Related papers: Latent Space Symmetry Discovery
Despite the success of equivariant neural networks in scientific applications, they require knowing the symmetry group a priori. However, it may be difficult to know which symmetry to use as an inductive bias in practice. Enforcing the…
Symmetry detection can improve various machine learning tasks. In the context of continuous symmetry detection, current state of the art experiments are limited to detecting affine transformations. Under the manifold assumption, we outline…
Equivariant neural networks incorporate symmetries into their architecture, achieving higher generalization performance. However, constructing equivariant neural networks typically requires prior knowledge of data types and symmetries,…
What are the symmetries of a dataset? Whereas the symmetries of an individual data element can be characterized by its invariance under various transformations, the symmetries of an ensemble of data elements are ambiguous due to Jacobian…
Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning. Both pursuits require knowledge of the underlying symmetries in data, yet discovering these symmetries…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…
Existing equivariant neural networks require prior knowledge of the symmetry group and discretization for continuous groups. We propose to work with Lie algebras (infinitesimal generators) instead of Lie groups. Our model, the Lie algebra…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
Symmetry is widely applied in problems such as the design of equivariant networks and the discovery of governing equations, but in complex scenarios, it is not known in advance. Most previous symmetry discovery methods are limited to linear…
Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…
Symmetries are ubiquitous across all kinds of objects, whether in nature or in man-made creations. While these symmetries may seem intuitive to the human eye, detecting them with a machine is nontrivial due to the vast search space.…
Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space. The linear Euclidean geometry of data space pulls back…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is…
Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…
Generative models based on latent variables, such as generative adversarial networks (GANs) and variational auto-encoders (VAEs), have gained lots of interests due to their impressive performance in many fields. However, many data such as…
Modeling group actions on latent representations enables controllable transformations of high-dimensional image data. Prior works applying group-theoretic priors or modeling transformations typically operate in the high-dimensional data…
Generative adversarial network (GAN) has achieved impressive success on cross-domain generation, but it faces difficulty in cross-modal generation due to the lack of a common distribution between heterogeneous data. Most existing methods of…
I present IGAN (Inferent Generative Adversarial Networks), a neural architecture that learns both a generative and an inference model on a complex high dimensional data distribution, i.e. a bidirectional mapping between data samples and a…
Generative Adversarial Networks (GAN) is currently widely used as an unsupervised image generation method. Current state-of-the-art GANs can generate photorealistic images with high resolution. However, a large amount of data is required,…