Geometric Science of Information

The 3-volume set LNCS 16033 - 16035 constitutes the proceedings of the 7th International Conference on Geometric Science of Information, GSI 2025, held in St. Malo, France, during October 2025. The main theme of GSI 2025 was: Geometric Structures of Statistical and Quantum Physics, Information Geometry, and Machine Learning: FROM CLASSICAL TO QUANTUM INFORMATION GEOMETRY.The 124 full papers included in the proceedings were carefully reviewed and selected from 146 submissions. They were organized in topical sections as follows:Part I: Geometric Learning and Differential Invariants on Homogeneous Spaces; Statistical Manifolds and Hessian information geometry; Applied Geometry-Informed Machine Learning; Geometric Green Learning on Groups and Quotient Spaces; Divergences in Statistics and Machine Learning;Part II: Geometric Statistics; Computational Information Geometry and Divergences; Geometric Methods in Thermodynamics; Classical & Quantum Information, Geometry and Topology; Geometric Mechanics; Stochastic Geometric Dynamics;  Part III: New trends in Nonholonomic Systems; Learning of Dynamic Processes; Optimization and learning on manifolds; Neurogeometry; Lie Group in Learning Distributions & in Filters; A geometric approach to differential equations; Information Geometry, Delzant Toric Manifold & Integrable System.