Pretraining Scaling Laws for Generative Evaluations of Language Models

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~1.5mathord-2.5 orders of magnitude, the gold reference likelihood law is uniquely stable, converging across mathord~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.