Compute Better Spent: Replacing Dense Layers with Structured Matrices
This work addresses the problem of compute inefficiency in large-scale AI models for researchers and practitioners, offering a novel structured matrix approach that is incremental but shows strong specific gains.
The paper tackles the computational bottleneck of dense linear layers in foundation models by exploring structured matrices as replacements, proposing the Block Tensor-Train (BTT) family that achieves better performance than dense matrices with less compute, such as matching ViT-S/32 performance on ImageNet-1k with 3.8 times less compute.
Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success of convolutional networks in the image domain. In this work, we systematically explore structured matrices as replacements for dense matrices. We show that different structures often require drastically different initialization scales and learning rates, which are crucial to performance, especially as models scale. Using insights from the Maximal Update Parameterization, we determine the optimal scaling for initialization and learning rates of these unconventional layers. Finally, we measure the scaling laws of different structures to compare how quickly their performance improves with compute. We propose a novel matrix family containing Monarch matrices, the Block Tensor-Train (BTT), which we show performs better than dense matrices for the same compute on multiple tasks. On CIFAR-10/100 with augmentation, BTT achieves exponentially lower training loss than dense when training MLPs and ViTs. BTT matches dense ViT-S/32 performance on ImageNet-1k with 3.8 times less compute and is more efficient than dense for training small GPT-2 language models.