Related papers: Symmetric Locality: Definition and Initial Results

Using the methods of the theory of formal symmetries, we obtain new easily verifiable sufficient conditions for a recursion operator to produce a hierarchy of local generalized symmetries. An important advantage of our approach is that…

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…

We develop a new unsupervised symmetry learning method that starts with raw data and provides the minimal generator of an underlying Lie group of symmetries, together with a symmetry-equivariant representation of the data, which turns the…

During our nearly constant use of digital devices, perhaps our most frequent need is to visually identify icons representing our content and invoke the actions to manipulate them. Almost since the inception of user interface design in the…

We propose a new method for local distance metric learning based on sample similarity as side information. These local metrics, which utilize conical combinations of metric weight matrices, are learned from the pooled spatial…

Symmetry is a fundamental aspect of many real-world robotic tasks. However, current deep reinforcement learning (DRL) approaches can seldom harness and exploit symmetry effectively. Often, the learned behaviors fail to achieve the desired…

Spatial reasoning requires both location-bound computation and location-invariant structure: agents must make local moves while preserving route, object, or constraint-level plans. We propose interaction locality, a task-geometry-aware…

This paper explores potential improvements to the Spatial-Temporal Matching algorithm for aligning the GPS trajectories to road networks. While this algorithm is effective, it presents some limitations in computational efficiency and the…

This document describes an attempt to develop a compiler-based approach for computations with symmetric tensors. Given a computation and the symmetries of its input tensors, we derive formulas for random access under a storage scheme that…

Simultaneous localization and mapping (SLAM) with implicit neural representations has received extensive attention due to the expressive representation power and the innovative paradigm of continual learning. However, deploying such a…

Task parallelism as employed by the OpenMP task construct, although ideal for tackling irregular problems or typical producer/consumer schemes, bears some potential for performance bottlenecks if locality of data access is important, which…

We design a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural networks to model the symmetry transformations and the corresponding…

Loop closures are essential for correcting odometry drift and creating consistent maps, especially in the context of large-scale navigation. Current methods using dense point clouds for accurate place recognition do not scale well due to…

Topological data analysis is an approach to study shape of a data set by means of topology. Its main object of study is the persistence diagram, which represents the topological features of the data set at different spatial resolutions.…

In this paper, we propose a novel trajectory learning method that exploits motion trajectories on topological map using recurrent neural network for temporally consistent geolocalization of object. Inspired by human's ability to both be…

This paper studies the properties of convergence of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semi-cyclic impulsive self-mappings on the union of a number of nonempty…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

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…

Local consistencies stronger than arc consistency have received a lot of attention since the early days of CSP research. %because of the strong pruning they can achieve. However, they have not been widely adopted by CSP solvers. This is…

Correctly capturing the symmetry transformations of data can lead to efficient models with strong generalization capabilities, though methods incorporating symmetries often require prior knowledge. While recent advancements have been made…