Zobrazeno 1 - 10
of 107
pro vyhledávání: '"VILLAR, SOLEDAD"'
Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables towards achieving disentangled representations of data. In this letter we show that orthogonality relations withi
Externí odkaz:
http://arxiv.org/abs/2408.16138
Autor:
Gregory, Wilson G., Tonelli-Cueto, Josué, Marshall, Nicholas F., Lee, Andrew S., Villar, Soledad
This work characterizes equivariant polynomial functions from tuples of tensor inputs to tensor outputs. Loosely motivated by physics, we focus on equivariant functions with respect to the diagonal action of the orthogonal group on tensors. We show h
Externí odkaz:
http://arxiv.org/abs/2406.01552
Autor:
Hogg, David W., Villar, Soledad
Machine learning (ML) methods are having a huge impact across all of the sciences. However, ML has a strong ontology - in which only the data exist - and a strong epistemology - in which a model is considered good if it performs well on held-out trai
Externí odkaz:
http://arxiv.org/abs/2405.18095
In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are invariant with re
Externí odkaz:
http://arxiv.org/abs/2405.08097
Graph neural networks (GNNs) are commonly described as being permutation equivariant with respect to node relabeling in the graph. This symmetry of GNNs is often compared to the translation equivariance of Euclidean convolution neural networks (CNNs)
Externí odkaz:
http://arxiv.org/abs/2308.10436
Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the
Externí odkaz:
http://arxiv.org/abs/2306.13924
Numerous recent works have analyzed the expressive power of message-passing graph neural networks (MPNNs), primarily utilizing combinatorial techniques such as the $1$-dimensional Weisfeiler-Leman test ($1$-WL) for the graph isomorphism problem. Howe
Externí odkaz:
http://arxiv.org/abs/2306.03698
Autor:
Gregory, Wilson, Hogg, David W., Blum-Smith, Ben, Arias, Maria Teresa, Wong, Kaze W. K., Villar, Soledad
Convolutional neural networks and their ilk have been very successful for many learning tasks involving images. These methods assume that the input is a scalar image representing the intensity in each pixel, possibly in multiple channels for color im
Externí odkaz:
http://arxiv.org/abs/2305.12585
Any representation of data involves arbitrary investigator choices. Because those choices are external to the data-generating process, each choice leads to an exact symmetry, corresponding to the group of transformations that takes one possible repre
Externí odkaz:
http://arxiv.org/abs/2301.13724
We introduce a sketch-and-solve approach to speed up the Peng-Wei semidefinite relaxation of k-means clustering. When the data is appropriately separated we identify the k-means optimal clustering. Otherwise, our approach provides a high-confidence l
Externí odkaz:
http://arxiv.org/abs/2211.15744