Meet Llemma: The Next-Gen Mathematical Open-Language Model Surpassing Current Benchmarks

Language models trained on diverse mixtures of text display remarkably general language understanding and generation capabilities, serving as base models that are adapted to a wide range of applications.

In this study, a team of researchers from Princeton University, EleutherAI, University of Toronto, Vector Institute, University of Cambridge, Carnegie Mellon University and University of Washington have developed a domain-specific language model tailored for mathematics. They have articulated several motivations for pursuing this endeavour. First, solving mathematical problems necessitates the ability to discern patterns within a substantial corpus of specialised prior knowledge, making it an ideal context for domain adaptation. Second, mathematical reasoning itself represents a central task within the field of artificial intelligence and continues to be a topic of contemporary research. Third, the development of language models capable of robust mathematical reasoning has broader implications for various research areas, including reward modelling, reinforcement learning for reasoning in the context, and algorithmic reasoning.

The above image demonstrates Continued pretraining on ProofPile-2 yields LLEMMA, a base model with improved mathematical capabilities. The contributions made by the authors are as follows:

• They have trained and made available the LLEMMA models, comprising 7B and 34B parameter language models that are specifically tailored for mathematical tasks. These LLEMMA models represent a new state-of-the-art in the realm of publicly released base models for mathematics.

• They have introduced the AlgebraicStack, a dataset encompassing 11B tokens of code that is intricately linked to mathematical contexts.

• Their research showcases the LLEMMA models’ proficiency in employing computational tools for solving mathematical problems, including the Python interpreter and formal theorem provers.

In contrast to earlier mathematics language models like Minerva (Lewkowycz et al., 2022), the LLEMMA models are openly accessible, and the authors have made their training data and code open source. This decision facilitates LLEMMA’s role as a platform for advancing future research in the field of mathematical reasoning.

Their work extends the research conducted in Minerva, as outlined by Lewkowycz et al. (2022), with several notable distinctions:

(1) Their model, LLEMMA, encompasses a broader spectrum of data and tasks during both training and evaluation. This includes the incorporation of code data, such as the AlgebraicStack, utilization of various tools, and engagement in formal mathematics tasks.

(2) The authors’ approach relies solely on publicly accessible tools and data sources.

(3) They introduce new analyses that pertain to aspects such as the composition of the training data mixture, memorization patterns, and supplementary supervised fine-tuning.

(4) Importantly, all the artefacts related to their work are made openly available to the public.

The researchers anticipate that LLEMMA and Proof-Pile-2 will provide a solid groundwork for future investigations. These resources are poised to support research efforts in areas such as language model generalization, dataset composition analysis, the extension of domain-specific language models, the utilization of language models as tools for mathematicians, and the enhancement of language models’ mathematical capabilities.

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