Related papers: Equivariant Filters are Equivariant
Extended Kalman Filter (EKF) has been a popular approach to localization a mobile robot. However, the performance of the EKF and the quality of the estimation depends on the correct a priori knowledge of process and measurement noise…
This paper is concerned with the coherent quantum filtering (CQF) problem, where a quantum observer is cascaded in a measurement-free fashion with a linear quantum plant so as to minimize a mean square error of estimating the plant…
Robotic pick and place tasks are symmetric under translations and rotations of both the object to be picked and the desired place pose. For example, if the pick object is rotated or translated, then the optimal pick action should also…
We develop theory and software for rotation equivariant operators on scalar and vector fields, with diverse applications in simulation, optimization and machine learning. Rotation equivariance (covariance) means all fields in the system…
Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…
Density functional theory (DFT) is a fundamental method for simulating quantum chemical properties, but it remains expensive due to the iterative self-consistent field (SCF) process required to solve the Kohn-Sham equations. Recently, deep…
Variational quantum machine learning is an extensively studied application of near-term quantum computers. The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes…
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…
We introduce Steerable Transformers, an extension of the Vision Transformer mechanism that maintains equivariance to the special Euclidean group $\mathrm{SE}(d)$. We propose an equivariant attention mechanism that operates on features…
We present a neural network architecture that is fully equivariant with respect to transformations under the Lorentz group, a fundamental symmetry of space and time in physics. The architecture is based on the theory of the…
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon…
Applications of machine learning techniques for materials modeling typically involve functions known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such tasks, they…
It has long been recognized that the invariance and equivariance properties of a representation are critically important for success in many vision tasks. In this paper we present Steerable Convolutional Neural Networks, an efficient and…
In many physical applications, the system's state varies with spatial variables as well as time. The state of such systems is modelled by partial differential equations and evolves on an infinite-dimensional space. Systems modelled by…
Filtering - the task of estimating the conditional distribution for states of a dynamical system given partial and noisy observations - is important in many areas of science and engineering, including weather and climate prediction.…
In Reinforcement Learning (RL), Convolutional Neural Networks(CNNs) have been successfully applied as function approximators in Deep Q-Learning algorithms, which seek to learn action-value functions and policies in various environments.…
Although group convolutional networks are able to learn powerful representations based on symmetry patterns, they lack explicit means to learn meaningful relationships among them (e.g., relative positions and poses). In this paper, we…
Convolutional Neural Networks(CNN) are inherently equivariant under translations, however, they do not have an equivalent embedded mechanism to handle other transformations such as rotations and change in scale. Several approaches exist…
Traditional supervised learning aims to learn an unknown mapping by fitting a function to a set of input-output pairs with a fixed dimension. The fitted function is then defined on inputs of the same dimension. However, in many settings,…
We present a comprehensive framework for studying and leveraging morphological symmetries in robotic systems. These are intrinsic properties of the robot's morphology, frequently observed in animal biology and robotics, which stem from the…