Pretraining Scaling Laws for Generative Evaluations of Language Models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910008130666496 |
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| author | Schaeffer, Rylan Levi, Noam Miranda, Brando Koyejo, Sanmi |
| author_facet | Schaeffer, Rylan Levi, Noam Miranda, Brando Koyejo, Sanmi |
| contents | Neural scaling laws have driven the field's ever-expanding exponential growth in parameters, data and compute. While scaling behaviors for pretraining losses and discriminative benchmarks are well established, generative benchmarks such as mathematical problem-solving or software engineering remain under-explored. We propose and evaluate three different pretraining scaling laws for fitting pass-at-$k$ on generative evaluations and for predicting pass-at-$k$ of the most expensive model using cheaper models. Our three scaling laws differ in the covariates used: (1) pretraining compute, (2) model parameters and pretraining tokens, (3) log likelihoods of gold reference solutions. First, we demonstrate that generative evaluations introduce new hyperparameters (in our setting, $k$) that act as a control lever for scaling behavior, modulating both the scaling law parameters and the predictability of performance. Second, we identify a stark difference in parameter stability: while the compute and parameters+tokens laws stabilize for only the last $\mathord{\sim}1.5\mathord{-}2.5$ orders of magnitude, the gold reference likelihood law is uniquely stable, converging across $\mathord{\sim}5$ orders. Third, in terms of predictive performance, we find all three scaling laws perform comparably, although the compute law predicts slightly worse for small $k$ and the gold reference law predicts slightly worse for large $k$. Finally, we establish a theoretical connection, proving that the compute scaling law emerges as the compute-optimal envelope of the parameters-and-tokens law. Our framework provides researchers and practitioners with insights and methodologies to forecast generative performance, accelerating progress toward models that can reason, solve, and create. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_24012 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pretraining Scaling Laws for Generative Evaluations of Language Models Schaeffer, Rylan Levi, Noam Miranda, Brando Koyejo, Sanmi Machine Learning Neural scaling laws have driven the field's ever-expanding exponential growth in parameters, data and compute. While scaling behaviors for pretraining losses and discriminative benchmarks are well established, generative benchmarks such as mathematical problem-solving or software engineering remain under-explored. We propose and evaluate three different pretraining scaling laws for fitting pass-at-$k$ on generative evaluations and for predicting pass-at-$k$ of the most expensive model using cheaper models. Our three scaling laws differ in the covariates used: (1) pretraining compute, (2) model parameters and pretraining tokens, (3) log likelihoods of gold reference solutions. First, we demonstrate that generative evaluations introduce new hyperparameters (in our setting, $k$) that act as a control lever for scaling behavior, modulating both the scaling law parameters and the predictability of performance. Second, we identify a stark difference in parameter stability: while the compute and parameters+tokens laws stabilize for only the last $\mathord{\sim}1.5\mathord{-}2.5$ orders of magnitude, the gold reference likelihood law is uniquely stable, converging across $\mathord{\sim}5$ orders. Third, in terms of predictive performance, we find all three scaling laws perform comparably, although the compute law predicts slightly worse for small $k$ and the gold reference law predicts slightly worse for large $k$. Finally, we establish a theoretical connection, proving that the compute scaling law emerges as the compute-optimal envelope of the parameters-and-tokens law. Our framework provides researchers and practitioners with insights and methodologies to forecast generative performance, accelerating progress toward models that can reason, solve, and create. |
| title | Pretraining Scaling Laws for Generative Evaluations of Language Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.24012 |