Design of a high-performance GEMM-like Tensor-Tensor Multiplication

Understand

We present "GEMM-like Tensor-Tensor multiplication" (GETT), a novel approach to tensor contractions that mirrors the design of a high-performance general matrix-matrix multiplication (GEMM).

• The critical insight behind GETT is the identification of three index sets, involved in the tensor contraction, which enable us to systematically reduce an arbitrary tensor contraction to loops around a highly tuned "macro-kernel".
• This macro-kernel operates on suitably prepared ("packed") sub-tensors that reside in a specified level of the cache hierarchy.
• In contrast to previous approaches to tensor contractions, GETT exhibits desirable features such as unit-stride memory accesses, cache-awareness, as well as full vectorization, without requiring auxiliary memory.