Item Details

title

Advances in Tensor Decompositions: Fast Matrix Multiplication Algorithms and Parallel Adaptive Compression Techniques

author

De Oliveira Pinheiro, João Victor

abstract

Tensors are essential in modern-day computational and data sciences. This work presents recent advances in tensor decompositions, which are techniques that break down complex high-dimensional arrays into smaller structured components. There are two projects presented in this thesis, each with its own abstract and chapter. Searching For Cyclic Invariant Fast Matrix Multiply Algorithms using the CP Decomposition: Fast matrix multiplication algorithms correspond to exact CP decompositions of tensors that encode matrix multiplication of fixed dimensions. This 3-way matrix multiplication tensor has cyclic symmetry: the entry values are invariant under cyclic permutation of the indices. The CP decomposition of Strassen's original fast matrix multiplication algorithm for 2x2 matrices is cyclic invariant, which means a cyclic permutation of the CP factors results in the same CP components, just in a different order. We describe how to search for cyclic invariant solutions using the damped Gauss-Newton optimization method along with heuristic rounding techniques. We not only summarize the algorithms discovered so far but also attempt to search for further symmetries in these algorithms by describing the requirements for an algorithms to admit such symmetries.

subject

CP

Decomposition

HOOI

Matrix

Tensor

Tucker

contributor

Ballard, Grey (advisor)

Moore, Frank (committee member)

Kannan, Ramakrishnan (committee member)

date

2025-06-24T08:36:31Z (accessioned)

2025-06-24T08:36:31Z (available)

2025 (issued)

degree

Computer Science (discipline)

identifier

http://hdl.handle.net/10339/111016 (uri)

language

en (iso)

publisher

Wake Forest University

type

Thesis