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Tutte Colloquium -Tammy Kolda -Fast and Accurate Tensor Decompositions on Infinite-Dimensional Function Spaces
2026-04-10 15:30 - 16:30 (America/Toronto)
SPEAKER:
Tammy Kolda

AFFILIATION:
MathSci.ai

LOCATION:
MC 5501

ABSTRACT: Tensor decompositions are fundamental tools in scientific
computing and data analysis. In many applications — such as
simulation data on irregular grids, surrogate modeling for
parameterized PDEs, or spectroscopic measurements — the data has
both discrete and continuous structure, and may only be observed at
scattered sample points. The CP-HIFI (hybrid infinite-finite)
decomposition generalizes the Canonical Polyadic (CP) tensor
decomposition to settings where some factors are finite-dimensional
vectors and others are functions drawn from infinite-dimensional
spaces — a natural framework when the underlying data has continuous
structure. The decomposition can be applied to a fully observed tensor
(aligned) or, when only scattered observations are available, to a
sparsely sampled tensor (unaligned). Current methods compute CP-HIFI
factors by solving a sequence of dense linear systems arising from
regularized least-squares problems, but these direct solves become
computationally prohibitive as problem size grows. We propose new
algorithms that achieve the same accuracy while being orders of
magnitude faster. For aligned tensors, we exploit the Kronecker
structure of the system to efficiently compute its eigendecomposition
without ever forming the full system, reducing the solve to
independent scalar equations. For unaligned tensors, we introduce a
preconditioned conjugate gradient method applied to a reformulated
system with favorable spectral properties. We analyze the
computational complexity and memory requirements of the new methods
and demonstrate their effectiveness on problems with smooth functional
modes. I will also discuss the “First Proof” project, which aims
to understand the capabilities of AI systems on problems that come up
in math research, and the role that results from that experiment
played in this project.
