Vahid Shahverdi

I’m a PhD graduate in Mathematics from KTH Royal Institute of Technology. I work on the theory of neural networks, and I’m a cofounder of neuroalgebraic geometry, where we use algebra and geometry to study the structure of these models.

Current position

PhD student in Mathematics

- Area: Algebraic geometry, machine learning, and signal processing
- Thesis: Manifolds of Learning
- Supervisors: Kathlén Kohn & Joakim Anden
- University: KTH

Contact details

- Email address: vahidsha at kth dot se
- Office: 7-th floor, LINDSTEDTSVÄGEN 25

Papers

Identifiable Equivariant Networks are Layerwise Equivariant with Giovanni Luca Marchetti, Georg Bökman and Kathlén Kohn
Learning on a Razor's Edge: the Singularity Bias of Polynomial Neural Networks (ICLR 2026) with Giovanni Luca Marchetti and Kathlén Kohn
Algebra Unveils Deep Learning: An Invitation to Neuroalgebraic Geometry (ICML 2025, Spotlight), with Giovanni Luca Marchetti, Stefano Mereta, Matthew Trager and Kathlén Kohn
On the Geometry and Optimization of Polynomial Convolutional Networks (AISTATS 2024), with Giovanni Luca Marchetti and Kathlén Kohn
Moment Constraints and Phase Recovery for Multireference Alignment (arXiv preprint arXiv:2409.04868), with Emanuel Ström and Joakim Andén
Function Space and Critical Points of Linear Convolutional Networks (SIAM Journal on Applied Algebra and Geometry), with Kathlén Kohn, Guido Montúfar, and Matthew Trager
Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups (SIAM Journal on Matrix Analysis and Applications), with Kathlén Kohn, and Anna-Laura Sattelberger
Algebraic Complexity and Neurovariety of Linear Convolutional Networks (Acta Univ. Sapientiae Math)
New Approach to Character-Free Proof for Frobenius Theorem (Bachelor Project) with Seyedeh Fatemeh ARFAEE ZARANDI

Previous study

MSc in Mathematics

- Area: Algebraic geometry
- Thesis: Local and global aspects of Deligne-Mumford moduli space of curves
- Supervisors: Dimitri Wyss & Francesca Carocci
- University: EPFL

Teaching

Modern Methods of Statistical Learning
Commutative Algebra and Algebraic Geometry
Groups and Rings

Lecture notes

Machine Learning and Algebraic Geometry

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