-based Meta Learning

This paper presents a novel optimization method for maximizing generalization over tasks in meta-learning. The goal of meta-learning is to learn a model for an agent adapting rapidly when presented with previously unseen tasks. Tasks are…

A novel method, named Curvature-Augmented Manifold Embedding and Learning (CAMEL), is proposed for high dimensional data classification, dimension reduction, and visualization. CAMEL utilizes a topology metric defined on the Riemannian…

Non-Euclidean constraints are inherent in many kinds of data in computer vision and machine learning, typically as a result of specific invariance requirements that need to be respected during high-level inference. Often, these geometric…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Widely used traditional supervised deep learning methods require a large number of training samples but often fail to generalize on unseen datasets. Therefore, a more general application of any trained model is quite limited for medical…

The aim of Few-Shot learning methods is to train models which can easily adapt to previously unseen tasks, based on small amounts of data. One of the most popular and elegant Few-Shot learning approaches is Model-Agnostic Meta-Learning…

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

Model-agnostic meta-learners aim to acquire meta-learned parameters from similar tasks to adapt to novel tasks from the same distribution with few gradient updates. With the flexibility in the choice of models, those frameworks demonstrate…

Meta-learning allows an intelligent agent to leverage prior learning episodes as a basis for quickly improving performance on a novel task. Bayesian hierarchical modeling provides a theoretical framework for formalizing meta-learning as…

Model-agnostic meta learning (MAML) is currently one of the dominating approaches for few-shot meta-learning. Albeit its effectiveness, the optimization of MAML can be challenging due to the innate bilevel problem structure. Specifically,…

The effectiveness of dimensionality reduction with quadratic manifolds hinges on the choice of a reduced basis and the associated quadratic correction terms. Existing approaches typically rely on subspaces spanned by the leading principal…

Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…

Euclidean representation learning methods have achieved promising results in image fusion tasks, which can be attributed to their clear advantages in handling with linear space. However, data collected from a realistic scene usually has a…

Optimization over the Stiefel manifold is a fundamental computational problem in many scientific and engineering applications. Despite considerable research effort, high-dimensional optimization problems over the Stiefel manifold remain…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

Symmetric positive definite (SPD) matrix has been demonstrated to be an effective feature descriptor in many scientific areas, as it can encode spatiotemporal statistics of the data adequately on a curved Riemannian manifold, i.e., SPD…

Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still…

In this paper, we introduce a discrete variant of the meta-learning framework. Meta-learning aims at exploiting prior experience and data to improve performance on future tasks. By now, there exist numerous formulations for meta-learning in…

Model-agnostic meta-learning (MAML) is a well-known optimization-based meta-learning algorithm that works well in various computer vision tasks, e.g., few-shot classification. MAML is to learn an initialization so that a model can adapt to…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…