AXPY is an algorithm used to quickly compute the linear combination of two vectors. It stands for “A Times X Plus Y”. The AXPY formula is expressed as y = ax + y, where a is a scalar, x and y are vectors, and y is the resultant vector. The algorithm works by computing the product of each element in x with a, then adding it to the corresponding element in y, producing the new elements in vector y. This makes it an efficient way to perform linear combinations without having to iterate through all elements manually. AXPY can also be applied to matrices and higher-dimensional arrangements using appropriate modifications. It has applications across various fields including computational mathematics, physics simulation, machine learning, signal processing, and more. AXPY has also been used to optimize code execution times in some cases. As one of the most widely used linear combination algorithms, AXPY is a valuable tool for researchers and scientists alike. 

Cerebras implements the AXPY algorithm in its systems to provide fast and efficient computing for its users. With the Cerebras on-chip SRAM-only memory, we can enable full performance all the way down to AXPY, which is a vector-scalar multiply. This capability is what enables unstructured sparsity acceleration because a sparse GEMM is simply a collection of AXPY operations, with one operation for every non-zero element. This level of memory bandwidth is the first key enabler for unstructured sparsity acceleration. We are able to deliver the best possible performance to their customers.