DMC4ML: Data Movement Complexity for Machine Learning

The greatest demand for today's computing is machine learning. This paper analyzes three machine learning algorithms: transformers, spatial convolution, and FFT. The analysis is novel in three aspects. First, it measures the cost of memory access on an abstract memory hierarchy, instead of traditional time or space complexity. Second, the analysis is asymptotic and identifies the primary sources of the memory cost. Finally, the result is symbolic, which can be used to select algorithmic parameters such as the group size in grouped query attention for any dimension size and number of heads and the batch size for batched convolution for any image size and kernel size.