LIFT the Veil for the Truth: Principal Weights Emerge after Rank Reduction for Reasoning-Focused Supervised Fine-Tuning

2025-06-01

AI Summary

Full-parameter fine-tuning of large language models (LLMs) incurs prohibitive computational costs, risks overfitting and catastrophic forgetting, while existing sparse fine-tuning methods lack precision in identifying inference-critical parameters. Method: We propose low-rank-guided sparse fine-tuning, which leverages singular value decomposition (SVD) or LoRA-style low-rank initialization and dynamically selects the top 5% parameters with largest magnitudes—termed “principal weights”—for updating. Crucially, we empirically discover that these principal weights, identified after low-rank approximation, are most critical for inference; moreover, we reveal an effectiveness reversal of magnitude-based pruning in the low-rank subspace. Results: Our method outperforms full fine-tuning on arithmetic reasoning tasks, achieves memory efficiency comparable to LoRA, and improves source-domain knowledge retention by ~20% over both full fine-tuning and LoRA—significantly advancing sparse fine-tuning performance on LLM inference tasks.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Natural Language Processing: (Large) Language Models
• Computer Vision: Large Vision Models

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Recent studies have shown that supervised fine-tuning of LLMs on a small number of high-quality datasets can yield strong reasoning capabilities. However, full fine-tuning (Full FT), while powerful, is computationally expensive and susceptible to overfitting and catastrophic forgetting, particularly when data is limited. Sparse fine-tuning, which previously achieved notable success by updating only a small subset of model parameters, offers a promising trade-off between efficiency and effectiveness. Yet, it has lagged behind in the LLM era due to the difficulty of identifying parameters truly critical for reasoning. In this work, we state that weights with the largest magnitude after low-rank approximation are critical weights for fine-tuning, which we call Principal Weights. Surprisingly, while magnitude-based sparse fine-tuning performs poorly as a baseline on LLM fine-tuning, it becomes highly effective after rank reduction. These insights motivate our method: Low-rank Informed Sparse Fine-Tuning (LIFT). LIFT only updates the top 5% Principal Weights throughout training and consistently achieves better performance on reasoning tasks than Full FT, while maintaining memory efficiency on par with popular parameter-efficient fine-tuning methods. In addition to strong performance on target domains such as arithmetic reasoning, LIFT also retains up to 20% more source-domain knowledge, compared to Full FT and LoRA. Our code is available at: https://github.com/zihanghliu/LIFT.

Problem

• Identifies critical weights for efficient LLM fine-tuning
• Improves reasoning performance with sparse parameter updates
• Reduces memory usage while retaining source-domain knowledge

Innovation

• Low-rank approximation identifies Principal Weights
• Sparse fine-tuning updates top 5% Principal Weights
• LIFT method balances efficiency and reasoning performance