Beyond Outliers: A Study of Optimizers Under Quantization
Authors: name: Georgios Vlassis, name: Saleh Ashkboos, name: Alexandra Volkova, name: Torsten Hoefler, name: Dan Alistarh
Organization: Scalable Parallel Computing Laboratory (SPCL)

As new optimizers gain traction and model quantization becomes standard for
efficient deployment, a key question arises: how does the choice of optimizer
affect model performance in the presence of quantization? Despite progress in
both areas, systematic evidence on optimizer-quantization interactions remains
limited. To fill this gap, we study the impact of optimizer choice on model
robustness under quantization, considering both post-training quantization
(PTQ), and quantization-aware training (QAT). We first train full-precision
models, ranging from 50M to 1.5B parameters, with six optimizers, to explore
the hyperparameter landscape, and establish well-tuned baselines. We then apply
PTQ to evaluate how model performance degrades when trained with different
optimizers. We find that outlier-related metrics, such as the max-to-mean ratio
(MMR) and Kurtosis, fail to predict the PTQ performance across different
optimizers. We show analytically that this is due to the MMR capturing only
isolated layer errors, while ignoring how quantization errors accumulate and
propagate through the network. To study the QAT degradation, we train quantized
models from scratch and compare them to our original-precision baselines. We
find that optimizers performing well in the original pretraining setup may not
remain optimal under QAT, and that models trained with Shampoo show the lowest
accuracy degradation. Finally, we derive scaling laws for quantization-aware
training under different optimizers, showing that Shampoo achieves the highest
parameter efficiency of all tested optimizers.