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

TL;DR

This paper tackles the problem of efficiently adapting extremely large language models to data-scarce, knowledge-dense domains such as materials science. It introduces a two-stage framework that first performs Penrose-tiled low-rank decomposition of weight matrices followed by frequency-domain pruning with KL-divergence-based distribution alignment, and then applies a section-wise Q&A fine-tuning regimen to inject domain knowledge while mitigating forgetting. The core contributions are the Penrose-tiled rank-block decomposition, spectral-domain compression with representation-alignment, and a reading-style adaptation strategy that progresses through document sections to build domain understanding. The approach aims to deliver domain-specialized LLMs that retain general language capabilities with lower computational and data requirements, enabling practical deployment in scientific domains. The paper outlines a principled experimental plan in materials science, addressing both compression fidelity and interpretable knowledge integration, and highlights broad opportunities for extensions to other fields with similar data-scarcity and knowledge-density characteristics.

Abstract

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.