Related papers: Equivariant Filters are Equivariant
In recent years the use of convolutional layers to encode an inductive bias (translational equivariance) in neural networks has proven to be a very fruitful idea. The successes of this approach have motivated a line of research into…
Latent representations are used extensively for downstream tasks, such as visualization, interpolation or feature extraction of deep learning models. Invariant and equivariant neural networks are powerful and well-established models for…
We present a framework for studying the dynamics of equivariant vector fields near relative equilibria. To overcome the lack of linearization at a relative equilibrium or the possible non-smoothness of the orbit space, we categorify the…
The principle of equivariance to symmetry transformations enables a theoretically grounded approach to neural network architecture design. Equivariant networks have shown excellent performance and data efficiency on vision and medical…
Flows are exact-likelihood generative neural networks that transform samples from a simple prior distribution to the samples of the probability distribution of interest. Boltzmann Generators (BG) combine flows and statistical mechanics to…
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead. While work has explored learning or relaxing constraints, selecting among…
This paper presents an Extended Kalman Filter (EKF) approach to localize a mobile robot with two quadrature encoders, a compass sensor, a laser range finder (LRF) and an omni-directional camera. The prediction step is performed by employing…
This paper explores the integration of symmetries into the Koopman-operator framework for the analysis and efficient learning of equivariant dynamical systems using a group-convolutional approach. Approximating the Koopman operator by…
This work addresses the problem of designing an equivariant observer for a first order dynamical system on the unit-sphere. Building upon the established case of unit bearing vector dynamics with angular velocity inputs, we introduce an…
The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The Invariant Extended Kalman Filter (IEKF) is a recent development of the EKF for the class of group-affine systems on…
This paper considers the distributed filtering problem for a class of stochastic uncertain systems under quantized data flowing over switching sensor networks. Employing the biased noisy observations of the local sensor and…
Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are…
How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…
Spatial understanding is a critical aspect of most robotic tasks, particularly when generalization is important. Despite the impressive results of deep generative models in complex manipulation tasks, the absence of a representation that…
Steerable networks, which process data with intrinsic symmetries, often use Fourier-based nonlinearities that require sampling from the entire group, leading to a need for discretization in continuous groups. As the number of samples…
Equivariance of linear neural network layers is well studied. In this work, we relax the equivariance condition to only be true in a projective sense. We propose a way to construct a projectively equivariant neural network through building…
Equivariance is central to graph generative models, as it ensures the model respects the permutation symmetry of graphs. However, strict equivariance can increase computational cost due to added architectural constraints, and can slow down…
In this study, we introduce a method for learning group (known or unknown) equivariant functions by learning the associated quadratic form $x^T A x$ corresponding to the group from the data. Certain groups, known as orthogonal groups,…
We show how the symmetry of attractors of equivariant dynamical systems can be observed by equivariant projections of the phase space. Equivariant projections have long been used, but they can give misleading results if used improperly and…
In myriad statistical applications, data are collected from related but heterogeneous sources. These sources share some commonalities while containing idiosyncratic characteristics. One of the most fundamental challenges in such scenarios…