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.
Tensor Algebra
Theoretical Fundamentals of Tensor Decompositions
Dense Tensor Decomposition Algorithms
Sparse Tensor Decomposition Algorithms
Tensor Network Methods
Student presentations and lectures on other topics based on student interest
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.
Homework 1: Preconditioning via Low-Rank Approximation »
Homework 2: Accelerating CP-ALS using Tucker »
Homework 3: Review of Tensor Computations »
Quiz 2: Computing the Maximum Ritz Value »
Quiz 3: Low Rank Approximation: Randomized SVD vs Krylov Subspace Methods »
Quiz 5: Kronecker Product as a Tensor Operation »
Quiz 6: Converting a CP Decomposition to a Tucker Decomposition »
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 »
CS 598 EVS: Provably Efficient Algorithms for Numerical and Combinatorial Problems, Spring '20
CS 450: Numerical Analysis, Fall '18
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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