# A Generalized Spectral Framework to Expain Neural Scaling and Compression Dynamics

arXiv: https://arxiv.org/abs/2511.07892 · HTML: https://mlsanity.com/paper/2511.07892/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 14 references that are in the map.
- First posted on arXiv 11 Nov 2025.

## Builds on (most cited first, 11 of 11)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [GPTQ: Accurate Post-Training Quantization for Generative Pre-trained Transformers](https://mlsanity.com/paper/2210.17323/) (2022)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [From Lazy to Rich: Exact Learning Dynamics in Deep Linear Networks](https://mlsanity.com/paper/2409.14623/) (2024)
- [Feature-Learning Networks Are Consistent Across Widths At Realistic Scales](https://mlsanity.com/paper/2305.18411/) (2023)
- [On the Predictability of Pruning Across Scales](https://mlsanity.com/paper/2006.10621/) (2020)
- [Spectral Evolution and Invariance in Linear-width Neural Networks](https://mlsanity.com/paper/2211.06506/) (2022)

## Built on by (most cited first, 3 of 3)

- [Data Curation Through the Lens of Spectral Dynamics: Static Limits, Dynamic Acceleration, and Practical Oracles](https://mlsanity.com/paper/2512.02409/) (2025)
- [Renormalizable Spectral-Shell Dynamics as the Origin of Neural Scaling Laws](https://mlsanity.com/paper/2512.10427/) (2025)
- [When Does Learning Renormalize? Sufficient Conditions for Power Law Spectral Dynamics](https://mlsanity.com/paper/2512.18209/) (2025)

## Abstract (arXiv)

Empirical scaling laws describe how test loss and other performance metrics depend on model size, dataset size, and compute. While such laws are consistent within specific regimes, apparently distinct scaling behaviors have been reported for related settings such as model compression. Motivated by recent progress in spectral analyses of neural representations, this paper develops a generalized spectral framework that unifies learning dynamics and compression phenomena under a common functional ansatz. We generalize the spectral evolution function from the linear kernel form g(λ t)=λ t to an asymptotically polynomial function g(λ,t;β), characterized by an effective spectral--temporal elasticity ρ(β). This framework recovers existing lazy and feature-learning theories as special cases and yields an invariant relation between learning and compression