The current paper deals with some new classes of Finsler metrics with reversible geodesics. We construct weighted quasi-metrics associated with these metrics. Further, we investigate some important geometric properties of weighted quasi-metric space. Finally, we discuss the embedding of quasi-metric spaces with general…
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11 results for “quasi-metric”
Study of classification in asymmetric quasi-metric spaces.
problem Classification in asymmetric quasi-metric spaces.
method Sample compression and nearest neighbor algorithm.
result Algorithm has favorable statistical properties.
We investigate the relation between weighted quasi-metric Spaces and Finsler Spaces. We show that the induced metric of a Randers space with reversible geodesics is a weighted quasi-metric space.
New RL approach speeds up training across tasks.
problem Training reinforcement learning models quickly and efficiently.
method Combines planning quasi-metric and task-specific aimers.
result Achieves multiple-fold speed-up on bit-flip and robotic arm tasks.
Characterizes isometries between non-reversible Finsler manifolds.
problem Understanding isometries in non-reversible Finsler manifolds.
method Generalization of Myers-Nakai Theorem for Riemannian manifolds, modification of function spaces to accommodate asymmetric structure.
result Functional characterization of isometries between non-reversible Finsler manifolds.
For any geodesic current we associated a quasi-metric space. For a subclass of geodesic currents, called filling, it defines a metric and we study the critical exponent associated to this space. We show that is is equal to the exponential growth rate of the intersection function for closed curves.
We develop the basics of a theory of almost isometries for spaces endowed with a quasi-metric. The case of non-reversible Finsler (more specifically, Randers) metrics is of particular interest, and it is studied in more detail. The main motivation arises from General Relativity, and more specifically in spacetimes endo…
Obtaining continuous representations of structural data such as directed acyclic graphs (DAGs) has gained attention in machine learning and artificial intelligence. However, embedding complex DAGs in which both ancestors and descendants of nodes are exponentially increasing is difficult. Tackling in this problem, we de…
Neural Spacetimes learn DAGs by embedding nodes in a spacetime manifold.
problem Learning representations of weighted directed acyclic graphs (DAGs).
method Trainable deep learning-based geometries (Neural Spacetimes) that encode both edge weights and causality.
result Universal embedding theorem for DAGs with sub-cubic parameters and low distortion.
Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
problem Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
method Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
result Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
Dreaming machine learning: Lipschitz extensions for reinforcement learning on financial marketsq-fin.ST
We consider a quasi-metric topological structure for the construction of a new reinforcement learning model in the framework of financial markets. It is based on a Lipschitz type extension of reward functions defined in metric spaces. Specifically, the McShane and Whitney extensions are considered for a reward function…