YC Root AccessLeanAgent: Lifelong Learning for Formal Theorem Proving
At a glance
WHAT IT’S REALLY ABOUT
LeanAgent uses lifelong learning to improve automated Lean theorem proving
- LeanAgent frames formal theorem proving in Lean as a lifelong learning problem, balancing stability (not forgetting) and plasticity (learning new material).
- The system builds a curriculum by scraping Lean GitHub repos, estimating theorem difficulty via proof-step complexity, and ordering training from easier to harder content.
- At each stage it updates a premise retriever with a light-touch one-epoch training strategy, then uses best-first tree search with a tactic generator to construct proofs.
- The framework reports proving 155 new formal proofs across 23 domains and observes “backwards transfer,” where learning new domains improves performance on earlier ones.
- The discussion contrasts LeanAgent’s search-centric approach with newer agent/RL-heavy methods, arguing stepwise search remains effective and more compute-efficient, especially with small open models.
IDEAS WORTH REMEMBERING
5 ideasFormal math is a stress test for lifelong learning.
Because math is cumulative, adding new knowledge can easily cause interference; LeanAgent uses this setting to measure whether a system can keep learning without losing earlier capabilities.
Premise retrieval is the central scaling challenge in Lean proving.
Lean proofs rely on selecting the right previously-proven lemmas/definitions (“premises”) from an ever-growing library, so retrieving relevant context at each step is often harder than generating tactics.
Curriculum order is induced from proof-step complexity across repos.
LeanAgent estimates theorem difficulty using the number of proof steps (with exponential growth in search complexity) and then prioritizes repositories with more “easy” theorems to build foundations first.
Minimal continual updates (one epoch) help avoid catastrophic forgetting.
Instead of heavy retraining, LeanAgent incrementally trains the retriever for a single pass on new material, aiming for a practical stability–plasticity sweet spot.
Search + retrieval + tactic generation forms a closed learning loop.
New proofs found by best-first tree search are written back into a dynamic database, which then improves future retrieval and proof attempts—creating compounding capability over time.
WORDS WORTH SAVING
5 quotesSo one of the hardest problems right now in AI is the continual or lifelong learning problem. How do you learn new things without forgetting what came previously?
— Adarsh Kumarappan
So the key to lifelong learning is to be in the sweet spot in between, and for this we chose the domain of formal math because it's one of the hardest places where you can do this.
— Adarsh Kumarappan
So it's a programming language where you code your proof and the compiler checks that your proof is correct.
— Adarsh Kumarappan
And as you can tell, there are so many premises in math that one of the hardest problems is how do you retrieve the relevant premises at each step of the proof?
— Adarsh Kumarappan
So as you learn you actually do better on previous domains. So if I learn algebra and then topology, now I'm better at algebra.
— Adarsh Kumarappan
High quality AI-generated summary created from speaker-labeled transcript.
