Efficient Orthogonal Finetuning of Large Models via Butterfly Factorization

Core Concepts

The authors propose Orthogonal Butterfly (BOFT), a novel parameter-efficient finetuning method that leverages butterfly factorization to construct dense orthogonal matrices, enabling more efficient adaptation of large foundation models.

Abstract

The paper studies the problem of parameter efficiency in orthogonal finetuning, a principled approach for downstream task adaptation. The authors propose an information transmission framework to transform the task of crafting a parameter-efficient dense orthogonal matrix into an information transmission problem within a grid-structured graph. Inspired by the butterfly structures in the Cooley-Tukey fast Fourier transform algorithm, the authors introduce Orthogonal Butterfly (BOFT), a parameter-efficient orthogonal finetuning method. BOFT subsumes the original orthogonal finetuning (OFT) as a special case and provides a generalized orthogonal finetuning framework. The authors provide theoretical insights on the expressivity and inductive bias of BOFT, showing that it can significantly reduce the number of trainable parameters while still yielding good performance. BOFT also comes with an intriguing weight interpolation property. The authors extensively evaluate BOFT on a wide range of adaptation tasks, including natural language understanding, mathematical reasoning, high-quality image segmentation, and controllable text-to-image generation. BOFT outperforms current state-of-the-art methods by a considerable margin, validating its superior parameter-efficiency and generalization ability.

Stats

The GPT-3 model has around 175 billion parameters. The Llama-2-7B model has 7 billion parameters. The DINOv2-large model has more than 300 million parameters.

Quotes

"Recent models such as ChatGPT and Stable Diffusion demonstrate the remarkable generalization ability of large foundation models. The rapid increase in the performance of such models is paired with a dramatic increase in the number of parameters." "Broad progress in the field therefore requires the ability to adapt such models without retraining them from scratch. That is, we must be able to efficiently adapt existing foundation models to downstream tasks."

Key Insights Distilled From

Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization

by Weiy... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2311.06243.pdf

Deeper Inquiries

How can the butterfly structure in BOFT be further extended or generalized to achieve even higher parameter efficiency?

The butterfly structure in BOFT can be extended or generalized in several ways to achieve even higher parameter efficiency. One approach could involve exploring different block sizes and depths in the butterfly factorization. By varying the block sizes and the number of levels in the butterfly structure, it may be possible to find an optimal configuration that strikes a balance between expressivity and parameter efficiency. Additionally, incorporating adaptive mechanisms that dynamically adjust the butterfly structure during training based on the task requirements or model complexity could further enhance parameter efficiency. Another avenue for improvement could be investigating alternative sparse matrix factorization techniques within the butterfly structure. By exploring different sparse matrix patterns or introducing additional constraints to the factorization process, it may be possible to reduce the number of trainable parameters even further while maintaining model performance. Additionally, exploring hierarchical or nested butterfly structures could potentially lead to more efficient parameterizations for specific types of models or tasks.

What are the potential drawbacks or limitations of the orthogonal finetuning approach compared to other parameter-efficient finetuning methods like LoRA?

While orthogonal finetuning (OFT) offers several advantages, such as strong generalization and training stability, there are also potential drawbacks and limitations compared to other parameter-efficient finetuning methods like LoRA. One limitation of OFT is its higher computational complexity and memory requirements due to the need to compute and store multiple sparse matrices in the butterfly factorization. This can lead to increased training time and resource consumption, especially for large models or datasets. Another drawback of OFT is its sensitivity to the choice of hyperparameters, such as the block size or the depth of the butterfly structure. Finding the optimal configuration for these hyperparameters can be challenging and may require extensive experimentation. In contrast, methods like LoRA have simpler hyperparameter settings and may be easier to tune for specific tasks or models. Additionally, the interpretability of the orthogonal matrices in OFT may be limited compared to other methods. Understanding the impact of the orthogonal transformations on the model's behavior or performance can be more challenging, making it harder to diagnose or debug potential issues during training.

How can the insights from the information transmission view on orthogonal finetuning be applied to other areas of machine learning beyond model adaptation, such as neural architecture search or meta-learning?

The insights from the information transmission view on orthogonal finetuning can be applied to other areas of machine learning, such as neural architecture search or meta-learning, in several ways: Structured Parameterization: The concept of representing dense matrices with sparse structures, as seen in the butterfly factorization, can be applied to parameter-efficient neural architecture search. By incorporating structured parameterizations in the search space, it may be possible to reduce the search complexity and improve the efficiency of discovering optimal architectures. Regularization and Generalization: The emphasis on preserving pairwise relationships and angles in orthogonal matrices can inspire regularization techniques in meta-learning. By enforcing similar constraints on meta-parameters or learning rates, it may be possible to improve the generalization and adaptation capabilities of meta-learning algorithms. Efficient Information Exchange: The idea of efficient information transmission in the butterfly structure can be leveraged in meta-learning frameworks for better knowledge transfer between tasks or domains. By designing meta-learning algorithms that facilitate efficient information exchange and transfer, it may be possible to enhance the learning efficiency and performance of meta-learners across diverse tasks. By applying these insights to neural architecture search and meta-learning, researchers can potentially develop more efficient and effective machine learning algorithms with improved parameter efficiency and generalization capabilities.