Summary L LEMMA An Open Language Model for Mathematics arxiv.org
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L LEMMA is a high-performing language model for mathematical reasoning, pretrained on Proof-Pile-2 dataset consisting of scientific papers, web data, and mathematical code.
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Key Points
- L LEMMA is a large language model for mathematics that outperforms other models on mathematical problem-solving tasks.
- It has been trained on a mixture of scientific papers, web data containing mathematics, and mathematical code.
- The L LEMMA models, including 7 billion and 34 billion parameter models, have been openly released.
- Proof-Pile-2 is a dataset created for training or fine-tuning large language models in mathematics.
- The dataset consists of various subsets, including mathematical code from different programming languages, papers from ArXiv, and web content from OpenWebMath.
- The dataset has been used for training language models in mathematics tasks such as proof autoformalization and theorem proving.
- Maintenance of the dataset will be supported by the authors, and others can contribute to it by using the provided codebase to extend or augment the dataset.
- A datasheet for Proof-Pile-2 is provided, ensuring transparency and facilitating understanding and usage of the dataset.
Summaries
33 word summary
L LEMMA is a powerful language model that enhances mathematical reasoning, outperforming other models on the MATH benchmark. It was pretrained on Proof-Pile-2, a dataset of scientific papers, web data, and mathematical code.
98 word summary
L LEMMA is a powerful language model for mathematics that outperforms other models on the MATH benchmark. It can perform tool use and formal theorem proving without fine-tuning. The authors developed L LEMMA to enhance mathematical reasoning in AI language models. They adapted the model to mathematics by pretraining it on Proof-Pile-2, a dataset of scientific papers, web data, and mathematical code. The authors found that a 2:4:1 mixture ratio of arXiv:Web:Code yielded the best performance. Proof-Pile-2 is a self-contained dataset for training or fine-tuning large language models in mathematics, available via the HuggingFace Hub with transparent documentation.
142 word summary
L LEMMA is a powerful language model for mathematics that surpasses other open base models on the MATH benchmark. It can perform tool use and formal theorem proving without additional fine-tuning. The authors developed L LEMMA to address the need for strong mathematical reasoning capabilities in AI language models. They present a method for adapting a language model to mathematics through continued pretraining on Proof-Pile-2, a dataset that includes scientific papers, web data with mathematics, and mathematical code. The authors analyze the impact of data mixture on L LEMMA's performance and find that a 2:4:1 mixture ratio of arXiv:Web:Code works best. Proof-Pile-2 is a self-contained dataset for training or fine-tuning large language models in mathematics, distributed under applicable terms of use via the HuggingFace Hub. Detailed information about the dataset is provided in a datasheet, ensuring transparency and facilitating understanding and usage.
381 word summary
L LEMMA is a powerful language model for mathematics that outperforms other open base models on the MATH benchmark. It can perform tool use and formal theorem proving without further fine-tuning. The models, datasets, and code used in the experiments have all been released openly.
The authors developed L LEMMA to address the need for strong mathematical reasoning capabilities in AI language models. Previous domain-specific models for mathematics were either closed access or behind the state-of-the-art. To overcome this, the authors present a method for adapting a language model to mathematics through continued pretraining on Proof-Pile-2.
Proof-Pile-2 is a dataset that includes scientific papers, web data with mathematics, and mathematical code. It contains the AlgebraicStack dataset, the OpenWebMath dataset, and the ArXiv subset of RedPajama.
The L LEMMA models are initialized from Code Llama and further trained on Proof-Pile-2. The training is done using bfloat16 mixed precision and Tensor Parallelism across multiple GPUs.
Evaluation of L LEMMA as a base model for mathematical text shows its superiority over other models on various mathematical problem-solving benchmarks. It also demonstrates the ability to use computational tools to solve mathematical problems and promising results in few-shot tool use and formal theorem proving.
The authors analyze the impact of data mixture on L LEMMA's performance and find that a 2:4:1 mixture ratio of arXiv:Web:Code works best. They also examine the overlap between test examples and training documents and conclude that any hits do not imply memorization of correct answers.
Proof-Pile-2 is a self-contained dataset specifically created for training or fine-tuning large language models in mathematics. It consists of subsets such as mathematical code, ArXiv papers, and web content from OpenWebMath. The dataset has undergone preprocessing and cleaning to ensure high-quality language modeling data in the mathematics domain.
Maintenance of the dataset will be supported by the authors, and they can be contacted via email for inquiries. The dataset is distributed under applicable terms of use and can be accessed via the HuggingFace Hub.
Additional results include evaluations on Isabelle proof autoformalization and supervised fine-tuning on MetaMathQA, demonstrating the performance of models trained on Proof-Pile-2 in these tasks.
A datasheet for Proof-Pile-2 provides detailed information about the dataset's composition, collection process, preprocessing, and distribution. This datasheet ensures transparency and facilitates understanding and usage of the dataset.
529 word summary
L LEMMA is a powerful language model for mathematics that has been trained on a mixture of scientific papers, web data containing mathematics, and mathematical code. It surpasses other open base models on the MATH benchmark and can perform tool use and formal theorem proving without further fine-tuning. The models, datasets, and code to replicate the experiments have all been openly released.
The authors developed L LEMMA because solving mathematical problems requires pattern matching against specialized prior knowledge. Mathematical reasoning is an important AI task, and language models with strong mathematical reasoning capabilities are crucial for various research topics. However, previous domain-specific models for mathematics have either been closed access or behind the state-of-the-art. To address this, the authors present a method for adapting a language model to mathematics through continued pretraining on Proof-Pile-2.
Proof-Pile-2 is a dataset that includes scientific papers, web data with mathematics, and mathematical code. It contains the AlgebraicStack dataset with 11 billion tokens of code related to mathematics, the OpenWebMath dataset with high-quality web pages filtered for mathematical content, and the ArXiv subset of RedPajama, which reproduces the LLaMA training dataset.
The L LEMMA models are initialized from Code Llama and further trained on Proof-Pile-2 using a standard autoregressive language modeling objective. The 7 billion parameter model is trained for 200 billion tokens, and the 34 billion parameter model is trained for 50 billion tokens. Training is done using bfloat16 mixed precision and Tensor Parallelism across multiple GPUs.
Evaluation of L LEMMA as a base model for mathematical text demonstrates its superiority over other models on various mathematical problem-solving benchmarks, including MATH and GSM8k. It also shows the ability to use computational tools to solve mathematical problems and promising results in few-shot tool use and formal theorem proving.
The authors analyze the impact of data mixture on L LEMMA's performance and find that a 2:4:1 mixture ratio of arXiv:Web:Code works best. They also examine the overlap between test examples and training documents and conclude that any hits do not imply memorization of correct answers.
Proof-Pile-2 is a dataset specifically created for training or fine-tuning large language models in mathematics. It is self-contained, does not rely on external resources, and does not contain confidential or offensive data. It consists of subsets such as mathematical code, ArXiv papers, and web content from OpenWebMath. The dataset was collected, filtered, and labeled by the authors.
The dataset has undergone preprocessing and cleaning to ensure high-quality language modeling data in the mathematics domain. Both the cleaned and raw data are available for distribution. The dataset is distributed under applicable terms of use and can be accessed via the HuggingFace Hub.
Maintenance of the dataset will be supported by the authors, and they can be contacted via email for inquiries. Although the dataset will not be updated, others can contribute to it using the provided codebase.
Additional results include evaluations on Isabelle proof autoformalization and supervised fine-tuning on MetaMathQA, demonstrating the performance of models trained on Proof-Pile-2 in these tasks.
A datasheet for Proof-Pile-2 is provided, offering detailed information about the dataset's composition, collection process, preprocessing, and distribution. This datasheet ensures transparency and facilitates understanding and usage of the dataset.
750 word summary
L LEMMA is a large language model for mathematics that has been trained on a mixture of scientific papers, web data containing mathematics, and mathematical code. It outperforms all known open base models on the MATH benchmark and is capable of tool use and formal theorem proving without further fine-tuning. The L LEMMA models, including 7 billion and 34 billion parameter models, the Proof-Pile-2 dataset, and code to replicate the experiments, have all been openly released.
The authors trained a domain-specific language model for mathematics because solving mathematical problems requires pattern matching against specialized prior knowledge. Mathematical reasoning is also a central AI task, and language models capable of strong mathematical reasoning are upstream of several research topics. However, previous domain-specific models for mathematics have either been closed access or lagged behind the state-of-the-art. Therefore, the authors present a recipe for adapting a language model to mathematics through continued pretraining on Proof-Pile-2.
Proof-Pile-2 is a mixture of scientific papers, web data containing mathematics, and mathematical code. It includes the AlgebraicStack dataset, which consists of 11 billion tokens of code specifically related to mathematics. The dataset also includes the OpenWebMath dataset, which contains high-quality web pages filtered for mathematical content, and the ArXiv subset of RedPajama, an open-access reproduction of the LLaMA training dataset.
The L LEMMA models are initialized from Code Llama and then further trained on Proof-Pile-2 using a standard autoregressive language modeling objective. The 7 billion parameter model is trained for 200 billion tokens, while the 34 billion parameter model is trained for 50 billion tokens. The models are trained using bfloat16 mixed precision and Tensor Parallelism across multiple GPUs.
Evaluation of L LEMMA as a base model for mathematical text shows that it outperforms other models on various mathematical problem-solving benchmarks, including MATH and GSM8k. It also demonstrates the ability to use computational tools to solve mathematical problems and shows promising results in few-shot tool use and formal theorem proving.
The authors also investigate the impact of data mixture on L LEMMA's performance and find that a mixture ratio of 2:4:1 (arXiv:Web:Code) works best. They also analyze the overlap between test examples and training documents and find that while there are some hits, they do not necessarily imply memorization of correct answers.
In conclusion, L LEMMA is a powerful language model for mathematics that outperforms other models on mathematical problem-solving tasks. It provides a platform for further research in mathematical reasoning and is openly available for use.
Proof-Pile-2 is a dataset created for training or fine-tuning large language models in the field of mathematics. It was created by the authors of this paper and funded by their grants and employers. The dataset includes text-only documents and does not contain labels or targets associated with each instance.
The dataset is self-contained and does not rely on external resources, although it can be reconstructed based on publicly available data sources and datasets. The dataset does not contain any confidential or offensive data, but it may contain instances with errors, noise, or redundant information.
Proof-Pile-2 consists of various subsets, including mathematical code from different programming languages, papers from ArXiv, and web content from OpenWebMath. The data was collected by sourcing existing public subsets and filtering them based on quality assessments. The collection process involved the authors locating, retrieving, and filtering the dataset.
Preprocessing and cleaning were performed on the data to ensure high-quality language modeling data in the mathematics domain. The cleaned and labeled data, as well as the raw data, are available for distribution. The dataset is distributed under applicable terms of use and can be accessed via the HuggingFace Hub.
The dataset has been used for training language models in mathematics tasks, such as proof autoformalization and theorem proving. It can also be used for general-purpose language modeling or other downstream tasks in the mathematics domain.
Maintenance of the dataset will be supported by the authors, and they can be contacted via email for any inquiries. The dataset will not be updated, but others can contribute to it by using the provided codebase to extend or augment the dataset.
Additional results include evaluations on Isabelle proof autoformalization and supervised finetuning on MetaMathQA. The evaluations show the performance of the models trained on Proof-Pile-2 in these specific tasks.
A datasheet for Proof-Pile-2 is provided, following the framework introduced by Gebru et al. It provides detailed information about the dataset, including its composition, collection process, preprocessing, and distribution. The datasheet ensures transparency and facilitates understanding and usage of the dataset.