Training spikes in language models replicated by simple quadratic models with heavy-tailed data

The authors show that power-law random feature models, a class of convex linear regression models, reproduce the spiky loss behavior observed during pre-training, and their simulation framework predicts spikes from a given checkpoint.

Big Tech
Ran Tian · Courtney Paquette

Google Deepmind

Research Digest··3 min read
The authors introduce Power-Law Random Feature (PLRF) models—simple quadratic models with heavy-tailed, power-law distributed inputs—that exhibit the same intermittent training spikes seen in large language model (LLM) pre-training.

The authors formalized training spikes as sharp surges in loss that, unlike ordinary noise, depend on model initialization and data shuffling.

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Training spikes in deep neural networks reproduce with simple quadratic models on heavy-tailed power-law inputs, enabling spike prediction and mitigation.

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