3 papers
math.AG2025
Bethe subspaces and wonderful models for toric arrangements
Aleksei Ilin, Leonid Rybnikov
We study the family of commutative subspaces in the trigonometric holonomy Lie algebra , introduced by Toledano Laredo, for an arbitrary root system . We…
math.RT2025
Gaudin models and moduli space of flower curves
Aleksei Ilin, Joel Kamnitzer, Leonid Rybnikov
We introduce and study the family of trigonometric Gaudin subalgebras in for arbitrary simple Lie algebra . This is the family of commutative subalgebras of ma…
cs.LG2025
Lightweight Safety Guardrails via Synthetic Data and RL-guided Adversarial Training
Aleksei Ilin, Gor Matevosyan, Xueying Ma +5
We introduce a lightweight yet highly effective safety guardrail framework for language models, demonstrating that small-scale language models can achieve, and even surpass, the pe…