Related papers: A study of the classification of low-dimensional d…
A fundamental problem in supervised learning is to find a good set of features or distance measures. If the new set of features is of lower dimensionality and can be obtained by a simple transformation of the original data, they can make…
This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…
Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…
Autoencoders have achieved great success in various computer vision applications. The autoencoder learns appropriate low dimensional image representations through the self-supervised paradigm, i.e., reconstruction. Existing studies mainly…
Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on lower-dimensional manifolds. In this paper, we establish a…
We present a novel view of nonlinear manifold learning using derivative-free optimization techniques. Specifically, we propose an extension of the classical multi-dimensional scaling (MDS) method, where instead of performing gradient…
Transformer models have consistently achieved remarkable results in various domains such as natural language processing and computer vision. However, despite ongoing research efforts to better understand these models, the field still lacks…
Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…
In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…
We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the…
We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden…
Learning-based single image super-resolution (SISR) methods are continuously showing superior effectiveness and efficiency over traditional model-based methods, largely due to the end-to-end training. However, different from model-based…
Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which…
We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density…
Over the past decades, the increasing dimensionality of data has increased the need for effective data decomposition methods. Existing approaches, however, often rely on linear models or lack sufficient interpretability or flexibility. To…
In this work, we investigate several methods and strategies to learn deep embeddings for face recognition, using joint sample- and set-based optimization. We explain our framework that expands traditional learning with set-based supervision…
We investigate the geometric structure of learning dynamics in overparameterized transformer models through carefully controlled modular arithmetic tasks. Our primary finding is that despite operating in high-dimensional parameter spaces…
Unsupervised learning has always been appealing to machine learning researchers and practitioners, allowing them to avoid an expensive and complicated process of labeling the data. However, unsupervised learning of complex data is…
We show how to incorporate information from labeled examples into nonnegative matrix factorization (NMF), a popular unsupervised learning algorithm for dimensionality reduction. In addition to mapping the data into a space of lower…