Mathematical Colloquium with David Þorsteinsson (KU Leuven)

2-8-2025, 13:20 (note the unusual day!) in room 157, VR-II

David Þorsteinsson (KU Leuven)

Chiselling Algorithms for Computing Block Term Decompositions of Tensors.

Block term decomposition (BTD) is a unifying generalisation of the two most common tensor decompositions, namely canonical polyadic decomposition (CPD) and higher-order singular value decomposition (HOSVD). While BTD has found applications in various fields, including machine learning, optimisation, and blind source separation, all known algorithms for its computation were optimisation-based until recently. We will investigate the relationship between two recently proposed BTD algorithms, identifying both as examples of the general tensor sparsification framework newly presented by Brooksbank, Kassabov, & Wilson. Working from this shared theoretical basis, we show that algebraic and Lie-theoretic methods can be used to better interpret the underlying mechanism of the algorithms, and to derive necessary and sufficient conditions for uniqueness of the decompositions uncovered by these algorithms, improving on the bounds presented by the original authors.