# High-Rank Structured Modulation for Parameter-Efficient Fine-Tuning

arXiv: https://arxiv.org/abs/2601.07507 · HTML: https://mlsanity.com/paper/2601.07507/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 12 Jan 2026.

## Builds on (most cited first, 18 of 18)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [P-Tuning v2: Prompt Tuning Can Be Comparable to Fine-tuning Universally Across Scales and Tasks](https://mlsanity.com/paper/2110.07602/) (2021)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [Learning multiple visual domains with residual adapters](https://mlsanity.com/paper/1705.08045/) (2017)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [VeRA: Vector-based Random Matrix Adaptation](https://mlsanity.com/paper/2310.11454/) (2023)
- [ReLoRA: High-Rank Training Through Low-Rank Updates](https://mlsanity.com/paper/2307.05695/) (2023)
- [The Second Conversational Intelligence Challenge (ConvAI2)](https://mlsanity.com/paper/1902.00098/) (2019)
- [Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning](https://mlsanity.com/paper/2401.04151/) (2024)
- [Batched Low-Rank Adaptation of Foundation Models](https://mlsanity.com/paper/2312.05677/) (2023)
- [Look Within or Look Beyond? A Theoretical Comparison Between Parameter-Efficient and Full Fine-Tuning](https://mlsanity.com/paper/2505.22355/) (2025)

## Built on by (most cited first, 2 of 2)

- [A Guide to Large Language Models in Modeling and Simulation: From Core Techniques to Critical Challenges](https://mlsanity.com/paper/2602.05883/) (2026)
- [ChunkFT: Byte-Streamed Optimization for Memory-Efficient Full Fine-Tuning](https://mlsanity.com/paper/2605.21177/) (2026)

## Abstract (arXiv)

As the number of model parameters increases, parameter-efficient fine-tuning (PEFT) has become the go-to choice for tailoring pre-trained large language models. Low-rank Adaptation (LoRA) uses a low-rank update method to simulate full parameter fine-tuning, which is widely used to reduce resource requirements. However, decreasing the rank encounters challenges with limited representational capacity when compared to full parameter fine-tuning. We present SMoA, a high-rank Structured MOdulation Adapter that uses fewer trainable parameters while maintaining a higher rank, thereby improving the model's representational capacity and offering improved performance potential. The core idea is to freeze the original pretrained weights and selectively amplify or suppress important features of the original weights across multiple subspaces. The subspace mechanism provides an efficient way to increase the capacity and complexity of a model. We conduct both theoretical analyses and empirical studies on various tasks. Experiment results show that SMoA outperforms LoRA and its variants on 10 tasks, with extensive ablation studies validating its effectiveness.