Alexey Kravatskiy

Summer Undergraduate Research Fellow 2026

About:
I am Alexey Kravatskiy, and in the summer of 2026, I will be working as a research intern at INSAIT, the Institute for Computer Science, Artificial Intelligence and Technology at Sofia University. My academic interests include optimization, deep learning, and artificial intelligence for mathematical discovery.

Education:

Moscow Institute of Physics and Technology (MIPT), Russia (September 2022 – July 2026)
School of Applied Mathematics and Computer Science
B.Sc. in Applied Mathematics and Physics with honors (CGPA: 5.00/5.00)

Research Experience:

AI4Math, LLM-guided evolution (11/2025-06/2026)
Worked on improving math agents like AlphaEvolve by probabilistic optimization. Introduced LLM-driven basin-hopping and obtained state-of-the-art results for algebraic and geometric problems (hexagon packing, the second autocorrelation inequality, and spherical codes), surpassing DeepMind’s AlphaEvolve. The work is accepted to ICML 2026 AI4Math Workshop.

SignSGD, differential privacy, federated learning (02/2025-05/2026)
Developed DP-SSD, a clipping-free differentially private algorithm, by designing a novel stochastic sign operator that natively enforces privacy without requiring traditional gradient clipping or noise addition. The work has been submitted to NeurIPS 2026.

Muon, matrix norms, linear minimization oracle (LMO) (04/2025-12/2025)
Developed novel matrix optimization algorithms by generalizing the Muon optimizer using duals to Ky Fan norms and conic combinations of norms. Demonstrated that competitive performance is not unique to Muon’s spectral norm and can be achieved with a broader family of norm constraints. Presented the work orally at ICOMP 2025, winning The Best Paper Presented at ICOMP 2025 award. The article is submitted to the special ICOMP issue of the Journal of Optimization Theory and Applications.

Awards:

All-Russian Student Olympiad “I am a Professional” in Mathematics (2026), Winner

All-Russian Student Olympiad “I am a Professional” in Mathematical Modelling (2026), Winner

The Best Paper Presented at ICOMP 2025, Abu Dhabi

All-Russian Olympiad for School Students in Physics, Final Round (2022), Winner

All-Russian Olympiad for School Students in Economics, Final Round (2022), Winner

All-Russian Olympiad for School Students in Art, Final Round (2021), Prize-Winner

All-Russian Olympiad for School Students in Physics, Final Round (2021), Prize-Winner

All-Russian Olympiad for School Students in Economics, Final Round (2021), Absolute Winner

among 10th-Graders

III International Olympiad in Exact Sciences, Baku, Azerbaijan (2019), Absolute Winner

Scholarships:

Polyak Scholarship for Contributions to the Development of Numerical Optimization Methods (Spring 2026, Fall 2025)
Marchuk Scientific Academic Scholarship (Spring 2026)
Rudakov Scientific Academic Scholarship (Spring 2026, Fall 2025)
Yandex Scholarship (2022-2024)

Publications:

[Ky Fan Norms and Beyond: Dual Norms and Combinations for Matrix Optimization](https://arxiv.org/abs/2512.09678), International Conference on Computational Optimization 2025
Alexey Kravatskiy, Ivan Kozyrev, Nikolai Kozlov, Alexander Vinogradov, Daniil Merkulov, Ivan Oseledets

[ImprovEvolve: Basin-Hopping Meets LLM-Guided Evolutionary Search](https://openreview.net/forum?id=nE1q0gRDNr), ICML AI for Math Workshop: Toward Self-Evolving Scientific Agents, 2026
Alexey Kravatskiy, Valentin Khrulkov, Ivan Oseledets

Differentially Private Clipping-Free Stochastic Sign Descent, Under review at NeurIPS 2026
Alexey Kravatskiy, Anton Pliusnin, Aleksandr Shestakov, Savelii Chezhegov, Daniil Medyakov, Aleksandr Beznosikov