# Diffract: Spectral View of LLM Domain Adaptation

arXiv: https://arxiv.org/abs/2608.10850 · HTML: https://mlsanity.com/paper/2608.10850/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 50 references that are in the map.
- First posted on arXiv 11 Aug 2026.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Code Llama: Open Foundation Models for Code](https://mlsanity.com/paper/2308.12950/) (2023)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [DROP: A Reading Comprehension Benchmark Requiring Discrete Reasoning Over Paragraphs](https://mlsanity.com/paper/1903.00161/) (2019)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Language Models are Super Mario: Absorbing Abilities from Homologous Models as a Free Lunch](https://mlsanity.com/paper/2311.03099/) (2023)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [DataComp-LM: In search of the next generation of training sets for language models](https://mlsanity.com/paper/2406.11794/) (2024)
- [Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning](https://mlsanity.com/paper/1810.01075/) (2018)
- [Diverse Weight Averaging for Out-of-Distribution Generalization](https://mlsanity.com/paper/2205.09739/) (2022)
- [Task Singular Vectors: Reducing Task Interference in Model Merging](https://mlsanity.com/paper/2412.00081/) (2024)
- [Continual Pre-Training of Large Language Models: How to (re)warm your model?](https://mlsanity.com/paper/2308.04014/) (2023)
- [Simple and Scalable Strategies to Continually Pre-train Large Language Models](https://mlsanity.com/paper/2403.08763/) (2024)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [OLMES: A Standard for Language Model Evaluations](https://mlsanity.com/paper/2406.08446/) (2024)
- [Traditional and Heavy-Tailed Self Regularization in Neural Network Models](https://mlsanity.com/paper/1901.08276/) (2019)
- [Does your data spark joy? Performance gains from domain upsampling at the end of training](https://mlsanity.com/paper/2406.03476/) (2024)

## Built on by (most cited first, 1 of 1)

- [Reuse or Relearn? A Spectral View of Earth Observation Foundation Models](https://mlsanity.com/paper/2609.32756/) (2026)

## Abstract (arXiv)

We study continual pre-training (CPT) as a mechanism for adapting general-purpose large language models to specialized domains: mathematics, instruction, code, and natural text. Using singular value decomposition of weight matrices, we find that CPT leaves singular value spectra largely invariant, with adaptation driven mainly by changes in singular vectors. An analysis of attention-head projection matrices reveals strong, domain-dependent head heterogeneity, which we exploit to define a head importance criterion: up to 60% of head updates can be removed without measurable quality loss. Selectively rewinding low-importance heads to their pre-trained state improves benchmark accuracy by up to 4% versus the fully trained baseline. Finally, we identify domain connectivity - linear interpolation between CPT checkpoints yields smooth domain-quality interpolation without notable degradation on either domain - and release Diffract, an open-source toolkit for scalable spectral analysis of billion-parameter models.