Parameter-Efficient Fine-Tuning of State Space Models (2410.09016v3)

Abstract: Deep State Space Models (SSMs), such as Mamba (Gu & Dao, 2024), have become powerful tools for LLMing, offering high performance and linear scalability with sequence length. However, the application of parameter-efficient fine-tuning (PEFT) methods to SSM-based models remains largely underexplored. We start by investigating two fundamental questions on existing PEFT methods: (i) How do they perform on SSM-based models? (ii) Which parameters should they target for optimal results? Our analysis shows that LoRA and its variants consistently outperform all other PEFT methods. While LoRA is effective for linear projection matrices, it fails on SSM modules-yet still outperforms other methods applicable to SSMs, indicating their limitations. This underscores the need for a specialized SSM tuning approach. To address this, we propose Sparse Dimension Tuning (SDT), a PEFT method tailored for SSM modules. Combining SDT for SSMs with LoRA for linear projection matrices, we achieve state-of-the-art performance across extensive experiments.

• The paper demonstrates that prompt-based methods are ineffective for SSMs, as they offer limited expressivity by tuning only the initial hidden state.
• The paper shows that LoRA effectively fine-tunes linear projection matrices in SSMs, yielding superior performance compared to prompt-based strategies.
• The paper introduces SDLoRA, which combines selective dimension tuning with LoRA to update critical SSM channels for optimal fine-tuning efficiency.

Analyzing Parameter-Efficient Fine-Tuning Methods for State Space Models

The paper "Parameter-Efficient Fine-Tuning of State Space Models" investigates the adaptation of Parameter-Efficient Fine-Tuning (PEFT) methods to Deep State Space Models (SSMs), specifically focusing on models such as Mamba. SSMs have gained attention due to their efficient training and inference capabilities, operating with linear scaling concerning sequence length. This paper addresses an overlooked domain: optimizing PEFT strategies for SSMs, which diverge from the more extensively studied Transformer-based architectures.

Key Findings and Contributions

The research systematically explores how different PEFT methods perform on SSM-based models and identifies which components are most effective for fine-tuning. Through empirical benchmarking, several critical conclusions are drawn:

1. Ineffectiveness of Prompt-Based Methods: Prompt-based methods, such as prefix-tuning, fail to demonstrate efficacy in SSM-based models. The empirical observation is supported by theoretical analyses indicating their limited expressivity equivalent to tuning only the initial hidden state.
2. Efficacy of LoRA: Low-Rank Adaptation (LoRA) effectively fine-tunes linear projection matrices in SSM models, outperforming prompt-based strategies. Remarkably, the paper shows that updating these matrices yields substantial benefits while tuning SSM modules with LoRA provides limited gains.
3. Selective Tuning with SDLoRA: To enhance fine-tuning, the authors propose SDLoRA, which combines selective dimension tuning in SSM modules with applying LoRA to linear projection matrices. This approach selectively updates critical channels and state dimensions, demonstrating superior performance compared to standard LoRA.

Theoretical Insights

The theoretical framework presented in the paper strongly supports the empirical findings. A detailed analysis explores the expressivity limits of prompt-based methods and the adequacy of targeting linear projection matrices with LoRA. The expressivity of selectively updated SSM channels and dimensions is also mathematically formulated, shedding light on the modular nature of the tuning process.

Implications and Future Directions

The implications of these findings are significant for resource-constrained environments where full model fine-tuning is impractical. By establishing a robust and efficient fine-tuning methodology for SSMs, this research opens pathways for adapting SSM-based models to diverse applications efficiently.

For future research, further exploration into SSM-Transformer hybrid models and the potential of selective dimension tuning without full fine-tuning could yield valuable insights. Extending these methodologies to broader machine learning contexts could enhance the adaptability and efficiency of large-scale LLMs across various domains.

Conclusion

This paper provides a comprehensive exploration of PEFT methods applied to SSMs, introducing novel tuning strategies like SDLoRA that outperform existing methods in this domain. The research offers a solid theoretical foundation complemented by promising empirical results, contributing valuable knowledge to the fields of model fine-tuning and efficient machine learning architecture adaptation.