Mixed Precision Compression of Tucker Decomposition

We present a mixed precision approach for improving Tucker-based lossy compression of multiway data. Current Tucker decomposition algorithms use a uniform floating-point precision and obtain compression by minimizing the multilinear ranks of the representation subject to the target error tolerance. Our algorithm automatically determines which parameters of the representation can be stored in lower precision to improve the compression ratio without exceeding the error tolerance. Crucially, we show that the opportunities to reduce precision are not uniform across parameters, and thus using multiple precisions allows for smoothly transitioning across tolerances between the precisions of standard formats. Theoretical error bounds and numerical experiments validate the approach, and we obtain up to \(2\times\) and \(4\times\) compression improvement factors over initial Tucker approximations of single and double precision real-world numerical simulation data, respectively.