What Does the Rank Buy? A Spectral and Distributional Analysis of Low-Rank Adaptation

arXiv:2609.32002 · cs.AI, cs.LG, stat.ML · Submitted 2026-09-25 · Read on arXiv

cs.AI, cs.LG, stat.ML

Submitted: 2026-09-25

Updated: 2026-09-25

Terminology

• Adaptation — 38× in this paper · explained in 1 episode
• Fine-Tuning — 19× in this paper · explained in 5 episodes
• Alignment — 14× in this paper · explained in 1 episode
• Generalization — 9× in this paper · explained in 13 episodes
• Parameter-Efficient Fine-Tuning — 7× in this paper · explained in 2 episodes
• Transferability — 7× in this paper · explained in 4 episodes
• Domain Adaptation — 5× in this paper · explained in 5 episodes
• International Conference on Learning Representations — 4× in this paper
• Verification — 3× in this paper · explained in 2 episodes
• Wasserstein Distance — 3× in this paper · explained in 4 episodes
• Admissibility — 2× in this paper · explained in 2 episodes
• Decoupling — 2× in this paper · explained in 2 episodes
• Generalization Bounds — 2× in this paper · explained in 2 episodes
• Parameter Efficiency — 2× in this paper · explained in 3 episodes
• Score Function — 2× in this paper · explained in 4 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Optimal Transport — 1× in this paper · explained in 5 episodes
• Parameter-Efficient Fine-Tuning (PEFT) — 1× in this paper · explained in 4 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes

Sources

• Parameter-Efficient Transfer Learning for NLP
• Prefix-Tuning: Optimizing Continuous Prompts for Generation
• DoRA: Enhancing Parameter-Efficient Fine-Tuning with Dynamic Rank Distribution
• GoRA: Gradient-driven Adaptive Low Rank Adaptation
• ReLoRA: High-Rank Training Through Low-Rank Updates
• Less is More: Extreme Gradient Boost Rank-1 Adaption for Efficient Finetuning of LLMs
• Localized LoRA: A Structured Low-Rank Approximation for Efficient Fine-Tuning
• LoLDU: Low-Rank Adaptation via Lower-Diag-Upper Decomposition for Parameter-Efficient Fine-Tuning
• SVFit: Parameter-Efficient Fine-Tuning of Large Pre-Trained Models Using Singular Values
• DeLoRA: Decoupling Angles and Strength in Low-rank Adaptation
• LoR2C : Low-Rank Residual Connection Adaptation for Parameter-Efficient Fine-Tuning
• VB-LoRA: Extreme Parameter Efficient Fine-Tuning with Vector Banks
• LoraHub: Efficient Cross-Task Generalization via Dynamic LoRA Composition
• K-LoRA: Unlocking Training-Free Fusion of Any Subject and Style LoRAs
• LoRAMoE: Alleviate World Knowledge Forgetting in Large Language Models via MoE-Style Plugin
• MoRAL: MoE Augmented LoRA for LLMs' Lifelong Learning
• Hyperbolic Fine-Tuning for Large Language Models
• Keeping Yourself is Important in Downstream Tuning Multimodal Large Language Model
• LoRA vs. Full Fine-Tuning: A Theoretical Perspective
• RefLoRA: Refactored Low-Rank Adaptation for Efficient Fine-Tuning of Large Models

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