Efficient Low-rank Backpropagation for Vision Transformer Adaptation

The increasing scale of vision transformers (ViT) has made the efficient finetuning of these large models for specific needs a significant challenge in various applications. This issue originates from the computationally demanding matrix multiplications required during the backpropagation process through linear layers in ViT. In this paper, we tackle this problem by proposing a new Low-rank Back-Propagation via Walsh-Hadamard Transformation (LBP-WHT) method. Intuitively, LBP-WHT projects the gradient into a low-rank space and carries out backpropagation. This approach substantially reduces the computation needed for adapting ViT, as matrix multiplication in the low-rank space is far less resource-intensive. We conduct extensive experiments with different models (ViT, hybrid convolution-ViT model) on multiple datasets to demonstrate the effectiveness of our method. For instance, when adapting an EfficientFormer-L1 model on CIFAR100, our LBP-WHT achieves 10.4% higher accuracy than the state-of-the-art baseline, while requiring 9 MFLOPs less computation. As the first work to accelerate ViT adaptation with low-rank backpropagation, our LBP-WHT method is complementary to many prior efforts and can be combined with them for better performance. How can we decrease the computational cost for all operations, including gradient computations for weights and inputs, involved in backpropagation (BP) through any linear layer in the ViT model? To answer this question, we introduce a new Low-rank BackPropagation via Walsh-Hadamard Transformation (LBP-WHT) method. As shown in Figure 1 , our method intuitively performs BP for gradients w.r.t. inputs and weights in a low-rank space. To achieve this, we project the gradient w.r.t. the output into a low-rank space using WHT [15], then perform low-rank matrix multiplications, and 37th Conference on Neural Information Processing Systems (NeurIPS 2023).