Exact Causal Attention with 10% Fewer Operations

We present Fast Causal Attention (FCA), an algorithm that computes exact Causal Attention using 10\% fewer operations. FCA accelerates a special class of matrix multiplications where either one operand or the output matrix is upper- or lower-triangular. This includes all operations in forward and backward pass of Causal Attention, such as masked product $\mathrm{Mask}(QK^{T})$. For these matrix multiplications on GPU, FCA reaches noticeable accelerations over the default PyTorch implementations and Triton compiled kernels. FCA is built upon algebraic identities discovered via machine learning and combinatorial search.