6 papers
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…
A Non-Adversarial Approach to Idempotent Generative Modelling
Mohammed Al-Jaff, Giovanni Luca Marchetti, Michael C Welle +5
Idempotent Generative Networks (IGNs) are deep generative models that also function as local data manifold projectors, mapping arbitrary inputs back onto the manifold. They are tra…
Alternating Gradient Flows: A Theory of Feature Learning in Two-layer Neural Networks
Daniel Kunin, Giovanni Luca Marchetti, Feng Chen +5
What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dy…
Rubik's Abstract Polytopes
Giovanni Luca Marchetti
We generalize the Rubik's cube, together with its group of configurations, to any abstract regular polytope. After discussing general aspects, we study the Rubik's simplex of arbit…
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…
The (he)art of gluing
Giovanni Luca Marchetti, Domenico Fiorenza
We introduce a notion of gluability for poset-indexed Bridgeland slicings on triangulated categories and show how a gluing abelian slicing on the heart of a bounded -structure n…