Papers › Llemma: An Open Language Model For Mathematics

Llemma: An Open Language Model For Mathematics

16 Oct 2023arXiv:2310.10631archive 2025-07-28

Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster, Marco Dos Santos, Stephen Mcaleer, Albert Q. Jiang, Jia Deng, Stella Biderman, Sean Welleck

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

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EleutherAI/math-lm officialmentioned in papermentioned on GitHubMIT report
eleutherai/gpt-neox officialmentioned in papermentioned on GitHubpytorchApache-2.0 report
wellecks/llmstep officialmentioned in papermentioned on GitHubpytorchMIT report
wellecks/llemma_formal2formal mentioned on GitHubMIT report

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create_outputs EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_isabelle_proofsteps.py official repository ran MIT (permissive) · 404e4e000ce8e5a4 · report
extract_theory_file EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_isabelle_proofsteps.py official repository ran fingerprinted MIT (permissive) · a748289feeef8b50 · report
numerical_density EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_stack.py official repository ran MIT (permissive) · dc657f552ea0c7e4 · report
r_filter EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_stack.py official repository ran MIT (permissive) · 90d0c5e777c36f13 · report
split_list EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_isabelle_proofsteps.py official repository ran MIT (permissive) · a3b15e19e090eb8d · report
standard_filter EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_stack.py official repository ran MIT (permissive) · 6557b371083607b5 · report
row_of_name EleutherAI/math-lm/proof_pile_2/algebraic_stack/process_lean_proofsteps.py official repository unverified MIT (permissive) · 328e227d602c1b9a · report
resume_from wellecks/llemma_formal2formal/proofsearch.py community (archive-listed) unverified MIT (permissive) · f227a3efda0fb0e6 · report

Tasks

Arithmetic ReasoningAutomated Theorem ProvingLanguage ModelingLanguage ModellingLarge Language ModelMathmodel

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Arithmetic Reasoning GSM8K Llemma 34B Accuracy 51.5 #132 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Llemma 34B Parameters (Billion) 34 #132 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Llemma 7B Accuracy 36.4 #142 of 164 Archive leaderboard report
Arithmetic Reasoning GSM8K Llemma 7B Parameters (Billion) 7 #142 of 164 Archive leaderboard report
Automated Theorem Proving miniF2F-test LLEMMA-7b ITP Lean #21 of 29 Archive leaderboard report
Automated Theorem Proving miniF2F-test LLEMMA-7b Pass@32 26.2 #21 of 29 Archive leaderboard report
Automated Theorem Proving miniF2F-test LLEMMA-7b cumulative 26.2 #21 of 29 Archive leaderboard report
Automated Theorem Proving miniF2F-test LLEMMA-34b ITP Lean #22 of 29 Archive leaderboard report
Automated Theorem Proving miniF2F-test LLEMMA-34b Pass@32 25.8 #22 of 29 Archive leaderboard report
Automated Theorem Proving miniF2F-test LLEMMA-34b cumulative 25.8 #22 of 29 Archive leaderboard report

Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.

Methods

BASE

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