Breaking the curse of dimensionality


In our new publication, “Breaking the curse of dimensionality, or how to use SVD in many dimensions” we present a simple recursive decomposition for multidimensional functions, operators, vectors and matrices. We prove that in the case when the canonical decomposition exists our new Tree-Tucker decomposition also exists with the same (and often fewer) number of parameters. However, unlike the canonical decomposition, the Tree-Tucker format is stable and robustly computable by exploiting the SVD decomposition (or any rank-revealing decomposition). We show how to perform a simple operation (multidimensional convolution) in such format and provide numerical experiments for the dimensions up to d=200 on a notebook in several minutes.


26/05/2016 A TT-eigenvalue solver that finally works Papers
12/05/2016 Exponential machines and tensor trains Papers
06/04/2016 Convergence analysis of a projected fixed-point iteration Papers
30/03/2016 Compress-and-eliminate solver for sparse matrices Papers
01/12/2015 New paper in SIMAX Papers


We are located at the 2-nd floor of the new "Technopark-3” building in Skolkovo (few kilometers outside Moscow Ring Road). The building is accessible from Skolkovo Road (Сколковское шоссе) and Minskoe Highway (Минское шоссе).