Finsler Geometry

Latest papers

8 papers2 papers in the last four weeks, against 1 the four weeks before. 0.0% of all new papers.

Finsler Flow Matching: Dynamics-Aware Geodesic Interpolation for Single-Snapshot Trajectory Inference
Oct 8, 2026Niklas Canova, Jonas Simon FleckFinsler Geometry Flow-Based Generative Modeling
Institute of Human Biology (IHB), Roche, Basel, Switzerland
A Finslerian Approach for Embedding Directed Data
Sep 29, 2026Gwendal Debaussart-Joniec, Théau Blanchard, Argyris KalogeratosFinsler Geometry Graph Embedding
CB, ENS Paris Saclay · UMR 1346 HeKA, Universit´e Paris Cit´e, Inria, Inserm GE Healthcare F-75015 Paris, France · HeKA | U1346, GE Healthcare
$\mathbb{SL}(n)$ Representation Learning: An Intrinsic Mixed-Curvature Space with Higher Curvature Capacities and Deeper Order-Aware Composition
Sep 14, 2026Xingrun Li, Yusuke Mukuta, Xin Yang +2Finsler Geometry Graph Representation Learning
The University of Tokyo · Stanford University
Finsler Geometry, Graph Neural Networks, and You
Jun 15, 2026T. Mitchell Roddenberry, Richard G. BaraniukFinsler Geometry Graph Neural Networks
Rice University, Houston, TX, USA
Geodesics with Unified Tangent-constrained Priors and Curvature Regularization
May 28, 2026Chong Di, Li Liu, Jinglin Zhang +3Finsler Geometry Medical Image Segmentation
Shandong Artificial Intelligence Institute, Qilu University of Technology (Shandong Academy of Sciences), Jinan, Shandong, China · Yuanshen Rehabilitation Institute, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China · School of Control Science and Engineering, Shandong University, Jinan, Shandong, China +2
Learning Lineage-guided Geodesics with Finsler Geometry
Mar 17, 2026Aaron Zweig, Mingxuan Zhang, David A. Knowles +1Finsler Geometry Trajectory Inference
New York Genome Center · Irving Institute for Cancer Dynamics, Columbia University · Department of Systems Biology, Columbia University +3
Harnessing Data Asymmetry: Manifold Learning in the Finsler World
Mar 12, 2026Thomas Dagès, Simon Weber, Daniel Cremers +1Finsler Geometry Manifold Learning
Technion – Israel Institute of Technology · Technical University of Munich · Munich Center for Machine Learning +1
Geometric structures and deviations on James' symmetric positive-definite matrix bicone domain
Mar 3, 2026Jacek Karwowski, Frank NielsenFinsler Geometry Information Geometry
Department of Computer Science University of Oxford, UK · Sony Computer Science Laboratories Inc. Tokyo, Japan

Oct 8, 2026J/K move · Enter open · S save

Finsler Flow Matching: Dynamics-Aware Geodesic Interpolation for Single-Snapshot Trajectory Inference

Niklas Canova, Jonas Simon Fleck

Institute of Human Biology (IHB), Roche, Basel, Switzerland

Finsler Geometry Flow-Based Generative Modeling Single-Cell Transcriptomics Single-Cell RNA Sequencing Conditional Flow Matching

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Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin--Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.