# Variance Control via Weight Rescaling in LLM Pre-training

arXiv: https://arxiv.org/abs/2503.17500 · HTML: https://mlsanity.com/paper/2503.17500/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 21 Mar 2025.

## Builds on (most cited first, 23 of 23)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Massive Activations in Large Language Models](https://mlsanity.com/paper/2402.17762/) (2024)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Implicit Under-Parameterization Inhibits Data-Efficient Deep Reinforcement Learning](https://mlsanity.com/paper/2010.14498/) (2020)
- [Disentangling the Causes of Plasticity Loss in Neural Networks](https://mlsanity.com/paper/2402.18762/) (2024)
- [Maintaining Plasticity in Continual Learning via Regenerative Regularization](https://mlsanity.com/paper/2308.11958/) (2023)
- [Improving Deep Transformer with Depth-Scaled Initialization and Merged Attention](https://mlsanity.com/paper/1908.11365/) (2019)
- [A study on the plasticity of neural networks](https://mlsanity.com/paper/2106.00042/) (2021)
- [Weight Clipping for Deep Continual and Reinforcement Learning](https://mlsanity.com/paper/2407.01704/) (2024)
- [Mitigating Quantization Errors Due to Activation Spikes in GLU-Based LLMs](https://mlsanity.com/paper/2405.14428/) (2024)
- [Exploring Quantization for Efficient Pre-Training of Transformer Language Models](https://mlsanity.com/paper/2407.11722/) (2024)
- [Improve Generalization and Robustness of Neural Networks via Weight Scale Shifting Invariant Regularizations](https://mlsanity.com/paper/2008.02965/) (2020)
- [Weight Rescaling: Effective and Robust Regularization for Deep Neural Networks with Batch Normalization](https://mlsanity.com/paper/2102.03497/) (2021)

## Built on by (most cited first, 4 of 4)

- [The Spike, the Sparse and the Sink: Anatomy of Massive Activations and Attention Sinks](https://mlsanity.com/paper/2603.05498/) (2026)
- [A Unified View of Attention and Residual Sinks: Outlier-Driven Rescaling is Essential for Transformer Training](https://mlsanity.com/paper/2601.22966/) (2026)
- [Fantastic Pretraining Optimizers and Where to Find Them II: Hyperball Optimization](https://mlsanity.com/paper/2606.16899/) (2026)
- [Improving Neural Network Training by Decoupling the Magnitude and Direction of Weight Vectors](https://mlsanity.com/paper/2606.25971/) (2026)

## Abstract (arXiv)

The outcome of Large Language Model (LLM) pre-training strongly depends on weight initialization and variance control strategies. Although the importance of initial variance control has been well documented in neural networks in general, the literature on initialization and management of its growth during LLM pre-training, specifically, is somewhat sparse. In this paper, we introduce the Layer Index Rescaling (LIR) weight initialization scheme, and the Target Variance Rescaling (TVR) variance control strategy. Experiments on a 1B parameter LLaMA model demonstrate that better variance management using these techniques yields substantial improvements in downstream task performance (up to 4.6% on common pre-training benchmarks) and reduces extreme activation values, thus mitigating challenges associated with quantization and low-precision training. Our code is available at: https://github.com/bluorion-com/weight_rescaling.