Speaker
Description
The Tensor Train (TT) format provides a compact and scalable way to represent high-dimensional tensors, making it essential for solving certain parametrized partial differential equations and other large-scale problems. A critical operation in TT-based computations is rounding, which reduces the ranks of a tensor in TT format to maintain efficiency. While recent randomized rounding algorithms have improved performance over traditional deterministic approaches, they typically require manual rank specification, limiting their practicality in many applications.
In this talk, I will present a new adaptive randomized TT-rounding algorithm based on Khatri-Rao random projections. Unlike previous methods, our algorithm automatically determines the TT ranks needed to meet a user-specified approximation tolerance, eliminating the need for manual tuning. It achieves up to 45× speedup over deterministic rounding and a 2× improvement over the fastest existing randomized approach (which requires specifying target ranks), particularly in the context of rounding sums of TT tensors—a key bottleneck in adaptation of GMRES to vectors in TT format. I will discuss the algorithm's design, performance benefits, and its implications for high-dimensional numerical computing.