Transformer Based Linear Attention with Optimized GPU Kernel Implementation

The original softmax-based attention mechanism (regular attention) in the extremely successful Transformer architecture computes attention between N tokens, each embedded in a D-dimensional head, with a time complexity of O(N2D). Given the success of Transformers, improving their runtime during both training and inference is a popular research area. One such approach is the introduction of the linear attention (LA) mechanisms, which offers a linear time complexity of O(ND2) and have demonstrated comparable accuracy to regular attention. However, LA in practice lags behind its theoretical efficiency. We propose a novel method for LA's forward and backward passes, along with a highly-optimized CUDA implementation. Our approach outperforms the state-of-the-art by 3.3 times in speed and reduces memory consumption by 3.6 times. We validate these improvements in both single-layer and end-to-end settings by training a 1.4 billion parameter language model, which demonstrates similar expressivity to regular attention on major reasoning benchmarks.