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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260410T153000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-tammy-kolda-fast-and-accurate-tensor
SUMMARY:Tutte Colloquium -Tammy Kolda -Fast and Accurate Tensor Decompositi
 ons\non Infinite-Dimensional Function Spaces
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Tammy Kolda\n\nAFFILIATION:\n MathSci.ai\n\nLOCATION
 :\n MC 5501\n\nABSTRACT: Tensor decompositions are fundamental tools in s
 cientific\ncomputing and data analysis. In many applications — such as\n
 simulation data on irregular grids\, surrogate modeling for\nparameterized
  PDEs\, or spectroscopic measurements — the data has\nboth discrete and 
 continuous structure\, and may only be observed at\nscattered sample point
 s. The CP-HIFI (hybrid infinite-finite)\ndecomposition generalizes the Can
 onical Polyadic (CP) tensor\ndecomposition to settings where some factors 
 are finite-dimensional\nvectors and others are functions drawn from infini
 te-dimensional\nspaces — a natural framework when the underlying data ha
 s continuous\nstructure. The decomposition can be applied to a fully obser
 ved tensor\n(aligned) or\, when only scattered observations are available\
 , to a\nsparsely sampled tensor (unaligned). Current methods compute CP-HI
 FI\nfactors by solving a sequence of dense linear systems arising from\nre
 gularized least-squares problems\, but these direct solves become\ncomputa
 tionally prohibitive as problem size grows. We propose new\nalgorithms tha
 t achieve the same accuracy while being orders of\nmagnitude faster. For a
 ligned tensors\, we exploit the Kronecker\nstructure of the system to effi
 ciently compute its eigendecomposition\nwithout ever forming the full syst
 em\, reducing the solve to\nindependent scalar equations. For unaligned te
 nsors\, we introduce a\npreconditioned conjugate gradient method applied t
 o a reformulated\nsystem with favorable spectral properties. We analyze th
 e\ncomputational complexity and memory requirements of the new methods\nan
 d demonstrate their effectiveness on problems with smooth functional\nmode
 s. I will also discuss the “First Proof” project\, which aims\nto unde
 rstand the capabilities of AI systems on problems that come up\nin math re
 search\, and the role that results from that experiment\nplayed in this pr
 oject.
DTSTAMP:20260410T011819Z
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