Papers › A singular Riemannian Geometry Approach to Deep Neural Networks III. Piecewise...
A singular Riemannian Geometry Approach to Deep Neural Networks III. Piecewise Differentiable Layers and Random Walks on n-dimensional Classes
Alessandro Benfenati, Alessio Marta
Neural networks are playing a crucial role in everyday life, with the most modern generative models able to achieve impressive results. Nonetheless, their functioning is still not very clear, and several strategies have been adopted to study how and why these model reach their outputs. A common approach is to consider the data in an Euclidean settings: recent years has witnessed instead a shift from this paradigm, moving thus to more general framework, namely Riemannian Geometry. Two recent works introduced a geometric framework to study neural networks making use of singular Riemannian metrics. In this paper we extend these results to convolutional, residual and recursive neural networks, studying also the case of non-differentiable activation functions, such as ReLU. We illustrate our findings with some numerical experiments on classification of images and thermodynamic problems.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections