Drop-in efficient self-attention approximation method

Transformers have achieved state-of-the-art performance in most common tasks to which they have been applied. Those achievements are attributed to the Self-Attention mechanism at their core. Self-Attention is understood to map the relationship between tokens of any given sequence. This exhaustive mapping incurs massive costs in memory and inference time, as Self-Attention scales quadratically with regard to sequence length. Standard Self-Attention has required increasingly large compute and memory usage when applied to long input sequences because of this memory and time bottleneck. Efficient Transformers emerged as performant alternatives demonstrating good scalability and occasionally better tracking of long-range dependencies. Their efficiency gains are obtained through different methods, usually focusing on the linear scaling of the attention matrix through sparsification, approximation, or other methods. Among existing approaches, those using low-rank approximation present particular advantages because of their compatibility with standard Self-Attention-based models, allowing for weight transfers and other time-saving schemes. More recently, hardware-aware versions of Self-Attention (e.g., FlashAttention) have mitigated all memory bottlenecks and have alleviated its compute burden. Unfortunately, hardware-aware Self-Attentions have stricter hardware compatibility requirements making Efficient Transformers still relevant for use on older or less powerful hardware. Furthermore, some Efficient Transformers can even be applied in an hardware-aware manner to further improve training and inference speed. In this paper, we propose a novel linear approximation method for Self-Attention inspired by the CUR approximation method. This method, proposed in two versions (one leveraging FlashAttention), is conceived as a drop-in replacement for standard Self-Attention with weights compatibility. Our method compares favorably to standard Transformers’ and Efficient Transformers’ performances on varied tasks and demonstrates a significant decrease in memory footprint as well as competitive performance in training speed, even compared to similar methods.