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Predicting Large Model Test Losses with a Noisy Quadratic System

Machine Learning 2026-05-12 v1

Abstract

We introduce a predictive model that estimates the pre-training loss of large models from model size (N), batch size (B) and number of weight updates (K). This is the first loss prediction model that can handle changing batch size. The model outperforms Chinchilla's loss model, a model of the test loss using the batch size and number of tokens, in terms of projecting the loss at extrapolated compute budgets (up to 1000 folds). A natural use of the model is to find optimal N, B, K configurations under explicit and compound resource constraints like time, memory and compute. In our experiments, the model-selected configurations are close to ground-truth optimal. Our work advocates for loss prediction as a better alternative to heuristic-based laws, which are growing in complexity. The implementation is available on https://github.com/chuningxdy/Noisy-Quadratic-System.

Keywords

Cite

@article{arxiv.2605.09154,
  title  = {Predicting Large Model Test Losses with a Noisy Quadratic System},
  author = {Chuning Li and Chris J. Maddison},
  journal= {arXiv preprint arXiv:2605.09154},
  year   = {2026}
}

Comments

ICML 2026

R2 v1 2026-07-01T13:00:50.614Z