Spring 2023: Tensor decomposition and algorithms

Time and Location: Thursday, 8:30AM - 10:30AM in McB 563

Tensor decomposition

1. Linus (Jan. 25): Overview,  Tensor Decompositions and Applications (Section 1-3.2), Notes, Code

2. Mike (Feb. 1): CP decompisition and algorithms,  Tensor Decompositions and Applications (Section 3.3-3.5), Notes

3. Yichen (Feb. 9): Matrix multiplication and tensors -- Strassen’s algorithm, Numerical Tensor Calculus (Section 2.5)

   • Matrix multiplication as tensor decomposition

   • Discovering faster matrix multiplication algorithms with reinforcement learning (see also here)

4. Yichen (Feb. 16):  Tucker decomposition and algorithms,  Tensor Decompositions and Applications (Section 4)

Sam: FFT and tensors

5. Sam (Feb 23): Hierarchical Tensor Format, Numerical Tensor Calculus (Section 7), Notes 

6. Sam (Mar. 2): Hierarchical Tensor Format

   • A New Scheme for the Tensor Representation

   • htucker – A Matlab toolbox for tensors in hierarchical Tucker format

7. Sam (Mar. 16): Hierarchical Tensor Format, Yichen: Fast Multipole method and Hierarchical matrices

   • An Introduction to Hierarchical (H-) Rank and TT-Rank of Tensors with Examples

   • A pedestrian introduction to fast multipole methods

   • Hierarchical Matrices (Chp 1.1, 1.2)

8. Cankat (Mar. 23, Mar. 30): Tensor Train, Tensor-Train Decomposition 

9. Yichen (Apr. 13): Parallel algorithms for tentor train arithmetic, Communication-avoiding parallel and sequential QR factorizations

10. Linus (Apr. 20): Krylov Subspace Methods for Linear Systems with Tensor Product Structure

Resource:

1. Matlab Tensor Toolbox

2. Tensor Network: introduce tensor network algorithms, theory, and software with lots of figures. 

We appreciate Dr. Cazeaux, Dr. Beattie and Dr. Miedlar for suggestions on papers and help on reservation of rooms.