9 citations · 13 across the 9 of their papers we have counts for
6 papers · 1 filter
Critical Points of Degenerate Metrics on Algebraic Varieties: A Tale of Overparametrization
Giovanni Luca Marchetti, Erin Connelly, Paul Breiding +1
We study the critical points over an algebraic variety of an optimization problem defined by a quadratic objective that is degenerate. This scenario arises in machine learning when…
The Riemannian Geometry Associated to Gradient Flows of Linear Convolutional Networks
El Mehdi Achour, Kathlén Kohn, Holger Rauhut
We study geometric properties of the gradient flow for learning deep linear convolutional networks. For linear fully connected networks, it has been shown recently that the corresp…
An Algebraic Geometry Approach to Viewing Graph Solvability
Federica Arrigoni, Kathlén Kohn, Andrea Fusiello +1
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associ…
A Framework for Reducing the Complexity of Geometric Vision Problems and its Application to Two-View Triangulation with Approximation Bounds
Felix Rydell, Georg Bökman, Fredrik Kahl +1
In this paper, we present a new framework for reducing the computational complexity of geometric vision problems through targeted reweighting of the cost functions used to minimize…
PLMP -- Point-Line Minimal Problems for Projective SfM
Kim Kiehn, Albin Ahlbäck, Kathlén Kohn
We completely classify all minimal problems for Structure-from-Motion (SfM) where arrangements of points and lines are fully observed by multiple uncalibrated pinhole cameras. We f…
Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Giovanni Luca Marchetti, Vahid Shahverdi, Stefano Mereta +2
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic…