Related papers: Symmetry Discovery for Different Data Types
Deep learning (DL) has been widely investigated in a vast majority of applications in electroencephalography (EEG)-based brain-computer interfaces (BCIs), especially for motor imagery (MI) classification in the past five years. The…
Recent advances in deep learning from probability distributions successfully achieve classification or regression from distribution samples, thus invariant under permutation of the samples. The first contribution of the paper is to extend…
Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated…
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently this idea has been…
The coincidence between polynomial neural networks and matrix Lie maps is discussed in the article. The matrix form of Lie transform is an approximation of the general solution of the nonlinear system of ordinary differential equations. It…
Group equivariance (e.g. SE(3) equivariance) is a critical physical symmetry in science, from classical and quantum physics to computational biology. It enables robust and accurate prediction under arbitrary reference transformations. In…
Equivariant machine learning methods have shown wide success at 3D learning applications in recent years. These models explicitly build in the reflection, translation and rotation symmetries of Euclidean space and have facilitated large…
Equivariant neural networks provide a principled framework for incorporating symmetry into learning architectures and have been extensively analyzed through the lens of their separation power, that is, the ability to distinguish inputs…
Recently, leveraging on the development of end-to-end convolutional neural networks (CNNs), deep stereo matching networks have achieved remarkable performance far exceeding traditional approaches. However, state-of-the-art stereo frameworks…
Recent works have highlighted scale invariance or symmetry present in the weight space of a typical deep network and the adverse effect it has on the Euclidean gradient based stochastic gradient descent optimization. In this work, we show…
In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…
Incorporating Euclidean symmetries (e.g. rotation equivariance) as inductive biases into graph neural networks has improved their generalization ability and data efficiency in unbounded physical dynamics modeling. However, in various…
Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector.…
Non-linear dimensionality reduction can be performed by \textit{manifold learning} approaches, such as Stochastic Neighbour Embedding (SNE), Locally Linear Embedding (LLE) and Isometric Feature Mapping (ISOMAP). These methods aim to produce…
Many structured prediction tasks in machine vision have a collection of acceptable answers, instead of one definitive ground truth answer. Segmentation of images, for example, is subject to human labeling bias. Similarly, there are multiple…
We consider the problem of learning a function respecting a symmetry from among a class of symmetries. We develop a unified framework that enables symmetry discovery across a broad range of subgroups including locally symmetric, dihedral…
Recent advanced studies have spent considerable human efforts on optimizing network architectures for stereo matching but hardly achieved both high accuracy and fast inference speed. To ease the workload in network design, neural…
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use…
Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by…