Efficient Fine-Tuning of Large Foundation Models Using Discrete Fourier Transform

Core Concepts

The proposed FourierFT method achieves significant parameter reduction for fine-tuning large foundation models by learning sparse spectral coefficients of the weight changes, outperforming state-of-the-art low-rank adaptation methods.

Abstract

The paper introduces FourierFT, a parameter-efficient fine-tuning method that treats the weight change as a matrix in the spatial domain and learns only a small fraction of its spectral coefficients. Specifically:

FourierFT randomly selects a set of spectral entries that are shared across all layers, and learns the corresponding spectral coefficients. It then applies the inverse discrete Fourier transform to recover the weight change.

Empirically, FourierFT shows comparable or better performance than the state-of-the-art LoRA method, while using only 6.0%, 9.4%, 0.2% and 9.2% of LoRA's trainable parameters for natural language understanding, natural language generation, instruction tuning, and image classification tasks, respectively.

The authors demonstrate that the Fourier basis exhibits stronger expressive power compared to random or orthogonal bases, which contributes to the parameter efficiency of FourierFT.

Extensive experiments on various NLP and CV tasks validate the effectiveness and scalability of the proposed FourierFT method in fine-tuning large foundation models with significantly fewer trainable parameters.

Stats

"FourierFT can achieve comparable or even better performance than LoRA with only 0.064M trainable parameters, compared to LoRA's 33.5M on the instruction tuning task."
"On the image classification task, FourierFT uses only 12.4% and 9.2% of LoRA's parameter count for ViT Base and Large models, respectively, while achieving matched performance."

Quotes

"FourierFT can always achieve comparable or even better performance than LoRA, with about 6.0%, 9.4%, 0.2% and 9.2% of LoRA's trainable parameters for these 4 tasks, respectively."
"Notably, when we increase the parameter count of FourierFT to 41.1% (ViT Base) and 30.6% (ViT Large) of LoRA's, it can outperform LoRA by 3.5% and 2.0% respectively."

Key Insights Distilled From

Parameter-Efficient Fine-Tuning with Discrete Fourier Transform

by Ziqi Gao,Qic... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2405.03003.pdf

Deeper Inquiries

How can the frequency bias in the spectral entry initialization be further optimized to improve the performance of FourierFT?

In FourierFT, the frequency bias in the spectral entry initialization plays a crucial role in determining which spectral coefficients are learned during fine-tuning. To further optimize the frequency bias and improve the performance of FourierFT, several strategies can be considered:

Dynamic Frequency Bias: Instead of using a fixed favored central frequency (fc) for all spectral entries, the frequency bias can be dynamically adjusted during training. This dynamic adjustment can be based on the gradients of the loss function, allowing the model to adaptively focus on different frequency components based on their importance for the task at hand.

Learnable Frequency Bias: Introduce learnable parameters that control the frequency bias. By making the favored central frequency a learnable parameter, the model can optimize the frequency bias during training to better capture the relevant spectral information in the weight changes.

Frequency Bias Exploration: Conduct a systematic exploration of different favored central frequencies to identify the optimal frequency bias for different tasks or datasets. This exploration can involve training multiple models with varying frequency biases and selecting the one that yields the best performance.

Adaptive Frequency Bias: Implement an adaptive mechanism that automatically adjusts the frequency bias based on the characteristics of the input data or the complexity of the task. This adaptive approach can enhance the flexibility and adaptability of FourierFT in capturing diverse weight change patterns.

By incorporating these strategies, the frequency bias in the spectral entry initialization can be further optimized to enhance the performance of FourierFT across a wide range of tasks and datasets.

How can the potential limitations of the Fourier basis in capturing the weight changes be addressed, and how can the method be extended to handle more complex weight structures?

While the Fourier basis is powerful in capturing sparse spectral information and compressing weight changes, it may have limitations in handling more complex weight structures that are not well-represented in the frequency domain. To address these limitations and extend the method to handle more complex weight structures, the following approaches can be considered:

Hybrid Basis Representation: Combine the Fourier basis with other basis functions, such as wavelets or spline functions, to create a hybrid basis representation. This hybrid approach can capture a wider range of weight structures and provide a more comprehensive representation of weight changes.

Adaptive Basis Selection: Develop a mechanism that dynamically selects the most suitable basis functions based on the characteristics of the weight changes. By adaptively choosing the basis functions during training, the model can effectively capture diverse weight structures and improve the expressiveness of FourierFT.

Hierarchical Basis Decomposition: Implement a hierarchical decomposition of weight changes using multiple levels of basis functions. By decomposing the weight changes into hierarchical components, the model can capture both global and local patterns in the weight structures, enhancing the representation capacity of FourierFT.

Sparse Coding Techniques: Incorporate sparse coding techniques to promote sparsity in the basis representation of weight changes. By encouraging sparsity, the model can focus on the most relevant basis functions and effectively capture the essential features of the weight structures.

By integrating these advanced techniques, FourierFT can overcome the limitations of the Fourier basis and handle more complex weight structures with improved accuracy and efficiency.

Can the proposed FourierFT approach be generalized to other types of neural network architectures beyond transformers, and what modifications would be required?

The FourierFT approach can be generalized to other types of neural network architectures beyond transformers by adapting the method to suit the specific characteristics and requirements of different architectures. To apply FourierFT to diverse neural network models, the following modifications and considerations may be necessary:

Layer-specific Adaptations: Tailor the FourierFT method to the specific architecture of the neural network, considering the layer types, connectivity patterns, and parameter structures unique to each model. Customizing the spectral coefficient learning process for different layers can optimize the performance of FourierFT across various architectures.

Input Representation: Adjust the input representation and transformation process to align with the input format and data flow of the target neural network architecture. This may involve modifying the spectral entry initialization, basis transformation, and weight change calculation to accommodate the input requirements of different models.

Loss Function Design: Design task-specific loss functions that are compatible with the objectives and output formats of the neural network architecture. Adapting the loss function to the architecture's output structure can ensure that FourierFT effectively fine-tunes the model for diverse tasks and applications.

Hyperparameter Tuning: Conduct extensive hyperparameter tuning to optimize the performance of FourierFT on different architectures. Fine-tuning the scaling factor, spectral coefficient count, and frequency bias parameters based on the architecture's characteristics can enhance the method's effectiveness across a range of neural network models.

By incorporating these modifications and considerations, FourierFT can be successfully extended to various neural network architectures, enabling parameter-efficient fine-tuning and performance optimization in diverse machine learning applications.