# Penrose Tiled Low-Rank Compression and Section-Wise Q&A Fine-Tuning: A General Framework for Domain-Specific Large Language Model Adaptation

arXiv: https://arxiv.org/abs/2503.22074 · HTML: https://mlsanity.com/paper/2503.22074/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 28 Mar 2025.

## Builds on (most cited first, 20 of 20)

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- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [FitNets: Hints for Thin Deep Nets](https://mlsanity.com/paper/1412.6550/) (2014)
- [Don't Stop Pretraining: Adapt Language Models to Domains and Tasks](https://mlsanity.com/paper/2004.10964/) (2020)
- [Paying More Attention to Attention: Improving the Performance of Convolutional Neural Networks via Attention Transfer](https://mlsanity.com/paper/1612.03928/) (2016)
- [AdapterHub: A Framework for Adapting Transformers](https://mlsanity.com/paper/2007.07779/) (2020)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Speeding up Convolutional Neural Networks with Low Rank Expansions](https://mlsanity.com/paper/1405.3866/) (2014)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [FractalNet: Ultra-Deep Neural Networks without Residuals](https://mlsanity.com/paper/1605.07648/) (2016)
- [Compressing Neural Networks with the Hashing Trick](https://mlsanity.com/paper/1504.04788/) (2015)
- [LoSparse: Structured Compression of Large Language Models based on Low-Rank and Sparse Approximation](https://mlsanity.com/paper/2306.11222/) (2023)
- [MatSciBERT: A Materials Domain Language Model for Text Mining and Information Extraction](https://mlsanity.com/paper/2109.15290/) (2021)
- [Compressing Large Language Models using Low Rank and Low Precision Decomposition](https://mlsanity.com/paper/2405.18886/) (2024)
- [MoDeGPT: Modular Decomposition for Large Language Model Compression](https://mlsanity.com/paper/2408.09632/) (2024)
- [Structured Transforms for Small-Footprint Deep Learning](https://mlsanity.com/paper/1510.01722/) (2015)
- [C-LSTM: Enabling Efficient LSTM using Structured Compression Techniques on FPGAs](https://mlsanity.com/paper/1803.06305/) (2018)

## Abstract (arXiv)

Large language models (LLMs) hold great promise for specialized scientific domains such as materials science, yet adapting them efficiently and accurately to domain-specific knowledge remains challenging due to limited data and high knowledge density. We propose a two-stage framework that combines structured model compression with a scientific fine-tuning regimen to address this challenge. In the compression stage, we decompose the LLM's weight matrices into local low-rank "rank blocks" and arrange these blocks in a Penrose-like non-periodic tiling pattern. Each block is then compacted via spectral transformations (e.g., discrete cosine or Fourier transforms), and a Kullback-Leibler (KL) divergence-based alignment loss preserves the distributional similarity between the compressed model's representations and those of the original full model. In the adaptation stage, the compressed model is further tuned using a human-like scientific reading protocol: it processes technical materials science documents section by section, engaging in a structured question-and-answer routine for each section. This section-wise Q&A fine-tuning strategy extracts explicit reasoning traces and gradually injects domain knowledge, while minimizing catastrophic forgetting of the model's general language capabilities. By balancing efficient compression with targeted adaptation, our two-stage approach enables precise specialization of LLMs to high-value domains under data-scarce conditions. We present this principled yet exploratory pipeline and outline its potential for advancing materials science knowledge integration, laying the groundwork for comprehensive empirical evaluation in future work.