4 papers · 1 filter
The Agentic Researcher: A Practical Guide to AI-Assisted Research in Mathematics and Machine Learning
Max Zimmer, Nico Pelleriti, Christophe Roux +1
AI tools and agents are reshaping how researchers work, from proving theorems to training neural networks. Yet for many, it remains unclear how these tools fit into everyday resear…
Neural Sum-of-Squares: Certifying the Nonnegativity of Polynomials with Transformers
Nico Pelleriti, Christoph Spiegel, Shiwei Liu +3
Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condi…
Computational Algebra with Attention: Transformer Oracles for Border Basis Algorithms
Hiroshi Kera, Nico Pelleriti, Yuki Ishihara +2
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gröbner and…
Approximating Latent Manifolds in Neural Networks via Vanishing Ideals
Nico Pelleriti, Max Zimmer, Elias Wirth +1
Deep neural networks have reshaped modern machine learning by learning powerful latent representations that often align with the manifold hypothesis: high-dimensional data lie on l…