level: research
modern lean theorem provers need a lot of compute for training and inference. this is because verified proof data is scarce and formal proof searches create long reasoning traces. both supervised fine-tuning and sampling become expensive. pythagoras-prover is a new open-source family of lean provers built for practical compute budgets. it includes autoregressive models at 4b and 32b parameters, plus a first proof-of-concept diffusion-based prover at 4b that refines proofs step by step at inference time.
to train efficiently, the team built a lean-verified corpus split into easy, medium, and hard problems. this allows curriculum supervised fine-tuning, where models learn proof skills gradually from shorter to longer proofs. during training, a dynamic proof-reasoning filtering scheme keeps only the most informative proof traces. this avoids wasting compute on redundant or unhelpful examples, making the whole process more data-efficient.
the diffusion-based prover works differently from standard autoregressive models. it starts with a rough proof and iteratively improves it, which can be more flexible for complex reasoning. the 4b and 32b autoregressive models provide strong baselines. all models are open-source, so researchers can use and adapt them without large compute clusters. this could help more teams work on formal theorem proving without huge budgets.
why it matters: it lowers the compute barrier for formal theorem proving, making ai-assisted mathematics more accessible to researchers with limited resources.