Peiyang Song

I am a 3rd-year undergraduate student studying Computer Science at California Institute of Technology (Caltech), advised by Prof. Steven Low, with a minor in Robotics advised by Prof. Günter Niemeyer. I am a researcher in the Stanford AI Lab (SAIL), working with Prof. Noah Goodman and Gabriel Poesia in the Computation & Cognition Lab (CoCoLab). I will join Berkeley AI Research (BAIR) Lab, starting June 2025, advised by Prof. Dawn Song. I have also been fortunate to work with Prof. Anima Anandkumar (Caltech), Dr. Kaiyu Yang (Meta), Prof. Tim Sherwood (UC Santa Barbara), and Dr. Jeremy Lau (Google) during my undergrad.

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[Apr. 2025] Our paper Lean Copilot is accepted to NeuS 2025. See you in Philadelphia, PA!
[Mar. 2025] I am joining Prof. Dawn Song's group at UC Berkeley starting June 2025, working on AI for formal math and verifiable code.
[Mar. 2025] Our paper LeanProgress is accepted to ICLR 2025 VerifAI Workshop. See you in Singapore!
[Feb. 2025] Our ASPLOS 2024 paper Energy Efficient Convolutions with Temporal Arithmetic is awarded IEEE Micro Top Pick 2025.
[Nov. 2024] Thanks Scientific American for featuring my works on AI for mathematical reasoning, including LeanDojo and Lean Copilot.

My current research interest is mainly in LLM reasoning, especially neuro-symbolic AI for formal math and verifiable code generation. In the past, I also published on neuro-symbolic methods for energy-efficient ML systems and neural machine translation.

LLMs struggling with long proofs? We present LeanProgress, which uses a novel critic model where “distance” to the goal state acts as a key signal for step prediction, boosting performance on neural theorem proving in Lean. Our method achieves 75.1% prediction accuracy, with a 3.8% gain in proof search with step prediction.

LeanAgent continuously learns and improves on ever-expanding mathematical knowledge without forgetting what it learned before. It has a curriculum learning strategy that optimizes the learning trajectory in terms of mathematical difficulty, a dynamic database for efficient management of evolving mathematical knowledge, and progressive training to balance stability and plasticity.

We introduce Lean Copilot, a framework for running neural network inference directly in Lean. It enables various LLM-based proof automation tools that integrate seamlessly into the workflow of Lean users, including tools for suggesting proof steps (tactics), selecting premises, and searching for complete proofs using LLMs.

To compile a dictionary of East Asian idiom translations demands much time and creativity even for expert translators. To alleviate such burden, we automate high-quality data generation with GPT-4, and discover Pareto-optimal prompting strategies on both faithfulness and creativity, outperforming existing translation engines and human baseline.

Motivated by the crucial cognitive phenomenon of A-not-B errors, we present the first systematic evaluation on the surprisingly vulnerable inhibitory control abilities of LLMs. We reveal that this weakness undermines LLMs' trustworthy reasoning capabilities across diverse domains, and introduce various mitigations.

We introduce energy-efficient convolution that improves the energy per pixel of each convolution frame by more than 2× compared to the state-of-the-art while improving the energy delay product by four orders of magnitude, by developing a new temporal arithmetic with a negative log transformation.

Can LLMs generate mathematical proofs that can be rigorously checked? We release LeanDojo: an open-source playground consisting of toolkits, benchmarks, and models for LLMs to prove formal theorems in the Lean proof assistant.

My works have been covered by many media. Some representative ones include:

• Mathematicians’ Newest Assistants Are Artificially Intelligent, Scientific American, 2024
• LeanAgent: The First Life-Long Learning Agent for Formal Theorem Proving in Lean, MarkTechPost, 2024
• Lean Copilot: An AI Tool that Allows Large Language Models (LLMs) to be used in Lean for Proof Automation, MarkTechPost, 2024
• Can LLMs Generate Mathematical Proofs that can be Rigorously Checked?, MarkTechPost, 2023

• Reviewer for conferences: NeurIPS, ICLR, ARR, ACL, EMNLP, etc.
• Reviewer for workshops: MATH-AI, VerifAI, Re-Align, LLM-Cognition, BehaviorML, World-Models, etc.

Last updated: Apr. 2025. Website template credit: Jon Barron.