A Defense of the Quadratic Model
Due to the complexity of neural network loss landscapes, optimization theory is forced to rely on idealized models, and there is generally a tradeoff between how theoretically tractable the model is, and how accurately it describes the true optimization dynamics. In this work, we stress test the simplest possible model of optimization -- the quadratic model -- and show that it can be surprisingly predictive in an LLM setting with 150M parameters and 3B training tokens. Specifically, we show that Taylor expanding the model and the loss function at intermediate checkpoints through training can accurately predict the optimization dynamics over windows that can last up to 10\% of training. Ha...
| Authors | Alexandru Meterez, Pranav Ajit Nair, Depen Morwani et al. |
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| Primary category | cs.LG |
| Published | 23 July 2026 |
| Last updated at source | 23 July 2026 |
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