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Found 34 papers, 15 papers with code
Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach
Our approach decouples learning the transformation from the source language to the target language into (a) learning rotations for language-specific embeddings to align them to a common space, and (b) learning a similarity metric in the common space to model similarities between the embeddings.
A Unified Framework for Structured Low-rank Matrix Learning
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices.
Light-weight Document Image Cleanup using Perceptual Loss
Smartphones have enabled effortless capturing and sharing of documents in digital form.
McTorch, a manifold optimization library for deep learning
In this paper, we introduce McTorch, a manifold optimization library for deep learning that extends PyTorch.
A Gauss-Newton Approach for Min-Max Optimization in Generative Adversarial Networks
It modifies the Gauss-Newton method to approximate the min-max Hessian and uses the Sherman-Morrison inversion formula to calculate the inverse.
Riemannian adaptive stochastic gradient algorithms on matrix manifolds
We propose novel stochastic gradient algorithms for problems on Riemannian matrix manifolds by adapting the row and column subspaces of gradients.
Rieoptax: Riemannian Optimization in JAX
We present Rieoptax, an open source Python library for Riemannian optimization in JAX.
Manifold optimization for non-linear optimal transport problems
In this work, we discuss how to computationally approach general non-linear OT problems within the framework of Riemannian manifold optimization.
Efficient Robust Optimal Transport with Application to Multi-Label Classification
Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications.
Low-rank geometric mean metric learning
We propose a low-rank approach to learning a Mahalanobis metric from data.
On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry
We build on this to show that the BW metric is a more suitable and robust choice for several Riemannian optimization problems over ill-conditioned SPD matrices.
Riemannian block SPD coupling manifold and its application to optimal transport
In this work, we study the optimal transport (OT) problem between symmetric positive definite (SPD) matrix-valued measures.
Light-weight Deep Extreme Multilabel Classification
Extreme multi-label (XML) classification refers to the task of supervised multi-label learning that involves a large number of labels.
Structured low-rank matrix learning: algorithms and applications
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices.
A dual framework for low-rank tensor completion
One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization.
A Riemannian gossip approach to subspace learning on Grassmann manifold
Interesting applications in this setting include low-rank matrix completion and low-dimensional multivariate regression, among others.
Efficient Output Kernel Learning for Multiple Tasks
The paradigm of multi-task learning is that one can achieve better generalization by learning tasks jointly and thus exploiting the similarity between the tasks rather than learning them independently of each other.
Low-rank approximations of hyperbolic embeddings
While the hyperbolic manifold is well-studied in the literature, it has gained interest in the machine learning and natural language processing communities lately due to its usefulness in modeling continuous hierarchies.
Riemannian optimization on the simplex of positive definite matrices
In this work, we generalize the probability simplex constraint to matrices, i. e., $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_K = \mathbf{I}$, where $\mathbf{X}_i \succeq 0$ is a symmetric positive semidefinite matrix of size $n\times n$ for all $i = \{1,\ldots, K \}$.
Statistical Optimal Transport posed as Learning Kernel Embedding
This work takes the novel approach of posing statistical OT as that of learning the transport plan's kernel mean embedding from sample based estimates of marginal embeddings.
A Simple Approach to Learning Unsupervised Multilingual Embeddings
Recent progress on unsupervised learning of cross-lingual embeddings in bilingual setting has given impetus to learning a shared embedding space for several languages without any supervision.
Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings
We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages.
Learning Geometric Word Meta-Embeddings
We propose a geometric framework for learning meta-embeddings of words from different embedding sources.
MMD-Regularized Unbalanced Optimal Transport
Further, for real-world applications involving non-discrete measures, we present an estimator for the transport plan that is supported only on the given ($m$) samples.
SPOT: A framework for selection of prototypes using optimal transport
In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset.
Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry
Learning with symmetric positive definite (SPD) matrices has many applications in machine learning.
Confidence Score for Unsupervised Foreground Background Separation of Document Images
Foreground-background separation is an important problem in document image analysis.
Riemannian Hamiltonian methods for min-max optimization on manifolds
In this paper, we study min-max optimization problems on Riemannian manifolds.
Differentially private Riemannian optimization
We introduce a framework of differentially private Riemannian optimization by adding noise to the Riemannian gradient on the tangent space.
Riemannian accelerated gradient methods via extrapolation
In this paper, we propose a simple acceleration scheme for Riemannian gradient methods by extrapolating iterates on manifolds.
ProtoBandit: Efficient Prototype Selection via Multi-Armed Bandits
In this work, we propose a multi-armed bandit-based framework for identifying a compact set of informative data instances (i. e., the prototypes) from a source dataset $S$ that best represents a given target set $T$.
Generalised Spherical Text Embedding
The proposed modelling and the novel similarity metric exploits the matrix structure of embeddings.
A Framework for Bilevel Optimization on Riemannian Manifolds
We provide convergence and complexity analysis for the proposed hypergradient descent algorithm on manifolds.
Federated Learning on Riemannian Manifolds with Differential Privacy
To the best of our knowledge, this is the first federated learning framework on Riemannian manifold with a privacy guarantee and convergence results.
