aiqbench analysis
This arXiv preprint proposes a Finsler-Randers metric learning framework for deep neural network latent spaces. Its main claim is that direction-dependent distances, rather than curvature alone, can better model one-way processes like disease progression, enabling trajectories that respect monotonic constraints. The evidence so far is limited to controlled cross-sectional datasets, so practical value for real clinical or image data remains to be shown.
Learning Directional Randers Geometry for Latent-Space Exploration
arXiv:2611.03675v1 Announce Type: new Abstract: Deep neural networks extract powerful latent representations from images, enabling fast and efficient downstream analysis. However, these latent spaces lack explicit geometric structure, leading to possibly poor interpolation fidelity and misleading extrapolation. Latent interpolation techniques assume symmetric transition costs which are often not the case for real world data. Their symmetric nature cannot capture directional processes, such as disease progression, where certain transitions are impossible (e.g. tumor growth dynamics or cognitive improvement in Alzheimer's disease). Although Riemannian metrics extend Euclidean geometry by incorporating curvature, they remain symmetric. We show that understanding asymmetry and not curvature alone directly addresses these problems. To do so we propose a new Finsler-Randers metric learning framework. It incorporates direction-dependent distances, thus enabling the computation of trajectories respecting monotonic sequential constraints. We demonstrate its potential for interpolation and extrapolation on controlled cross-sectional datasets.
Abstract:Deep neural networks extract powerful latent representations from images, enabling fast and efficient downstream analysis. However, these latent spaces lack explicit geometric structure, leading to possibly poor interpolation fidelity and misleading extrapolation. Latent interpolation techniques assume symmetric transition costs which are often not the case for real world data. Their symmetric nature cannot capture directional processes, such as disease progression, where certain transitions are impossible (e.g. tumor growth dynamics or cognitive improvement in Alzheimer's disease). Although Riemannian metrics extend Euclidean geometry by incorporating curvature, they remain symmetric. We show that understanding asymmetry and not curvature alone directly addresses these problems. To do so we propose a new Finsler-Randers metric learning framework. It incorporates direction-dependent distances, thus enabling the computation of trajectories respecting monotonic sequential constraints. We demonstrate its potential for interpolation and extrapolation on controlled cross-sectional datasets.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Signal Processing (eess.SP); Differential Geometry (math.DG); Quantitative Methods (q-bio.QM)
arXiv:2611.03675 [cs.LG]
(or arXiv:2611.03675v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.03675 arXiv-issued DOI via DataCite (pending registration)
Full text under the publisher's open licence · 167 words