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Tensor Computations (CS 598 EVS) Fall 2020

What Where
Instructor Edgar Solomonik (solomon2@illinois.edu)
TA Samah Karim (swkarim2@illinois.edu)
Time/place M/W 9:30am-10:45am, (virtual + recorded via zoom, email or see piazza for link to zoom and recordings)
Office Hours After class (10:45-11:15 on zoom) or by appointment (via zoom or other videochat)
Class URL https://relate.cs.illinois.edu/course/cs598evs-f20/
Web forum View Piazza »
Calendar View Calendar »

The course will cover theory, algorithms, and applications of tensor decompositions and tensor networks. The key prerequisite for this material is familiarity with numerical linear algebra topics and algorithmic analysis.

The planned syllabus for the course is below. The major learning objectives for the courser are to establish fluency/inuition of understanding for computations involving tensor contractions and decompositions, to provide a general understanding of theoretical foundations of associated nonlinear optimization problems, to develop a methodology for efficient implementaton of tensor algorithms, and to provide a view of the application landscape of tensor computations.

Lectures will be supplemented with short in-class web assignments, which can also be completed asynchronously. Three short homework assignments are planned to test understanding, which can be completed individually or in small groups. Students have the choice of giving a presentation or preparing a report on a research project or review. In-class assignments, homeworks, and the presentation/report will each be worth 1/3 of the grade.

Mini-Homeworks

Homework 1: Preconditioning via Low-Rank Approximation »

Homework 2: Accelerating CP-ALS using Tucker »

Homework 3: Review of Tensor Computations »

Quizzes (in-class activities)

Quiz 1: Interest Survey »

Quiz 2: Computing the Maximum Ritz Value »

Quiz 3: Low Rank Approximation: Randomized SVD vs Krylov Subspace Methods »

Quiz 4: Gauss-Newton Method »

Quiz 5: Kronecker Product as a Tensor Operation »

Quiz 6: Converting a CP Decomposition to a Tucker Decomposition »

Quiz 7: HOSVD and TTSVD »

Quiz 8: Bilinear Algorithms for Convolution »

Quiz 9: Bilinear Algorithm for Multiplication of a Symmetric Matrix and a Vector »

Quiz 10: Tensor Contraction with Group Symmetry »

Quiz 11: Alternating Least Squares for CP Decomposition »

Quiz 12: Dimension Trees for CP ALS »

Quiz 13: Gauss-Newton Method for CP Decomposition »

Quiz 14: Sparse Tensor times Matrix using CSF Format »

Quiz 15: Nonnegative Tensor Factorization »

Quiz 16: Imaginary Time Evolution »

Quiz 17: Density Matrix Renormalization Group (DMRG) »

Quiz 18: Tensor Network Canonical Forms »

Quiz 19: Computing Eigenvalues of a Symmetric Tensor »

Student Presentation Activity: Symmetric CP Decomposition »

Course Outline

Related Courses

CS 598 EVS: Provably Efficient Algorithms for Numerical and Combinatorial Problems, Spring '20

CS 450: Numerical Analysis, Fall '18

Related Texts

Python Help

We will be using Python with the libraries numpy, scipy and matplotlib for in-class work and assignments.

Python Workshop Material

Numpy Help

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