Predict before you train: Scaling Laws for particle physics foundation models

Neural scaling laws describe how model performance improves as a power law in compute, model size, and dataset size. While well-established for large language models, these relationships are emerging for large models in particle physics. As with language, empirical studies show that the performance scales as a power law. However, unlike natural language or image domains, fundamental physics has high-fidelity simulators that produce synthetic data cheaply. This favors scaling regimes where additional data is cheaper than additional parameters, and allows the pretraining dataset itself to be engineered to influence the scaling. For the task of classifying hadronic jets produced in collisions of high-energy particle beams, we show that the scaling behavior can be engineered towards requiring more data rather than larger models by inclusion of pretraining data which is more diverse and better aligned with the downstream classification task.

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine whether a model has learned generalizable physical dynamics or only performs well under particular settings. We construct a benchmark with 8 physical dynamics, 3 training-data mixtures, and 25 test regimes induced by dynamic-scale and initial-condition complexity shifts, covering in-distribution, distribution-shift, and out-of-distribution settings. We evaluate five physics foundation model architectures and four model variants per architecture (scratch and three pretrained sizes), resulting in 60,000 measurements. Our results show that current physics foundation models behave as conditional rather than universal generalists: their generality depends on the physical regime, temporal scale, initial-condition setting, pretraining, model size, and architecture. Improving the training data distribution only partially mitigates this limitation. Pretraining and scaling are also unable to reliably remove their ability biases. We argue that improving physics foundation models requires moving beyond scaling models or expanding data, toward learning mechanisms that better capture transferable physical knowledge across regimes, temporal scales, and distribution shifts.