# Beyond Outliers: A Study of Optimizers Under Quantization

arXiv: https://arxiv.org/abs/2509.23500 · HTML: https://mlsanity.com/paper/2509.23500/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 37 references that are in the map.
- First posted on arXiv 27 Sep 2025.

## Builds on (most cited first, 30 of 30)

- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [2 OLMo 2 Furious](https://mlsanity.com/paper/2501.00656/) (2024)
- [Query-Key Normalization for Transformers](https://mlsanity.com/paper/2010.04245/) (2020)
- [Training Deep Learning Models with Norm-Constrained LMOs](https://mlsanity.com/paper/2502.07529/) (2025)
- [Outlier Suppression: Pushing the Limit of Low-bit Transformer Language Models](https://mlsanity.com/paper/2209.13325/) (2022)
- [Primer: Searching for Efficient Transformers for Language Modeling](https://mlsanity.com/paper/2109.08668/) (2021)
- [Quantizable Transformers: Removing Outliers by Helping Attention Heads Do Nothing](https://mlsanity.com/paper/2306.12929/) (2023)
- [A Spectral Condition for Feature Learning](https://mlsanity.com/paper/2310.17813/) (2023)
- [Fantastic Pretraining Optimizers and Where to Find Them](https://mlsanity.com/paper/2509.02046/) (2025)
- [Scalable Optimization in the Modular Norm](https://mlsanity.com/paper/2405.14813/) (2024)
- [Benchmarking Optimizers for Large Language Model Pretraining](https://mlsanity.com/paper/2509.01440/) (2025)
- [Nemotron-CLIMB: CLustering-based Iterative Data Mixture Bootstrapping for Language Model Pre-training](https://mlsanity.com/paper/2504.13161/) (2025)
- [Preconditioned Stochastic Gradient Descent](https://mlsanity.com/paper/1512.04202/) (2015)
- [QUIK: Towards End-to-End 4-Bit Inference on Generative Large Language Models](https://mlsanity.com/paper/2310.09259/) (2023)
- [Jetfire: Efficient and Accurate Transformer Pretraining with INT8 Data Flow and Per-Block Quantization](https://mlsanity.com/paper/2403.12422/) (2024)
- [Mitigating the Impact of Outlier Channels for Language Model Quantization with Activation Regularization](https://mlsanity.com/paper/2404.03605/) (2024)
- [QuEST: Stable Training of LLMs with 1-Bit Weights and Activations](https://mlsanity.com/paper/2502.05003/) (2025)
- [HALO: Hadamard-Assisted Lower-Precision Optimization for LLMs](https://mlsanity.com/paper/2501.02625/) (2025)
- [KurTail : Kurtosis-based LLM Quantization](https://mlsanity.com/paper/2503.01483/) (2025)

## Built on by (most cited first, 6 of 6)

- [Clarifying Shampoo: Adapting Spectral Descent to Stochasticity and the Parameter Trajectory](https://mlsanity.com/paper/2602.09314/) (2026)
- [Towards Robust Scaling Laws for Optimizers](https://mlsanity.com/paper/2602.07712/) (2026)
- [StableQAT: Stable Quantization-Aware Training at Ultra-Low Bitwidths](https://mlsanity.com/paper/2601.19320/) (2026)
- [DASH: Faster Shampoo via Batched Block Preconditioning and Efficient Inverse-Root Solvers](https://mlsanity.com/paper/2602.02016/) (2026)
- [Colinearity Decay: Training Quantization-Friendly ViTs with Outlier Decay](https://mlsanity.com/paper/2605.01330/) (2026)
- [One-Step Gradient Delay is Not a Barrier for Large-Scale Asynchronous Pipeline Parallel LLM Pretraining](https://mlsanity.com/paper/2606.30634/) (2026)

## Abstract (arXiv)

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.