Multi-Layer Transformers Gradient Can be Approximated in Almost Linear Time
This addresses a critical computational bottleneck for training and deploying long-context language models, though it appears incremental as an approximation method for an existing problem.
The paper tackles the quadratic time complexity bottleneck of gradient computation in multi-layer transformers, proving that a novel approximation method can compute gradients in almost linear time n^(1+o(1)) while maintaining polynomially small error 1/poly(n).
The computational complexity of the self-attention mechanism in popular transformer architectures poses significant challenges for training and inference, and becomes the bottleneck for long inputs. Is it possible to significantly reduce the quadratic time complexity of computing the gradients in multi-layer transformer models? This paper proves that a novel fast approximation method can calculate the gradients in almost linear time $n^{1+o(1)}$ where $n$ is the input sequence length, while it maintains a polynomially small approximation error $1 / \mathrm{poly}(n)$ across the entire model. Our theory holds for general loss functions and when the multi-layer transformer model contains many practical sub-modules, such as residual connection, casual mask, and multi-head attention. By improving the efficiency of gradient computation, we hope that this work will facilitate more effective training and deployment of long-context language models based on our theoretical results.