# CAST: History-Adaptive Spectral Clipping for LLM Pretraining

arXiv: https://arxiv.org/abs/2610.19761 · HTML: https://mlsanity.com/paper/2610.19761/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Vision mixture-of-experts, one of 12 directions in Mixture-of-experts.
- Builds on 14 of its 27 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Placed in

- Mixture-of-experts / [Vision mixture-of-experts](https://mlsanity.com/moe/vision-mixture-of-experts/)

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [Why gradient clipping accelerates training: A theoretical justification for adaptivity](https://mlsanity.com/paper/1905.11881/) (2019)
- [Shortcut-connected Expert Parallelism for Accelerating Mixture-of-Experts](https://mlsanity.com/paper/2404.05019/) (2024)
- [ZClip: Adaptive Spike Mitigation for LLM Pre-Training](https://mlsanity.com/paper/2504.02507/) (2025)
- [Enhancing LLM Training via Spectral Clipping](https://mlsanity.com/paper/2603.14315/) (2026)
- [GradPower: Powering Gradients for Faster Language Model Pre-Training](https://mlsanity.com/paper/2505.24275/) (2025)
- [AdaGC: Enhancing LLM Pretraining Stability via Adaptive Gradient Clipping](https://mlsanity.com/paper/2502.11034/) (2025)
- [GradientStabilizer:Fix the Norm, Not the Gradient](https://mlsanity.com/paper/2502.17055/) (2025)

## Abstract (arXiv)

Soft spectral clipping (SSC) reduces gradient singular values, but its effect depends on the gradient scale and clipping threshold. We introduce CAST (Clipping with Adaptive Scales and Thresholds), a history-adaptive extension of SSC. AdamW's previous second moment sets row and column scales. An exponential moving average of the clipped output's estimated spectral norm sets each matrix's threshold. CAST restores the original coordinates before the AdamW update. We train a mixture-of-experts (MoE) model with 19.08B total parameters for 83.89B tokens. CAST achieves lower training and mean validation losses than nine gradient-processing baselines, with the fewest relative gradient spikes. It reaches the best baseline's final smoothed training loss in 7.2% fewer steps.