{"ID":2847940,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.26266","arxiv_id":"2510.26266","title":"A Likely Geometry of Generative Models","abstract":"The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data dimension. In this paper, we construct a general geometry compatible with different metrics and probability distributions to analyze generative models that do not require additional training. We consider curves analogous to geodesics constrained to a suitable data distribution aimed at targeting high-density regions learned by generative models. We formulate this as a (pseudo)-metric and prove that this corresponds to a Newtonian system on a Riemannian manifold. We show that shortest paths in our framework can be characterized by a system of ordinary differential equations, which locally corresponds to geodesics under a suitable Riemannian metric. Numerically, we derive a novel algorithm to efficiently compute shortest paths and generalized Fréchet means. Quantitatively, we show that curves using our metric traverse regions of higher density than baselines across a range of models and datasets.","short_abstract":"The geometry of generative models serves as the basis for interpolation, model inspection, and more. Unfortunately, most generative models lack a principal notion of geometry without restrictive assumptions on either the model or the data dimension. In this paper, we construct a general geometry compatible with differe...","url_abs":"https://arxiv.org/abs/2510.26266","url_pdf":"https://arxiv.org/pdf/2510.26266v2","authors":"[\"Frederik Möbius Rygaard\",\"Shen Zhu\",\"Yinzhu Jin\",\"Søren Hauberg\",\"Tom Fletcher\"]","published":"2025-10-30T08:46:53Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[]","has_code":false}