24 citations · 72 across the 30 of their papers we have counts for
39 papers
Linear Independence of Polynomial Compositions and Identifiability of Deep Neural Networks
Kathlén Kohn, Giovanni Luca Marchetti, Alex Massarenti +1
Motivated by theoretical problems in deep learning, we conjecture that post-composing a fixed number of pairwise distinct nonconstant polynomials with a generic polynomial of suffi…
Singular Learning and Occam's Razor in Deep Monomial Networks
Kathlén Kohn, Giovanni Luca Marchetti, Farhan Shabir +2
In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture. These critical points occur where the Jacobian…
Single-View Rolling-Shutter SfM
Sofía Errázuriz Muñoz, Kim Kiehn, Petr Hruby +1
Rolling-shutter (RS) cameras are ubiquitous, but RS SfM (structure-from-motion) has not been fully solved yet. This work suggests an approach to remedy this: We characterize RS sin…
Identifiable Equivariant Networks are Layerwise Equivariant
Vahid Shahverdi, Giovanni Luca Marchetti, Georg Bökman +1
We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is e…
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…