# The Spectral Lifecycle of Transformer Training: Transient Compression Waves, Persistent Spectral Gradients, and the Q/K--V Asymmetry

arXiv: https://arxiv.org/abs/2604.22778 · HTML: https://mlsanity.com/paper/2604.22778/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
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- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Transformer Feed-Forward Layers Build Predictions by Promoting Concepts in the Vocabulary Space](https://mlsanity.com/paper/2203.14680/) (2022)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [ShortGPT: Layers in Large Language Models are More Redundant Than You Expect](https://mlsanity.com/paper/2403.03853/) (2024)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [The Break-Even Point on Optimization Trajectories of Deep Neural Networks](https://mlsanity.com/paper/2002.09572/) (2020)
- [Predicting trends in the quality of state-of-the-art neural networks without access to training or testing data](https://mlsanity.com/paper/2002.06716/) (2020)
- [AlphaPruning: Using Heavy-Tailed Self Regularization Theory for Improved Layer-wise Pruning of Large Language Models](https://mlsanity.com/paper/2410.10912/) (2024)
- [Approaching Deep Learning through the Spectral Dynamics of Weights](https://mlsanity.com/paper/2408.11804/) (2024)
- [From SGD to Spectra: A Theory of Neural Network Weight Dynamics](https://mlsanity.com/paper/2507.12709/) (2025)
- [The Norm-Separation Delay Law of Grokking: A First-Principles Theory of Delayed Generalization](https://mlsanity.com/paper/2603.13331/) (2026)
- [Spectral Edge Dynamics of Training Trajectories: Signal--Noise Geometry Across Scales](https://mlsanity.com/paper/2603.15678/) (2026)
- [Early-stopping for Transformer model training](https://mlsanity.com/paper/2510.16074/) (2025)

## Abstract (arXiv)

We present the first systematic study of weight matrix singular value spectra during transformer pretraining, tracking full SVD decompositions of every weight matrix at 25-step intervals across three model scales (30M--285M parameters). We discover three phenomena: (1)~Transient Compression Waves: stable rank compression propagates as a traveling wave from early to late layers, creating a dramatic gradient that peaks early then reverses -- late layers eventually over-compress past early layers. (2)~Persistent Spectral Gradients: the power-law exponent~α develops a permanent depth gradient forming a non-monotonic inverted-U in deeper models, with peaks shifting toward earlier layers as depth increases. (3)~Q/K--V Functional Asymmetry: value/output projections compress uniformly while query/key projections carry the full depth-dependent dynamics. The dissociation between transient compression and persistent spectral shape reveals that rank and spectral shape encode fundamentally different information about training. We formalize this as a two-timescale dynamical model and derive scaling laws (Deltaα propto L0.26, R2=0.99). We validate on nine models across three families (custom, GPT-2, Pythia; 30M--1B parameters; 8--36 layers), demonstrate that α predicts layer importance (ρ=0.69--0.84, p<0.02), and show that spectral-guided pruning outperforms Last-N heuristics by 1.1×--3.6× across seven models in two families (GPT-2 124M--774M, Pythia 160M--1B), with worst-vs-best gaps up to 23.7× confirming the causal role of spectral structure.