On The Computational Complexity of Self-Attention
This work addresses a fundamental bottleneck in transformer efficiency for AI researchers and practitioners, providing rigorous lower bounds that are foundational rather than incremental.
The paper tackles the computational complexity of self-attention in transformers, proving that its time complexity is necessarily quadratic in input length unless the Strong Exponential Time Hypothesis is false, even for approximate computations, while also showing a linear-time approximation method with exponential dependence on polynomial order.
Transformer architectures have led to remarkable progress in many state-of-art applications. However, despite their successes, modern transformers rely on the self-attention mechanism, whose time- and space-complexity is quadratic in the length of the input. Several approaches have been proposed to speed up self-attention mechanisms to achieve sub-quadratic running time; however, the large majority of these works are not accompanied by rigorous error guarantees. In this work, we establish lower bounds on the computational complexity of self-attention in a number of scenarios. We prove that the time complexity of self-attention is necessarily quadratic in the input length, unless the Strong Exponential Time Hypothesis (SETH) is false. This argument holds even if the attention computation is performed only approximately, and for a variety of attention mechanisms. As a complement to our lower bounds, we show that it is indeed possible to approximate dot-product self-attention using finite Taylor series in linear-time, at the cost of having an exponential dependence on the polynomial order.