MoRe Fine-Tuning with 10x Fewer Parameters (2408.17383v2)

Abstract: Parameter-efficient fine-tuning (PEFT) techniques have unlocked the potential to cheaply and easily specialize large pretrained models. However, the most prominent approaches, like low-rank adapters (LoRA), depend on heuristics or rules-of-thumb for their architectural choices -- potentially limiting their performance for new models and architectures. This limitation suggests that techniques from neural architecture search could be used to obtain optimal adapter architectures, but these are often expensive and difficult to implement. We address this challenge with Monarch Rectangular Fine-tuning (MoRe), a simple framework to search over adapter architectures that relies on the Monarch matrix class. Theoretically, we show that MoRe is more expressive than LoRA. Empirically, our approach is more parameter-efficient and performant than state-of-the-art PEFTs on a range of tasks and models, with as few as 5\% of LoRA's parameters.

• The paper introduces MoRe Fine-Tuning, a novel PEFT method that reduces parameters by up to 10x while achieving superior performance compared to LoRA.
• The methodology employs Monarch matrices, providing a flexible and more expressive alternative to heuristic-based low-rank adaptations.
• Empirical results demonstrate that MoRe consistently improves accuracy in commonsense reasoning and language tasks using significantly fewer parameters.

MoRe Fine-Tuning with 10x Fewer Parameters: An Overview

The paper "MoRe Fine-Tuning with 10x Fewer Parameters" introduces Monarch Rectangular Fine-tuning (MoRe), a novel approach for parameter-efficient fine-tuning (PEFT) by leveraging the Monarch matrix class. This paper addresses the limitations of current PEFT methods, such as Low-Rank Adaptation (LoRA), by proposing a more expressive and parameter-efficient alternative that reduces the dependency on heuristic architectural choices.

Context and Motivation

The increasing complexity of large pretrained models has led to the development of efficient fine-tuning techniques tailored for these models. Despite their benefits, existing methods like LoRA rely heavily on heuristic-based architectural choices, which may not necessarily be optimal across various models and tasks. Neural Architecture Search (NAS) has been proposed as a potential solution to optimize these choices; however, it is often computationally expensive.

Conceptual Grounding

The paper leverages Monarch matrices, a class of structured matrices known for their ability to represent a variety of transforms and structured matrices. This flexible parametrization allows for the learning of a range of parameter-efficient architectures without the computational overhead traditionally associated with NAS.

Theoretical Foundations

From a theoretical standpoint, the paper demonstrates that MoRe is more expressive than LoRA. This is substantiated through rigorous mathematical formulations and proofs indicating that Monarch matrices, with their block-diagonal structure and adaptable rank, offer a broader expressive capability compared to traditional low-rank adaptations. This theoretical advantage translates into practical improvements in various tasks and models.

Empirical Validation

Empirically, MoRe outperforms state-of-the-art PEFT techniques across multiple benchmarks with significantly fewer parameters. Notably, the MoRe framework achieves superior performance with as few as 5% of the parameters required by LoRA. The experimental results span a range of tasks, including commonsense reasoning, math reasoning, and language understanding, showcasing the robustness and versatility of the proposed method.

The results from Tables 1 and 2 clearly indicate that MoRe achieves higher accuracy and efficiency compared to LoRA and other PEFT methods across various benchmarks. For instance, in commonsense reasoning tasks, MoRe outperforms LoRA with just 0.047% of the parameters, achieving an average score of 84.9 compared to LoRA's 80.5 with 0.670% parameters. Similarly, in language understanding tasks, MoRe consistently shows superior performance and parameter efficiency.

Practical and Theoretical Implications

The practical implications of MoRe are significant, primarily in scenarios where computational resources are limited. By dramatically reducing the number of parameters required for fine-tuning, MoRe enables the deployment of LLMs in resource-constrained environments.

From a theoretical perspective, the expressiveness of Monarch matrices opens new avenues for research in adaptive architectures. This could lead to more adaptive, context-aware systems that dynamically adjust their structure based on specific requirements, further enhancing the efficiency and effectiveness of machine learning models.

Future Directions

The paper also hints at several promising future directions:

1. Optimization with ML Compilers: The current implementation of MoRe incurs some overhead due to multiple CUDA kernel launches. Future work could involve optimizing these operations using machine learning compilers like Triton.
2. General Adaptation for Structured Matrices: Extending the applicability of MoRe as a general drop-in replacement for low-rank projection modules is a potential area for exploration. This could further broaden its utility across different contexts and tasks.
3. Theoretical Analysis of Subspace Similarity: Delving deeper into the similarities between the subspaces learned by dense matrices and those by MoRe could provide valuable insights into the underlying mechanics of fine-tuning, leading to more informed initialization strategies and convergence improvements.

Conclusion

In summary, the introduction of MoRe represents a substantial advancement in the field of parameter-efficient fine-tuning. By leveraging the expressive power of Monarch matrices, it not only outperforms existing methods but also paves the way for more efficient and adaptable fine-tuning frameworks. The practical and theoretical contributions of this paper are poised to significantly impact the future development of machine learning models, particularly in the deployment of large-scale models in resource-constrained settings.