Yu Leon Liu

I am a researcher working on machine learning, with a focus on reasoning, interpretability, and alignment. I recently completed a PhD in mathematics at Harvard, where my research was in mathematical physics and topology. During that time, I also worked on quantitative research at a stealth high-frequency trading startup and on agentic AI systems as an engineering intern.

Email  /  GitHub  /  Google Scholar  /  CV (PDF)

Research Interests

My primary interest is building AI systems that reason well and that we can understand and trust. My work spans automated reasoning for mathematics, reinforcement learning for post-training language models, and interpretability and alignment. I am especially drawn to oversight: methods for understanding what a model is computing internally and steering its behavior toward what we intend. My background in mathematics shapes how I approach these problems.

Projects

Autonomous Mathematical Research Agent   (private)
An agent that attacks open problems in mathematics through generate-and-verify loops, with an external-LLM verification service and multi-model campaign orchestration. Produced a new result on an open Erdős problem and improvements on several others.
[writeup] [writeup] [writeup]

Phase Transitions in Flow Language Models   (research)
With the Albergo lab at Harvard: studying a token-commitment phase transition in continuous simplex flows for text. The transition is sharp and geometric, and matches interpolant theory on a trained model.

Parameter Golf (OpenAI Model Craft Challenge)   (open source)
An agent-assisted LLM training pipeline (frozen specs, autonomous GPU runs, post-run audits) that cut experiment iteration time roughly 5x. A recurrence-band mixing variant beat the then-SOTA on validation bits-per-byte by 3 sigma across 3 seeds.
[PR #1779] [PR #1801]

LLM Post-Training with GRPO / RLVR   (research)
Trained and evaluated Qwen2.5-3B on Countdown with GRPO/RLVR and built diagnostic evals. Outcome-only reward raised the addition/subtraction set from 25% to 87% but suppressed multiplication, a case of strategy narrowing rather than broad capability gain.

Agent Skills   (open source)
A public toolkit of production-tested skills for AI coding agents (external-LLM review loops, proof-verification loops, paper reading, LaTeX writeups), usable across Claude Code, Codex, Gemini CLI, and Cursor.
[code]

Quant and Agentic Systems   (industry)
C++ orderbook and execution-backtesting infrastructure at a stealth high-frequency trading startup; and an LLM-driven C++ optimization pipeline (dependency-DAG analysis plus agentic implementation gated by tests and benchmarks, around 1.5x speedups) as an agentic engineering intern.

Selected Publications

I have written around ten papers in mathematics; a few are below, and the full list is on the papers page.

The Smith Fiber Sequence of Invertible Field Theories
A. Debray, S. K. Devalapurkar, C. Krulewski, Y. L. Liu, N. Pacheco-Tallaj, R. Thorngren
Communications in Mathematical Physics, 2026   [arXiv]

A Long Exact Sequence in Symmetry Breaking
A. Debray, S. K. Devalapurkar, C. Krulewski, Y. L. Liu, N. Pacheco-Tallaj, R. Thorngren
Journal of High Energy Physics, 2025   [arXiv]

A Braided Monoidal (∞,2)-Category of Soergel Bimodules
Y. L. Liu, A. Mazel-Gee, D. Reutter, C. Stroppel, P. Wedrich
2024 (presented in an ICM plenary talk)   [arXiv]

Constructing the Virasoro Groups from Differential Cohomology
A. Debray, Y. L. Liu, C. Weis
International Mathematics Research Notices, 2023   [arXiv]