Finite-precision errors can break the zero-sum constraint of cross-entropy gradients. The resulting drift creates a feedback loop between classifier and feature means, termed Numerical Feature Inflation. This offers a numerical explanation for rapid norm growth and Slingshot loss spikes, while also predicting that parameter growth can occur without visible spikes.
@misc{liu2026grokking,title={Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes},author={Liu, Hanqing and Cao, Jianjun and Li, Yuanze and Zhou, Zijian},year={2026},archiveprefix={arXiv},primaryclass={cs.LG},url={https://arxiv.org/abs/2605.06152},note={Accepted to NeurIPS 2026},}