Geometry-Driven Layer Selection Method Enhances Parameter-Efficient LLM Fine-Tuning

A new research paper introduces a geometry-driven approach to identify critical layers for adaptation in large language models, addressing structural uncertainty in fine-tuning. The method models hidden state evolution as a high-dimensional geometric trajectory and applies the Ramer-Douglas-Peucker algorithm to detect pivotal breakpoints along representation paths. This parameter-free, training-free polygon simplification technique preserves global structural transitions while eliminating locally redundant changes. Researchers use these geometric pivots as direct decision signals to determine which layers should be adapted during parameter-efficient fine-tuning. The geometry-aware layer selection strategy was integrated into LoRA fine-tuning of Qwen3-8B-Base, demonstrating practical application. The approach moves beyond heuristic decisions about adaptation placement by analyzing layer-specific roles of internal representations. The research was announced on arXiv with identifier 2604.19321v1, categorized as a cross announcement. This work contributes to more efficient adaptation of large language models through geometric analysis of representation evolution.