Related papers: AtlasD: Automatic Local Symmetry Discovery
We introduce a machine-learning approach (denoted Symmetry Seeker Neural Network) capable of automatically discovering discrete symmetry groups in physical systems. This method identifies the finite set of parameter transformations that…
Stochastic filters for on-line state estimation are a core technology for autonomous systems. The performance of such filters is one of the key limiting factors to a system's capability. Both asymptotic behavior (e.g.,~for regular…
Robust and efficient local feature matching plays a crucial role in applications such as SLAM and visual localization for robotics. Despite great progress, it is still very challenging to extract robust and discriminative visual features in…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…
The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the…
Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject…
We describe a novel geometric methodology for analyzing free-energy and kinetics of assembly driven by short-range pair-potentials in an implicit solvent, and provides illustrations of its unique capabilities. An atlas is a labeled…
Lie-symmetry methods are used to determine the symmetry group of reduced magnetohydrodynamics. This group allows for arbitrary, continuous transformations of the fields themselves, along with space-time transformations. The derivation…
Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis…
Symmetry in combinatorial problems is an extensively studied topic. We continue this research in the context of model expansion problems, with the aim of automating the workflow of detecting and breaking symmetry. We focus on local domain…
We propose a simple method to identify a continuous Lie algebra symmetry in a dataset through regression by an artificial neural network. Our proposal takes advantage of the $ \mathcal{O}(\epsilon^2)$ scaling of the output variable under…
In this paper, we study a sequential decision-making problem, called Adaptive Sampling for Discovery (ASD). Starting with a large unlabeled dataset, algorithms for ASD adaptively label the points with the goal to maximize the sum of…
The detection of the abnormal area from urban data is a significant research problem. However, to the best of our knowledge, previous methods designed on spatio-temporal anomalies are road-based or grid-based, which usually causes the data…
In this paper, we focus on the intersections of a manifold's local structures to analyze the global structure of a manifold. We obtain local regions on data manifolds such as the latent space of StyleGAN2, using Mapper, a tool from…
We consider the popular and classical method of alternating projections for finding a point in the intersection of two closed sets. By situating the algorithm in a metric space, equipped only with well-behaved geodesics and angles (in the…
Due to the abundance of 2D product images from the Internet, developing efficient and scalable algorithms to recover the missing depth information is central to many applications. Recent works have addressed the single-view depth estimation…
Vehicle trajectories are a promising GNSS (Global Navigation Satellite System) data source to compute multi-scale traffic flow maps ranging from the city/regional level to the road level. The main obstacle is that trajectory data are prone…
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…
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…