相关论文: Equivariant Filter Design for Kinematic Systems on…

Graphs are mathematical tools that can be used to represent complex real-world interconnected systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently.…

The extended Kalman filter (EKF) has been the industry standard for state estimation problems over the past sixty years. The classical formulation of the EKF is posed for nonlinear systems defined on global Euclidean spaces. The design…

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,…

This paper presents a cost-effective inertial pedestrian dead reckoning method for the bipedal robot in the GPS-denied environment. Each time when the inertial measurement unit (IMU) is on the stance foot, a stationary pseudo-measurement…

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. Our main results…

Generative modeling has recently shown remarkable promise for visuomotor policy learning, enabling flexible and expressive control across diverse embodied AI tasks. However, existing generative policies often struggle with data…

In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining…

The simplicity and effectiveness of the UNet architecture makes it ubiquitous in image restoration, image segmentation, and diffusion models. They are often assumed to be equivariant to translations, yet they traditionally consist of layers…

The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…

In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…

We study the approximation of functions which are invariant with respect to certain permutations of the input indices using flow maps of dynamical systems. Such invariant functions includes the much studied translation-invariant ones…

This paper introduces a novel approach for modeling the dynamics of soft robots, utilizing a differentiable filter architecture. The proposed approach enables end-to-end training to learn system dynamics, noise characteristics, and temporal…

Equivariant neural networks, whose hidden features transform according to representations of a group G acting on the data, exhibit training efficiency and an improved generalisation performance. In this work, we extend group invariant and…

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very…

Building upon the theory of Kalman Filtering on Lie Groups, this paper describes an Extended Kalman Filter and Smoother for Loosely Coupled Integration of GNSS/INS tailored for post-processing applications. The approach employs a dynamic…

Graphs are mathematical tools that can be used to represent complex real-world systems, such as financial markets and social networks. Hence, machine learning (ML) over graphs has attracted significant attention recently. However, it has…

Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory…

Affine systems on Lie groups are a generalization of linear systems. For such systems, this paper studies what happens with the outer invariance entropy introduced by Colonius and Kawan. It is shown that, as for linear case, the outer…

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…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…