Vasily Ilin

About Me

I am a Ph.D. student at the University of Washington, working with Jingwei Hu and Jarod Alper. I am the deputy director of the UW Math AI Lab and I organize the UW Math AI Seminar.

I grew up in Russia before moving to Boston in 2015 for undergrad. Initially pursuing economics, I switched to mathematics and graduated in 2019, followed by a Master’s in computer science in 2020. I began my PhD at the University of Washington in algebraic topology, then pivoted to applied mathematics in 2022 after an internship at Google. My current research focuses scientific machine learning and AI for mathematics.

Research Interests

• Scientific Machine Learning: model chemical dynamics, plasma and particle systems using neural networks.
• AI for Math: accelerate mathematics research with Lean and AI.

News

• [Nov. 2025] Posted “From Kernels to Attention: A Transformer Framework for Density and Score Estimation” on Arxiv.
• [Oct. 2025] Posted “Stability of the spatially homogeneous Landau equation in relative entropy and applications to score-based numerical methods” on Arxiv.
• [Sep. 2025] Started part-time work as AI Researcher at Math.Inc.
• [Sep. 2025] Finished my fourth internship at Google, using LLMs to turn slides into videos.
• [Apr. 2025] Presented poster “Score-Based Deterministic Density Sampling” at ICLR 2025.
• [Mar. 2025] Presented poster “Transport-based particle methods for the Fokker-Planck-Landau equation” at the Kinetic Fluid Workshop in UW-Madison.
• [Feb. 2025] RealEdit paper accepted in CVPR, Landau paper accepted in the CMS journal.
• [Jan. 2025] Gave two talks at JMM 2025 on sampling and Lean.
• [Nov. 2024] Submitted a paper on image editing with diffusion models to CVPR 2025.
• [Sep. 2024] Finished my third internship at Google, working on detection of defective TPUs using maching learning.
• [Jun. 2024] Participated in the SLMath summer school on interacting particle systems.
• [May 2024] Released pre-print “Transport based particle methods for the Fokker-Planck-Landau equation”.
• [Feb. 2024] Passed my general exam.

Publications

Selected Talks

Work Experience

• [2024] ML Intern at Google Cloud (Python, SQL) - Trained XGBoost to predict defective TPUs from telemetry, achieved 80% accuracy and improved test efficiency 4x.
• [2023] ML Intern at YouTube (Python, C++, SQL) - Trained ML models to enhance cache efficiency achieving 2x Egress/Ingress improvement. Implemented better load balancing based on two random choices model.
• [2022] Data Engineering Intern at Google (FlumeJava, SQL) - Built distributed pipeline for Nearby Share. Reduced dashboard loading from 30s to 1s using approximate aggregation.
• [2021] Google Summer of Code (Julia) - Implemented and optimized jump process simulation algorithms, improving runtime by 70% (blog post).

Services

Teaching Volunteering

• Experimental Lean Lab 2021-present
• Directed Reading Program 2021
• UW Math Circle 2020-2021

Organizing

• Math AI Lab 2022-present
• Math AI Seminar 2024-present

Open Source Software

• JumpProcesses.jl 2019-2023
• Mathlib4 2024-present

Teaching

Instructor

• Introduction to Mathematical Formalization, 2024 - New class at the University of Washington, teaching mathematics students to use formalize theorems in Lean.

Teaching Assistant

• Introduction to Mathematical Formalization, 2025
• Linear Algebra, 2023-2024
• Discrete Mathematical Modeling, 2023
• Calculus, 2020-2022
• Data Science, 2020

Projects

• [2025] University course collector (Data scraping, Gemini API, Serper API) - Scraped a dataset of 100,000 university courses from Russian universities, to be used by the Urait educational platform.
• [2025] Climb Genie (Data scraping, SQL) - Made a bi-gram climbing route generator for the Kilter board.
• [2024] Conditional Score-based generative modeling (PyTorch) - Implemented conditional score-based generative modeling on MNIST from scratch.
• [2024] Formalizing Central Limit Theorem (Lean4) - Formalized several lemmas on the way to the full CLT formalization, pushed them upstream to mathlib4.
• [2024] AI DnD Bot (OpenAI API, PostgreSQL) - Telegram bot for Dungeons & Dragons with long- and short-term memory and image generation features.
• [2024] Mean-field limit of a ResNet (PDE, gradient flows) - Infinite-width limit of a ResNet trained with gradient descent is a Wasserstein gradient flow ( slides ).
• [2024] Stein Variational Gradient Descent (Jax) - Analyzed SVGD algorithm for deterministic sampling (report).
• [2022] Deep Reinforcement Learning in DeepRacer (Python) - Placed in top 3% out of 1000+ participants in AWS virtual race (video, report).
• [2020] Cartier Duals (Homological Algebra) - Several examples of Cartier duals.
• [2020] Fully Dynamic Connectivity (Python) - Benchmarked graph connectivity data structure, exponentially faster than DFS (report).
• [2020] Object-Oriented Projects (Java) - Built a Quest game (CLI, 3k LOC) and Bank terminal (GUI, data persistence, 11k LOC) with the best OOD practices.
• [2020] Dense Low Rank Subgraph (Julia) - Introduced a novel combinatorics problem, proved it is polynomial-time solvable, and developed algorithms (report).
• [2019] Data Mining Competition (Python) - Placed second in class of 100+ graduate students in the competition of predicting citation links between publications in DBLP.
• [2019] Stochastic Simulation Algorithms (Julia) - Implemented and compared numerical methods for chemical stochastic systems.
• [2019] Mini Language (Haskell) - Created an imperative language in Haskell and solved five Project Euler problems.
• [2018] Behavioral Economics Research - Researched intuitive belief propagation.

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