# It Takes a Good Model to Train a Good Model: Generalized Gaussian Priors for Optimized LLMs

arXiv: https://arxiv.org/abs/2506.00486 · HTML: https://mlsanity.com/paper/2506.00486/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 43 of its 67 references that are in the map.
- First posted on arXiv 31 May 2025.

## Builds on (most cited first, 30 of 43)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Longformer: The Long-Document Transformer](https://mlsanity.com/paper/2004.05150/) (2020)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [SmoothQuant: Accurate and Efficient Post-Training Quantization for Large Language Models](https://mlsanity.com/paper/2211.10438/) (2022)
- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Exact solutions to the nonlinear dynamics of learning in deep linear neural networks](https://mlsanity.com/paper/1312.6120/) (2013)
- [QuaRot: Outlier-Free 4-Bit Inference in Rotated LLMs](https://mlsanity.com/paper/2404.00456/) (2024)
- [Learned Step Size Quantization](https://mlsanity.com/paper/1902.08153/) (2019)
- [signSGD: Compressed Optimisation for Non-Convex Problems](https://mlsanity.com/paper/1802.04434/) (2018)
- [Deep Gradient Compression: Reducing the Communication Bandwidth for Distributed Training](https://mlsanity.com/paper/1712.01887/) (2017)
- [ThiNet: A Filter Level Pruning Method for Deep Neural Network Compression](https://mlsanity.com/paper/1707.06342/) (2017)
- [Sparsified SGD with Memory](https://mlsanity.com/paper/1809.07599/) (2018)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Deja Vu: Contextual Sparsity for Efficient LLMs at Inference Time](https://mlsanity.com/paper/2310.17157/) (2023)
- [Sparse Communication for Distributed Gradient Descent](https://mlsanity.com/paper/1704.05021/) (2017)
- [Speeding-up Convolutional Neural Networks Using Fine-tuned CP-Decomposition](https://mlsanity.com/paper/1412.6553/) (2014)
- [Qsparse-local-SGD: Distributed SGD with Quantization, Sparsification, and Local Computations](https://mlsanity.com/paper/1906.02367/) (2019)
- [Lessons on Parameter Sharing across Layers in Transformers](https://mlsanity.com/paper/2104.06022/) (2021)
- [Nonuniform-to-Uniform Quantization: Towards Accurate Quantization via Generalized Straight-Through Estimation](https://mlsanity.com/paper/2111.14826/) (2021)
- [Evaluating Quantized Large Language Models](https://mlsanity.com/paper/2402.18158/) (2024)
- [Error Compensated Quantized SGD and its Applications to Large-scale Distributed Optimization](https://mlsanity.com/paper/1806.08054/) (2018)
- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [Pufferfish: Communication-efficient Models At No Extra Cost](https://mlsanity.com/paper/2103.03936/) (2021)
- [DarkRank: Accelerating Deep Metric Learning via Cross Sample Similarities Transfer](https://mlsanity.com/paper/1707.01220/) (2017)
- [Sparser is Faster and Less is More: Efficient Sparse Attention for Long-Range Transformers](https://mlsanity.com/paper/2406.16747/) (2024)

## Abstract (arXiv)

Despite rapid progress in large language models (LLMs), the statistical structure of their weights, activations, and gradients-and its implications for initialization, training dynamics, and efficiency-remains largely unexplored. We empirically show that these quantities in LLMs are well modeled by generalized Gaussian (GG) distributions, and introduce a unified, end-to-end optimization framework grounded in this observation. Our contributions are threefold: (1) a GG-based initialization that aligns with trained model statistics, accelerating convergence and improving accuracy; (2) ACT, a progressive activation-constrained training method that reduces redundancy and propagation overhead; and (3) GCT, a gradient-constrained training algorithm that substantially lowers communication cost in distributed training. Experiments across diverse architectures demonstrate consistently smaller, faster models with minimal communication overhead that match or surpass standard baselines. By anchoring LLM optimization in principled statistical modeling, this work advances efficient, scalable, and hardware-aware AI systems.