Self-attention is the core mathematical operation of modern transformer architectures and is also a significant computational bottleneck due to its quadratic complexity in the sequence length.
In this work, we derive the scalar energy function whose gradient computes the self-attention block, thus elucidating the theoretical underpinnings of self-attention, providing a Bayesian interpretation of the operation and linking it closely with energy-based models such as Hopfield Networks.
Our formulation reveals that the reduction across the sequence axis can be efficiently computed in parallel through a tree reduction.
Our algorithm, for parallelizing attention computation across multiple GPUs enables cross-device decoding to be performedasymptoticallyfaster (up tofaster in our experiments)  than alternative approaches such as Ring Attention, while also requiring significantly less communication volume and incurringless peak memory.
Our code is publicly available here:https://github.com/Zyphra/tree_attention.