相关论文: Affine differential geometry and smoothness maximi…
Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper,…
Motion segmentation in dynamic scenes is highly challenging, as conventional methods heavily rely on estimating camera poses and point correspondences from inherently noisy motion cues. Existing statistical inference or iterative…
This paper presents and proves an equation for the time horizon of symmetric trajectories with zero boundary conditions and bounded derivatives of arbitrary order. This equation holds regardless of the number of phases comprising the…
Understanding the dynamics of neural network parameters during training is one of the key challenges in building a theoretical foundation for deep learning. A central obstacle is that the motion of a network in high-dimensional parameter…
In this paper, we study the dynamics of gradient descent in learning neural networks for classification problems. Unlike in existing works, we consider the linearly non-separable case where the training data of different classes lie in…
Search problems at various scales involve a searcher, be it a molecule before reaction or a foraging animal, which performs an intermittent motion. Here we analyze a generic model based on such type of intermittent motion, in which the…
A molecule's geometry, also known as conformation, is one of a molecule's most important properties, determining the reactions it participates in, the bonds it forms, and the interactions it has with other molecules. Conventional…
Understanding the optimization dynamics of neural networks is necessary for closing the gap between theory and practice. Stochastic first-order optimization algorithms are known to efficiently locate favorable minima in deep neural…
Current approaches to video analysis of human motion focus on raw pixels or keypoints as the basic units of reasoning. We posit that adding higher-level motion primitives, which can capture natural coarser units of motion such as backswing…
Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…
Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have…
Impressive progress in 3D shape extraction led to representations that can capture object geometries with high fidelity. In parallel, primitive-based methods seek to represent objects as semantically consistent part arrangements. However,…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
Trajectory segmentation refers to dividing a trajectory into meaningful consecutive sub-trajectories. This paper focuses on trajectory segmentation for 3D rigid-body motions. Most segmentation approaches in the literature represent the…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
Predicting human motion in unstructured and dynamic environments is difficult as humans naturally exhibit complex behaviors that can change drastically from one environment to the next. In order to alleviate this issue, we propose to encode…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
This letter presents a novel approach to extract reliable dense and long-range motion trajectories of articulated human in a video sequence. Compared with existing approaches that emphasize temporal consistency of each tracked point, we…
Sign-based optimization methods have become popular in machine learning due to their favorable communication cost in distributed optimization and their surprisingly good performance in neural network training. Furthermore, they are closely…