Related papers: Learning Lineage-guided Geodesics with Finsler Geo…

A graphical model is a structured representation of the data generating process. The traditional method to reason over random variables is to perform inference in this graphical model. However, in many cases the generating process is only a…

The prediction of humans' short-term trajectories has advanced significantly with the use of powerful sequential modeling and rich environment feature extraction. However, long-term prediction is still a major challenge for the current…

Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general…

We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…

Sparsity is a common issue in many trajectory datasets, including human mobility data. This issue frequently brings more difficulty to relevant learning tasks, such as trajectory imputation and prediction. Nowadays, little existing work…

Here, a non-linear analysis method is applied rather than classical one to study projective changes of Finsler metrics. More intuitively, a projectively invariant pseudo-distance is introduced and characterized with respect to the Ricci…

Here, it is introduced a concept of convolution metric in Finslerian Geometry. This convolution metric is a kind of function obtained by a given mathematical operation between two Finslerian metrics. Some basic properties of the Finslerian…

Reliable 4D aircraft trajectory prediction, whether in a real-time setting or for analysis of counterfactuals, is important to the efficiency of the aviation system. Toward this end, we first propose a highly generalizable efficient…

A useful inductive bias for temporal data is that trajectories should stay close to the data manifold. Traditional flow matching relies on straight conditional paths, and flow matching methods which learn geodesics rely on RBF kernels or…

Evaluating LLM reliability via scalar probabilities often fails to capture the structural dynamics of reasoning. We introduce TRACED, a framework that assesses reasoning quality through theoretically grounded geometric kinematics. By…

In this work, we propose to study the global geometrical properties of generative models. We introduce a new Riemannian metric to assess the similarity between any two data points. Importantly, our metric is agnostic to the parametrization…

Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…

Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…

Trajectory interpolation, the process of filling-in the gaps and removing noise from observed agent trajectories, is an essential task for the motion inference in multi-agent setting. A desired trajectory interpolation method should be…

Robotic systems often operate with uncertainties in their dynamics, for example, unknown inertial properties. Broadly, there are two approaches for controlling uncertain systems: design robust controllers in spite of uncertainty, or…

Trajectory prediction plays a vital role in automotive radar systems, facilitating precise tracking and decision-making in autonomous driving. Generative adversarial networks with the ability to learn a distribution over future trajectories…

Network inference, the task of reconstructing interactions in a complex system from experimental observables, is a central yet extremely challenging problem in systems biology. While much progress has been made in the last two decades,…

Robotics research has found numerous important applications of Riemannian geometry. Despite that, the concept remain challenging to many roboticists because the background material is complex and strikingly foreign. Beyond {\em Riemannian}…

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…